@Preamble{
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi"
#
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi"
}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special
Interest Group on Symbolic and
Algebraic Manipulation)"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AW = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr = "Reading, MA, USA"}
@String{pub-CAMBRIDGE = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
@String{pub-IEEE = "IEEE Computer Society Press"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver
Spring, MD 20910, USA"}
@String{pub-SIAM = "SIAM Press"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SV = "Springer-Verlag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/
London, UK~/ etc."}
@String{pub-WORLD-SCI = "World Scientific Publishing Co."}
@String{pub-WORLD-SCI:adr = "Singapore; Philadelphia, PA, USA; River
Edge, NJ, USA"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@InProceedings{Fateman:1981:CAN,
author = "Richard J. Fateman",
title = "Computer Algebra and Numerical Integration",
crossref = "Wang:1981:SPA",
pages = "228--232",
year = "1981",
bibdate = "Mon Apr 25 07:01:52 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algebraic manipulation systems such as MACSYMA include
algorithms and heuristic procedures for indefinite and
definite integration, yet these system facilities are
not as generally useful as might be thought. Most
isolated definite integration problems are more
efficiently tackled with numerical programs.
Unfortunately, the answers obtained are sometimes
incorrect, in spite of assurances of accuracy;
furthermore, large classes of problems can sometimes be
solved more rapidly by preliminary algebraic
transformations. In this paper we indicate various
directions for improving the usefulness of integration
programs given closed form integrands, via algebraic
manipulation techniques. These include expansions in
partial fractions or Taylor series, detection and
removal of singularities and symmetries, and various
approximation techniques for troublesome problems.",
acknowledgement = ack-nhfb,
}
@Book{Buchberger:1982:CAS,
author = "Bruno Buchberger and George Edward Collins and Rudiger
Loos and R. Albrecht",
title = "Computer algebra: symbolic and algebraic computation",
volume = "4",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 283",
year = "1982",
ISBN = "0-387-81684-4",
ISBN-13 = "978-0-387-81684-5",
LCCN = "QA155.7.E4 C65 1982",
bibdate = "Thu Dec 28 13:48:31 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "Computing. Supplementum",
acknowledgement = ack-nhfb,
keywords = "algorithms; measurement; theory",
subject = "S1 Algebra --- Data processing; S2 Machine theory",
}
@InProceedings{Abbott:1986:BAN,
author = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
title = "The {Bath} algebraic number package",
crossref = "Char:1986:PSS",
pages = "250--253",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p250-abbott/",
acknowledgement = ack-nhfb,
keywords = "design; measurement; performance",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
}
@InProceedings{Abdali:1986:OOA,
author = "S. K. Abdali and Guy W. Cherry and Neil Soiffer",
title = "An object-oriented approach to algebra system design",
crossref = "Char:1986:PSS",
pages = "24--30",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p24-abdali/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.3} Software, PROGRAMMING LANGUAGES, Language
Constructs and Features, Abstract data types. {\bf
D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
Run-time environments. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Specialized application languages. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Very high-level languages.",
}
@InProceedings{Akritis:1986:TNU,
author = "Alkiviadis G. Akritis",
title = "There is no ``{Uspensky}'s method''",
crossref = "Char:1986:PSS",
pages = "88--90",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p88-akritis/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.1.5} Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Polynomials, methods for. {\bf K.2} Computing Milieux,
HISTORY OF COMPUTING, Systems. {\bf G.1.5} Mathematics
of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Iterative methods. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Arnborg:1986:ADR,
author = "S. Arnborg and H. Feng",
title = "Algebraic decomposition of regular curves",
crossref = "Char:1986:PSS",
pages = "53--55",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p53-arnborg/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf I.1.m} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Miscellaneous.",
}
@InProceedings{Bachmair:1986:CPC,
author = "Leo Bachmair and Nachum Dershowitz",
title = "Critical-pair criteria for the {Knuth--Bendix}
completion procedure",
crossref = "Char:1986:PSS",
pages = "215--217",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p215-bachmair/",
acknowledgement = ack-nhfb,
keywords = "languages; theory; verification",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems, Parallel rewriting systems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions. {\bf F.2.3} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Tradeoffs between Complexity Measures. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Complexity of proof procedures.",
}
@InProceedings{Bajaj:1986:LAS,
author = "Chanderjit Bajaj",
title = "Limitations to algorithm solvability: {Galois} methods
and models of computation",
crossref = "Char:1986:PSS",
pages = "71--76",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p71-bajaj/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.2.m} Mathematics of Computing,
DISCRETE MATHEMATICS, Miscellaneous. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis.",
}
@InProceedings{Bayer:1986:DMS,
author = "D. Bayer and M. Stillman",
title = "The design of {Macaulay}: a system for computing in
algebraic geometry and commutative algebra",
crossref = "Char:1986:PSS",
pages = "157--162",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p157-bayer/",
acknowledgement = ack-nhfb,
keywords = "design; performance; theory",
subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
}
@InProceedings{Beck:1986:SAL,
author = "Robert E. Beck and Bernard Kolman",
title = "Symbolic algorithms for {Lie} algebra computation",
crossref = "Char:1986:PSS",
pages = "85--87",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p85-beck/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.2.2} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Automatic Programming. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, MACSYMA. {\bf K.2}
Computing Milieux, HISTORY OF COMPUTING, Systems.",
}
@InProceedings{Bradford:1986:ERD,
author = "R. J. Bradford and A. C. Hearn and J. A. Padget and E.
Schr{\"u}fer",
title = "Enlarging the {REDUCE} domain of computation",
crossref = "Char:1986:PSS",
pages = "100--106",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p100-bradford/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
}
@InProceedings{Bronstein:1986:GFA,
author = "Manuel Bronstein",
title = "Gsolve: a faster algorithm for solving systems of
algebraic equations",
crossref = "Char:1986:PSS",
pages = "247--249",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p247-bronstein/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.5}
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Systems of equations. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness.",
}
@InProceedings{Butler:1986:DCC,
author = "Greg Butler",
title = "Divide-and-conquer in computational group theory",
crossref = "Char:1986:PSS",
pages = "59--64",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p59-butler/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.2.0} Mathematics of Computing, DISCRETE
MATHEMATICS, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Chaffy:1986:HCM,
author = "C. Chaffy",
title = "How to compute multivariate {Pad{\'e}} approximants",
crossref = "Char:1986:PSS",
pages = "56--58",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p56-chaffy/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation.",
}
@InProceedings{Char:1986:CAU,
author = "B. W. Char and K. O. Geddes and G. H. Gonnet and B. J.
Marshman and P. J. Ponzo",
title = "Computer algebra in the undergraduate mathematics
classroom",
crossref = "Char:1986:PSS",
pages = "135--140",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p135-char/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; documentation; experimentation;
human factors; performance",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
Computer Uses in Education, Computer-assisted
instruction (CAI).",
}
@InProceedings{Cooperman:1986:SMC,
author = "Gene Cooperman",
title = "A semantic matcher for computer algebra",
crossref = "Char:1986:PSS",
pages = "132--134",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p132-cooperman/",
acknowledgement = ack-nhfb,
keywords = "experimentation; human factors; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf F.4.1} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Evaluation strategies. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Pattern matching. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Representations
(general and polynomial). {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Czapor:1986:IBA,
author = "S. R. Czapor and K. O. Geddes",
title = "On implementing {Buchberger}'s algorithm for
{Gr{\"o}bner} bases",
crossref = "Char:1986:PSS",
pages = "233--238",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p233-czapor/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
}
@InProceedings{Davenport:1986:PSM,
author = "J. H. Davenport and C. E. Roth",
title = "{PowerMath}: a system for the {Macintosh}",
crossref = "Char:1986:PSS",
pages = "13--15",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p13-davenport/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING,
Apple. {\bf I.1.3} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems.",
}
@InProceedings{Dora:1986:FSL,
author = "J. Della Dora and E. Tournier",
title = "Formal solutions of linear difference equations:
method of {Pincherle--Ramis}",
crossref = "Char:1986:PSS",
pages = "192--196",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p192-della_dora/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL
ANALYSIS, Miscellaneous. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms.",
}
@InProceedings{Fitch:1986:AIA,
author = "J. Fitch and A. Norman and M. A. Moore",
title = "Alkahest {III}: automatic analysis of periodic weakly
nonlinear {ODEs}",
crossref = "Char:1986:PSS",
pages = "34--38",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p34-fitch/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; human factors; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf D.2.2}
Software, SOFTWARE ENGINEERING, Design Tools and
Techniques, User interfaces.",
}
@InProceedings{Freeman:1986:SMP,
author = "T. Freeman and G. Imirzian and E. Kaltofen",
title = "A system for manipulating polynomials given by
straight-line programs",
crossref = "Char:1986:PSS",
pages = "169--175",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p169-freeman/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations, Polynomials, methods
for.",
}
@InProceedings{Furukawa:1986:GBM,
author = "A. Furukawa and T. Sasaki and H. Kobayashi",
title = "The {Gr{\"o}bner} basis of a module over
{KUX1,\ldots{},Xne} and polynomial solutions of a
system of linear equations",
crossref = "Char:1986:PSS",
pages = "222--224",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p222-furukawa/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods).",
}
@InProceedings{Gates:1986:NCG,
author = "Barbara L. Gates",
title = "A numerical code generation facility for {REDUCE}",
crossref = "Char:1986:PSS",
pages = "94--99",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p94-gates/",
acknowledgement = ack-nhfb,
keywords = "design; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation.",
}
@InProceedings{Gebauer:1986:BAS,
author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
title = "{Buchberger}'s algorithm and staggered linear bases",
crossref = "Char:1986:PSS",
pages = "218--221",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p218-gebauer/",
acknowledgement = ack-nhfb,
keywords = "algorithms; measurement; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Geddes:1986:NIS,
author = "K. O. Geddes",
title = "Numerical integration in a symbolic context",
crossref = "Char:1986:PSS",
pages = "185--191",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p185-geddes/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design",
subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Golden:1986:OAM,
author = "J. P. Golden",
title = "An operator algebra for {Macsyma}",
crossref = "Char:1986:PSS",
pages = "244--246",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p244-golden/",
acknowledgement = ack-nhfb,
keywords = "design; theory; verification",
subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, MACSYMA. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Gonnet:1986:IOS,
author = "G. H. Gonnet",
title = "An implementation of operators for symbolic algebra
systems",
crossref = "Char:1986:PSS",
pages = "239--243",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p239-gonnet/",
acknowledgement = ack-nhfb,
keywords = "design; languages; theory",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Representations (general and
polynomial). {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
}
@InProceedings{Gonnet:1986:NRR,
author = "Gaston H. Gonnet",
title = "New results for random determination of equivalence of
expressions",
crossref = "Char:1986:PSS",
pages = "127--131",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p127-gonnet/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf G.2.m} Mathematics of Computing,
DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Hadzikadic:1986:AKB,
author = "M. Hadzikadic and F. Lichtenberger and D. Y. Y. Yun",
title = "An application of knowledge-base technology in
education: a geometry theorem prover",
crossref = "Char:1986:PSS",
pages = "141--147",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p141-hadzikadic/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; human factors; languages;
performance; verification",
subject = "{\bf K.3.1} Computing Milieux, COMPUTERS AND
EDUCATION, Computer Uses in Education,
Computer-assisted instruction (CAI). {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Mechanical theorem
proving. {\bf I.2.3} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Deduction and Theorem
Proving.",
}
@InProceedings{Hayden:1986:SBC,
author = "Michael B. Hayden and Edmund A. Lamagna",
title = "Summation of binomial coefficients using
hypergeometric functions",
crossref = "Char:1986:PSS",
pages = "77--81",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p77-hayden/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf I.2.2} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Automatic Programming,
Automatic analysis of algorithms. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Iterative methods.",
}
@InProceedings{Hilali:1986:ACF,
author = "A. Hilali and A. Wazner",
title = "Algorithm for computing formal invariants of linear
differential systems",
crossref = "Char:1986:PSS",
pages = "197--201",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p197-hilali/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues and
eigenvectors (direct and iterative methods). {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Jurkovic:1986:EES,
author = "N. Jurkovic",
title = "Edusym --- educational symbolic manipulator on a
microcomputer",
crossref = "Char:1986:PSS",
pages = "154--156",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p154-jurkovic/",
acknowledgement = ack-nhfb,
keywords = "human factors; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, MuMATH.
{\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
Computer Uses in Education, Computer-assisted
instruction (CAI).",
}
@InProceedings{Kaltofen:1986:FPA,
author = "E. Kaltofen and M. Krishnamoorthy and B. D. Saunders",
title = "Fast parallel algorithms for similarity of matrices",
crossref = "Char:1986:PSS",
pages = "65--70",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p65-kaltofen/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
}
@InProceedings{Kapur:1986:GTP,
author = "Deepak Kapur",
title = "Geometry theorem proving using {Hilbert}'s
{Nullstellensatz}",
crossref = "Char:1986:PSS",
pages = "202--208",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p202-kapur/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf I.2.3}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Deduction and Theorem Proving. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Knowles:1986:ILF,
author = "P. H. Knowles",
title = "Integration of {Liouvillian} functions with special
functions",
crossref = "Char:1986:PSS",
pages = "179--184",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p179-knowles/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL
ANALYSIS, Miscellaneous.",
}
@InProceedings{Kobayashi:1986:GBI,
author = "H. Kobayashi and A. Furukawa and T. Sasaki",
title = "Gr{\"o}bner bases of ideals of convergent power
series",
crossref = "Char:1986:PSS",
pages = "225--227",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p225-kobayashi/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf G.m}
Mathematics of Computing, MISCELLANEOUS.",
}
@InProceedings{Kryukov:1986:CRA,
author = "A. P. Kryukov and Y. Rodionov and G. L. Litvinov",
title = "Construction of rational approximations by means of
{REDUCE}",
crossref = "Char:1986:PSS",
pages = "31--33",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p31-kryukov/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Rational approximation. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Kryukov:1986:DRE,
author = "A. P. Kryukov",
title = "Dialogue in {REDUCE}: experience and development",
crossref = "Char:1986:PSS",
pages = "107--109",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p107-kryukov/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.2.2} Software, SOFTWARE ENGINEERING, Design
Tools and Techniques, User interfaces.",
}
@InProceedings{Kryukov:1986:URC,
author = "A. P. Kryukov and A. Y. Rodionov",
title = "Usage of {REDUCE} for computations of
group-theoretical weight of {Feynman} diagrams in
{non-Abelian} gauge theories",
crossref = "Char:1986:PSS",
pages = "91--93",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p91-kryukov/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.2.m} Mathematics of Computing, DISCRETE
MATHEMATICS, Miscellaneous.",
}
@InProceedings{Kutzler:1986:AGT,
author = "B. Kutzler and S. Stifter",
title = "Automated geometry theorem proving using
{Buchberger}'s algorithm",
crossref = "Char:1986:PSS",
pages = "209--214",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p209-kutzler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf I.2.3} Computing
Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and
Theorem Proving. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Geometrical
problems and computations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Leff:1986:CSG,
author = "L. Leff and D. Y. Y. Yun",
title = "Constructive solid geometry: a symbolic computation
approach",
crossref = "Char:1986:PSS",
pages = "121--126",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p121-leff/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED
ENGINEERING. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Geometrical
problems and computations. {\bf I.1.m} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Miscellaneous.",
}
@InProceedings{Leong:1986:IDU,
author = "B. L. Leong",
title = "{Iris}: design of an user interface program for
symbolic algebra",
crossref = "Char:1986:PSS",
pages = "1--6",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p1-leong/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.2.2} Software, SOFTWARE ENGINEERING,
Design Tools and Techniques, User interfaces. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf H.1.2}
Information Systems, MODELS AND PRINCIPLES,
User/Machine Systems, Human factors.",
}
@InProceedings{Lucks:1986:FIP,
author = "Michael Lucks",
title = "A fast implementation of polynomial factorization",
crossref = "Char:1986:PSS",
pages = "228--232",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p228-lucks/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; experimentation; performance;
theory",
subject = "{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Polynomials,
methods for. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations.",
}
@InProceedings{Mawata:1986:SDR,
author = "C. P. Mawata",
title = "A sparse distributed representation using prime
numbers",
crossref = "Char:1986:PSS",
pages = "110--114",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p110-mawata/",
acknowledgement = ack-nhfb,
keywords = "experimentation; performance; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial). {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm design and analysis.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms.",
}
@InProceedings{Purtilo:1986:ASI,
author = "J. Purtilo",
title = "Applications of a software interconnection system in
mathematical problem solving environments",
crossref = "Char:1986:PSS",
pages = "16--23",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p16-purtilo/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.m} Mathematics of Computing, MISCELLANEOUS. {\bf
D.2.m} Software, SOFTWARE ENGINEERING, Miscellaneous.",
}
@InProceedings{Renbao:1986:CAS,
author = "Z. Renbao and X. Ling and R. Zhaoyang",
title = "The computer algebra system {CAS1} for the {IBM-PC}",
crossref = "Char:1986:PSS",
pages = "176--178",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p176-renbao/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING, IBM
PC. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Sasaki:1986:SAE,
author = "Tateaki Sasaki",
title = "Simplification of algebraic expression by multiterm
rewriting rules",
crossref = "Char:1986:PSS",
pages = "115--120",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p115-sasaki/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Grammars and Other Rewriting Systems,
Parallel rewriting systems.",
}
@InProceedings{Seymour:1986:CCM,
author = "Harlan R. Seymour",
title = "Conform: a conformal mapping system",
crossref = "Char:1986:PSS",
pages = "163--168",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p163-seymour/",
acknowledgement = ack-nhfb,
keywords = "design; languages; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf D.3.3} Software,
PROGRAMMING LANGUAGES, Language Constructs and
Features.",
}
@InProceedings{Shavlik:1986:CUG,
author = "Jude W. Shavlik and Gerald F. DeJong",
title = "Computer understanding and generalization of symbolic
mathematical calculations: a case study in physics
problem solving",
crossref = "Char:1986:PSS",
pages = "148--153",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p148-shavlik/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; languages; performance; theory;
verification",
subject = "{\bf I.2.6} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Learning. {\bf K.3.1} Computing Milieux,
COMPUTERS AND EDUCATION, Computer Uses in Education,
Computer-assisted instruction (CAI). {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation.
{\bf I.2.1} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Applications and Expert Systems. {\bf
J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf G.4} Mathematics of
Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Substitution mechanisms**. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Evaluation
strategies. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
}
@InProceedings{Smith:1986:MUI,
author = "C. J. Smith and N. Soiffer",
title = "{MathScribe}: a user interface for computer algebra
systems",
crossref = "Char:1986:PSS",
pages = "7--12",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p7-smith/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and
Techniques, User interfaces.",
}
@InProceedings{Yun:1986:FCF,
author = "D. Y. Y. Yun and C. N. Zhang",
title = "A fast carry-free algorithm and hardware design for
extended integer {GCD} computation",
crossref = "Char:1986:PSS",
pages = "82--84",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p82-yun/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis. {\bf B.7.1} Hardware,
INTEGRATED CIRCUITS, Types and Design Styles,
Algorithms implemented in hardware.",
}
@InProceedings{A:1989:SSG,
author = "R. A. and J. r. Ravenscroft and E. A. Lamagna",
title = "Symbolic summation with generating functions",
crossref = "Gonnet:1989:PAI",
pages = "228--233",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p228-ravenscroft/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods).",
}
@InProceedings{Abbot:1989:RAN,
author = "J. Abbot",
title = "Recovery of algebraic numbers from their $p$-adic
approximations",
crossref = "Gonnet:1989:PAI",
pages = "112--120",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes three ways to generalize
Lenstra's algebraic integer recovery method. One
direction adapts the algorithm so that rational numbers
are automatically produced given only upper bounds on
the sizes of the numerators and denominators. Another
direction produces a variant which recovers algebraic
numbers as elements of multiple generator algebraic
number fields. The third direction explains how the
method can work if a reducible minimal polynomial had
been given for an algebraic generator. Any two or all
three of the generalisations may be employed
simultaneously.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "Algebraic generator; Algebraic integer recovery
method; Algebraic numbers; Computer algebra;
Denominators; Factorisation; Lenstra; Multiple
generator algebraic number fields; Numerators; P-adic
approximations; Rational numbers; Reducible minimal
polynomial; Upper bounds",
thesaurus = "Computation theory; Number theory; Polynomials; Symbol
manipulation",
}
@InProceedings{Abbott:1989:RAN,
author = "John Abbott",
title = "Recovery of algebraic numbers from their $p$-adic
approximations",
crossref = "Gonnet:1989:PAI",
pages = "112--120",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p112-abbott/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Abdali:1989:EQR,
author = "S. K. Abdali and D. S. Wiset",
title = "Experiments with quadtree representation of matrices",
crossref = "Gianni:1989:SAC",
pages = "96--108",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The quadtrees matrix representation has been recently
proposed as an alternative to the conventional linear
storage of matrices. If all elements of a matrix are
zero, then the matrix is represented by an empty tree;
otherwise it is represented by a tree consisting of
four subtrees, each representing, recursively, a
quadrant of the matrix. Using four-way block
decomposition, algorithms on quadtrees accelerate on
blocks entirely of zeros, and thereby offer improved
performance on sparse matrices. The paper reports the
results of experiments done with a quadtree matrix
package implemented in REDUCE to compare the
performance of quadtree representation with REDUCE's
built-in sequential representation of matrices. Tests
on addition, multiplication, and inversion of dense,
triangular, tridiagonal, and diagonal matrices (both
symbolic and numeric) of sizes up to 100*100 show that
the quadtree algorithms perform well in a broad range
of circumstances, sometimes running orders of magnitude
faster than their sequential counterparts.",
acknowledgement = ack-nhfb,
affiliation = "Tektronix Labs., Beaverton, OR, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4140 (Linear algebra); C6120 (File organisation);
C7310 (Mathematics)",
keywords = "Addition; Dense matrices; Diagonal matrices; Empty
tree; Four-way block decomposition; Inversion;
Multiplication; Performance comparison; Quadrant;
Quadtree algorithms; Quadtree matrix package; Quadtrees
matrix representation; REDUCE; Sparse matrices;
Subtrees; Triangular matrices; Tridiagonal matrices;
Zero elements",
thesaurus = "Data structures; Mathematics computing; Matrix
algebra; Trees [mathematics]",
}
@InProceedings{Abdulrab:1989:EW,
author = "H. Abdulrab",
title = "Equations in words",
crossref = "Gianni:1989:SAC",
pages = "508--520",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The study of equations in words was introduced by
Lentin (1972). There is always a solution for any
equation with no constant. Makanin (1977) showed that
solving equations with constants is decidable. Pecuchet
(1981) unified the two theories of equations with or
without constants and gave a new description of
Makanin's algorithm. This paper describes some new
results in the field of solving equations in words.",
acknowledgement = ack-nhfb,
affiliation = "LITP, Fac. des Sci., Mont Saint Aignan, France",
classification = "C4210 (Formal logic)",
keywords = "Decidable; Equations in words",
thesaurus = "Decidability",
}
@InProceedings{Abhyankar:1989:CAC,
author = "S. S. Abhyankar and C. L. Bajaj",
title = "Computations with algebraic curves",
crossref = "Gianni:1989:SAC",
pages = "274--284",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present a variety of computational
techniques dealing with algebraic curves both in the
plane and in space. The main results are polynomial
time algorithms: (1) to compute the genus of plane
algebraic curves; (2) to compute the rational
parametric equations for implicitly defined rational
plane algebraic curves of arbitrary degree; (3) to
compute birational mappings between points on
irreducible space curves and points on projected plane
curves and thereby to compute the genus and rational
parametric equations for implicitly defined rational
space curves of arbitrary degree; and (4) to check for
the faithfulness (one to one) of parameterizations.",
acknowledgement = ack-nhfb,
affiliation = "Purdue Univ., West Lafayette, IN, USA",
classification = "C4130 (Interpolation and function approximation);
C4190 (Other numerical methods)",
keywords = "Algebraic curves; Birational mappings; Computational
techniques; Irreducible space curves; Polynomial time
algorithms; Rational parametric equations",
thesaurus = "Computational geometry; Polynomials",
}
@InProceedings{Alonso:1989:CAS,
author = "M. E. Alonso and T. Mora and M. Raimondo",
title = "Computing with algebraic series",
crossref = "Gonnet:1989:PAI",
pages = "101--111",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p101-alonso/",
abstract = "The authors develop a computational model for
algebraic formal power series, based on a symbolic
codification of the series by means of the implicit
function theorem: i.e. they consider algebraic series
as the unique solutions of suitable functional
equations. They show that most of the usual local
commutative algebra can be effectively performed on
algebraic series, since they can reduce to the
polynomial case, where the tangent cone algorithm can
be used to effectively perform local algebra. The main
result to the paper is an effective version of
Weierstrass theorems, which allows effective
elimination theory for algebraic series and an
effective noether normalization lemma.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Complutense, Madrid, Spain",
classification = "C1110 (Algebra); C1120 (Analysis); C4150 (Nonlinear
and functional equations); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic formal power series; Algebraic series;
algorithms; Computational model; Elimination theory;
Functional equations; Implicit function theorem; Local
commutative algebra; Noether normalization lemma;
Polynomial; Symbolic codification; Tangent cone
algorithm; theory; Weierstrass theorems",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Computational logic.",
thesaurus = "Computability; Functional equations; Polynomials;
Series [mathematics]; Symbol manipulation",
}
@InProceedings{Arnborg:1989:EPO,
author = "S. Arnborg",
title = "Experiments with a projection operator for algebraic
decomposition",
crossref = "Gianni:1989:SAC",
pages = "177--182",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Reports an experiment with the projection phase of an
algebraic decomposition problem. The decomposition
asked for is a collection of rational sample points, at
least one in each full-dimensional region of a
decomposition, sign-invariant with respect to a set of
polynomials and with a cylindrical structure. Such a
decomposition is less general than a cylindrical
algebraic decomposition, but still useful for purposes
such as solving collision and motion planning problems
in theoretical robotics. Specifically, there is no
information about the structure of less than
full-dimensional regions and intersections between
projections of regions. This makes quantifier
elimination with alternating quantifiers difficult or
impossible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Numer. Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
classification = "C1110 (Algebra)",
keywords = "Algebraic decomposition; Cylindrical structure;
Full-dimensional region; Polynomials; Projection
operator; Projection phase; Rational sample points;
Sign-invariant",
thesaurus = "Algebra; Polynomials",
}
@InProceedings{Ausiello:1989:DMP,
author = "G. Ausiello and A. Marchetti Spaccamela and U. Nanni",
title = "Dynamic maintenance of paths and path expressions on
graphs",
crossref = "Gianni:1989:SAC",
pages = "1--12",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In several applications it is necessary to deal with
data structures that may dynamically change during a
sequence of operations. In these cases the classical
worst case analysis of the cost of a single operation
may not adequately describe the behaviour of the
structure but it is rather more meaningful to analyze
the cost of the whole sequence of operations. The paper
first discusses some results on maintaining paths in
dynamic graphs. Besides, it considers paths problems on
dynamic labeled graphs and shows how to maintain path
expressions in the acyclic case when insertions of new
arcs are allowed.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Inf. e Sistemistica, Rome Univ.,
Italy",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory); C6120 (File
organisation)",
keywords = "Acyclic case; Data structures; Dynamic graphs; Dynamic
labeled graphs; Dynamic maintenance; Insertions; New
arcs; Path expressions; Paths problems",
thesaurus = "Computational complexity; Data structures; Graph
theory",
}
@InProceedings{Avenhaus:1989:URT,
author = "J. Avenhaus and D. Wi{\ss}mann",
title = "Using rewriting techniques to solve the generalized
word problem in polycyclic groups",
crossref = "Gonnet:1989:PAI",
pages = "322--337",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p322-avenhaus/",
abstract = "The authors apply rewriting techniques to the
generalized word problem GWP in polycyclic groups. They
assume the group $G$ to be given by a canonical
polycyclic string-rewriting system $R$ and consider GWP
in $G$ which is defined by $GWP(w,U)$ iff $w$ in $<U>$
for $w$ in $G$, finite $U$ contained in $G$, where
$<U>$ is the subgroup of $G$ generated by $U$. They
describe $<U>$ also by a rewrite system $S$ and define
a rewrite relation $\mbox{implies}_{S,R}$ in such a way
that $w$ implied by * $\mbox{implies}_{S,R} \lambda$
iff $w$ in $<U>$ ($\lambda$ the empty word). For this
rewrite relation the authors develop different critical
pair criteria for $\mbox{implies}_{S,R}$ to be
$\lambda$-confluent, i.e. confluent on the
left-congruence class $(\lambda )$ of implied by *
$\mbox{implies}_{S,R}$. Using any of these
$\lambda$-confluence criteria they construct a
completion procedure which stops for every input $S$
and computes a $\lambda$-confluent rewrite system
equivalent to $S$. This leads to a decision procedure
for GWP in G. Thus the authors give an explicit uniform
algorithm for deciding GWP in polycyclic groups and a
new proof based almost only on rewriting techniques for
the decidability of this problem. Further, they define
a rewrite relation $\mbox{implies}_{LM,U}$ which is
stronger than $\mbox{implies}_{S,R}$. They show that if
$G$ is given by a nilpotent string-rewriting system,
then by a completion procedure the input $U$ can be
transformed into $V$ such that $\mbox{implies}_{LM,V}$
is even confluent, not just $\lambda$-confluent.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "$\Lambda$-confluent; algorithms; Canonical polycyclic
string-rewriting system; Completion procedure; Critical
pair criteria; Decidability; design; Explicit uniform
algorithm; Generalized word problem; Group theory;
Nilpotent string-rewriting system; Polycyclic groups;
Rewrite relation; Rewriting techniques; theory",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Decidability; Group theory; Rewriting systems; Symbol
manipulation",
}
@InProceedings{Bajaj:1989:FRP,
author = "C. Bajaj and J. Canny and T. Garrity and J. Warren",
title = "Factoring rational polynomials over the complexes",
crossref = "Gonnet:1989:PAI",
pages = "81--90",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p81-bajaj/",
abstract = "The authors give NC algorithms for determining the
number and degrees of the absolute factors (factors
irreducible over the complex numbers $C$) of a
multivariate polynomial with rational coefficients. NC
is the class of functions computable by
logspace-uniform boolean circuits of polynomial size
and polylogarithmic dept. The measures of size of the
input polynomial are its degree $d$, coefficient length
$c$, number of variables $n$, and for sparse
polynomials, the number of nonzero coefficients $s$.
For the general case, the authors give a random
(Monte-Carlo) NC algorithm in these input measures. If
$n$ is fixed, or if the polynomial is dense, they give
a deterministic NC algorithm. The algorithm also works
in random NC for polynomial represented by
straight-line programs, provided the polynomial can be
evaluated at integer points in NC. The authors discuss
a method for obtaining an approximation to the
coefficients of each factor whose running time is
polynomial in the size of the original (dense)
polynomial. These methods rely on the fact that the
connected components of a complex hypersurface
$P(z_1,\ldots{},z_n)=0$ minus its singular points
correspond to the absolute factors of $P$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Purdue Univ., Lafayette, IN,
USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "Absolute factors; algorithms; Complex numbers;
Factorisation; Functions; Logspace-uniform boolean
circuits; measurement; Monte-Carlo; Multivariate
polynomial; NC algorithms; Rational coefficients;
Rational polynomials; Set theory; theory;
verification",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Mechanical theorem proving.",
thesaurus = "Approximation theory; Computability; Computational
complexity; Monte Carlo methods; Polynomials; Set
theory; Symbol manipulation",
xxauthor = "C. Bajaj and J. Canny and R. Garrity and J. Warren",
}
@InProceedings{Barkatou:1989:RLS,
author = "M. A. Barkatou",
title = "On the reduction of linear systems of difference
equations",
crossref = "Gonnet:1989:PAI",
pages = "1--6",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p1-barkatou/",
abstract = "The author deals with linear systems of difference
equations whose coefficients admit generalized
factorial series representations at $z=\infty$. He
gives a criterion by which a given system is determined
to have a regular singularity. He gives an algorithm,
implementable in a computer algebra system, which
reduces in a finite number of steps the system of
difference equations on an irreducible form.",
acknowledgement = ack-nhfb,
affiliation = "Lab. TIM3-IMAG, Grenoble, France",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Convergence;
Generalized factorial series; Irreducible form; Linear
difference equations; Regular singularity; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Convergence; Difference equations; Linear differential
equations; Mathematics computing; Matrix algebra;
Series [mathematics]; Symbol manipulation",
}
@InProceedings{Barkatou:1989:RNA,
author = "M. A. Barkatou",
title = "Rational {Newton} algorithm for computing formal
solutions of linear differential equations",
crossref = "Gianni:1989:SAC",
pages = "183--195",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a new algorithm for solving linear
differential equations in the neighbourhood of an
irregular singular point. This algorithm is based upon
the same principles as the Newton algorithm, however it
has a lower cost and is more suitable for computing
algebra.",
acknowledgement = ack-nhfb,
affiliation = "CNRS, INPG, IMAG, Grenoble, France",
classification = "C1120 (Analysis); C4170 (Differential equations)",
keywords = "Formal solutions; Irregular singular point; Linear
differential equations; Neighbourhood; Rational Newton
algorithm",
thesaurus = "Linear differential equations",
}
@InProceedings{BoydelaTour:1989:FAS,
author = "T. {Boy de la Tour} and R. Caferra",
title = "A formal approach to some usually informal techniques
used in mathematical reasoning",
crossref = "Gianni:1989:SAC",
pages = "402--406",
year = "1989",
bibdate = "Mon Dec 01 16:57:16 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "One of the striking characteristics of mathematical
reasoning is the contrast between the formal aspects of
mathematical truth and the informal character of the
ways to that truth. Among the many important and
usually informal mathematical activities the authors
are interested in proof analogy (i.e. common pattern
between proofs of different theorems) in the context of
interactive theorem proving.",
acknowledgement = ack-nhfb,
affiliation = "LIFIA-INPG, Grenoble, France",
classification = "C4210 (Formal logic)",
keywords = "Formal approach; Informal character; Interactive
theorem proving; Mathematical reasoning; Mathematical
truth; Usually informal techniques",
thesaurus = "Theorem proving",
}
@InProceedings{Bradford:1989:ETC,
author = "R. J. Bradford and J. H. Davenport",
title = "Effective tests for cyclotomic polynomials",
crossref = "Gianni:1989:SAC",
pages = "244--251",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present two efficient tests that determine
if a given polynomial is cyclotomic, or is a product of
cyclotomics. The first method uses the fact that all
the roots of a cyclotomic polynomial are roots of
unity, and the second the fact that the degree of a
cyclotomic polynomial is a value of $\phi (n)$, for
some $n$. The authors also find the cyclotomic factors
of any polynomial.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Cyclotomic polynomials; Roots",
thesaurus = "Polynomials",
}
@InProceedings{Bradford:1989:SRD,
author = "R. Bradford",
title = "Some results on the defect",
crossref = "Gonnet:1989:PAI",
pages = "129--135",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p129-bradford/",
abstract = "The defect of an algebraic number field (or, more
correctly, of a presentation of the field) is the
largest rational integer that divides the denominator
of any algebraic integer in the field when written
using that presentation. Knowing the defect, or
estimating it accurately is extremely valuable in many
algorithms, the factorization of polynomials over
algebraic number fields being a prime example. The
author presents a few results that are a move in the
right direction.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C4240
(Programming and algorithm theory)",
keywords = "Algebraic integer; Algebraic number field; algorithms;
Defect; Factorization; Polynomials; Rational integer;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2}
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation. {\bf G.1.9} Mathematics of Computing,
NUMERICAL ANALYSIS, Integral Equations.",
thesaurus = "Computation theory; Number theory; Polynomials; Symbol
manipulation",
}
@InProceedings{Bronstein:1989:FRR,
author = "M. Bronstein",
title = "Fast reduction of the {Risch} differential equation",
crossref = "Gianni:1989:SAC",
pages = "64--72",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a weaker definition of weak-normality which:
can always be obtained in a tower of transcendental
elementary extensions, and gives an explicit formula
for the denominator of $y$, so the equation $y'+fy=g$
can be reduced to a polynomial equation in one
reduction step. As a consequence, a new algorithm is
obtained for solving y'+fy=g. The algorithm is very
similar to the one described by Rothstein (1976),
except that the present one uses weak normality to
prevent finite cancellation, rather than having to find
integer roots of polynomials over the constant field of
$K$ in order to detect it.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1120 (Analysis); C4170 (Differential equations)",
keywords = "Denominator; Explicit formula; Fast reduction;
Polynomial equation; Reduction step; Risch differential
equation; Transcendental elementary extensions;
Weak-normality",
thesaurus = "Differential equations",
}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
crossref = "Gonnet:1989:PAI",
pages = "207--211",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p207-bronstein/",
abstract = "The author describes an algorithm, based on Risch's
real structure theorem, that determines explicitly all
the algebraic relations among a given set of real
elementary functions. He provides examples from its
implementation in the scratchpad computer algebra
system that illustrate the advantages over the use of
complex logarithms and exponentials.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Real elementary
functions; Real structure theorem; Scratchpad; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations.",
thesaurus = "Functions; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Brown:1989:SPP,
author = "C. Brown and G. Cooperman and L. Finkelstein",
title = "Solving permutation problems using rewriting systems",
crossref = "Gianni:1989:SAC",
pages = "364--377",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A new approach is described for finding short
expressions for arbitrary elements of a permutation
group in terms of the original generators which uses
rewriting methods. This forms an important component in
a long term plan to find short solutions for `large'
permutation problems (such as Rubik's cube), which are
difficult to solve by existing search techniques. In
order for this methodology to be successful, it is
important to start with a short presentation for a
finite permutation group. A new method is described for
giving a presentation for an arbitrary permutation
group acting on $n$ letters. This can be used to show
that any such permutation group has a presentation with
at most $n-1$ generators and $(n-1)^2$ relations. As an
application of this method, an $O(n^4)$ algorithm is
described for determining if a set of generators for a
permutation group of $n$ letters is a strong generating
set (in the sense of Sims). The `back end' includes a
novel implementation of the Knuth--Bendix technique on
symmetrization classes for groups.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4210 (Formal logic)",
keywords = "Knuth--Bendix technique; Permutation problems;
Rewriting systems",
thesaurus = "Rewriting systems",
}
@InProceedings{Butler:1989:CVU,
author = "G. Butler and J. Cannon",
title = "{Cayley}, version 4: the user language",
crossref = "Gianni:1989:SAC",
pages = "456--466",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Cayley, version 4, is a proposed knowledge-based
system for modern algebra. The proposal integrates the
existing powerful algorithm base of Cayley with modest
deductive facilities and large sophisticated databases
of groups and related algebraic structures. The outcome
will be a revolutionary computer algebra system. The
user language of Cayley, version 4, is the first stage
of the project to develop a computer algebra system
which integrates algorithmic, deductive, and factual
knowledge. The language plays an important role in
shaping the users' communication of their knowledge to
the system, and in presenting the results to the user.
The very survival of a system depends upon its
acceptance by the users, so the language must be
natural, extensible, and powerful. The major changes in
the language (over version 3) are the definitions of
algebraic structures, set constructors and associated
control structures, the definitions of maps and
homomorphisms, the provision of packages for procedural
abstraction and encapsulation, database facilities, and
other input/output. The motivation for these changes
has been the need to provide facilities for a
knowledge-based system; to allow sets to be defined by
properties; and to remove semantic ambiguities of
structure definitions.",
acknowledgement = ack-nhfb,
affiliation = "Sydney Univ., NSW, Australia",
classification = "C6170 (Expert systems); C7310 (Mathematics)",
keywords = "Algebra; Algebraic structures; Associated control
structures; Cayley; Computer algebra system; Deductive
facilities; Encapsulation; Factual knowledge;
Homomorphisms; Knowledge-based system; Procedural
abstraction; Set constructors; Sophisticated databases;
User language; Version 4",
thesaurus = "Knowledge based systems; Symbol manipulation",
}
@InProceedings{Cabay:1989:FRA,
author = "S. Cabay and G. Labahn",
title = "A fast, reliable algorithm for calculating
{Pad{\'e}--Hermite} forms",
crossref = "Gonnet:1989:PAI",
pages = "95--100",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p95-cabay/",
abstract = "The authors present a new fast algorithm for the
calculation of a Pad{\'e}--Hermite form for a vector of
power series. When the vector of power series is
normal, the algorithm is shown to calculate a
Pad{\'e}--Hermite form of type $(n_0, \ldots{}, n_k)$
in $O(k.(n_0^2+\ldots{} +n_k^2))$ operations. This
complexity is the same as that of other fast algorithms
for computing Pad{\'e}--Hermite approximants. However,
unlike other algorithms, the new algorithm also
succeeds in the nonnormal case, usually with only a
moderate increase in cost.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Alberta Univ., Edmonton, Alta.,
Canada",
classification = "C1120 (Analysis); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Complexity; Iterative methods; Nonnormal
case; Pad{\'e}--Hermite approximants; Pad{\'e}--Hermite
forms; theory; Vector of power series",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf G.1.9} Mathematics of
Computing, NUMERICAL ANALYSIS, Integral Equations.",
thesaurus = "Computational complexity; Iterative methods; Linear
differential equations; Series [mathematics]; Vectors",
}
@InProceedings{Canny:1989:GCP,
author = "J. Canny",
title = "Generalized characteristic polynomials",
crossref = "Gianni:1989:SAC",
pages = "293--299",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author generalises the notion of characteristic
polynomial for a system of linear equations to systems
of multivariate polynomial equations. The
generalization is natural in the sense that it reduces
to the usual definition when all the polynomials are
linear. Whereas the constant coefficient of the
characteristic polynomial of a linear system is the
determinant, the constant coefficient of the general
characteristic polynomial is the resultant of the
system. This construction is applied to solve a
traditional problem with efficient methods for solving
systems of polynomial equations: the presence of
infinitely many solutions `at infinity'. The author
gives a single-exponential time method for finding all
the isolated solution points of a system of
polynomials, even in the presence of infinitely many
solutions at infinity or elsewhere.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Generalised characteristic polynomials; Multivariate
polynomial equations; Single-exponential time method;
System of linear equations",
thesaurus = "Polynomials",
}
@InProceedings{Canny:1989:SSN,
author = "J. F. Canny and E. Kaltofen and L. Yagati",
title = "Solving systems of non-linear polynomial equations
faster",
crossref = "Gonnet:1989:PAI",
pages = "121--128",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p121-canny/",
abstract = "Finding the solution to a system of $n$ non-linear
polynomial equations in $n$ unknowns over a given
field, say the algebraic closure of the coefficient
field, is a classical and fundamental problem in
computational algebra. The authors give a method that
allows the computation of resultants and $u$-resultants
of polynomial systems in essentially linear space and
quadratic time. The algorithm constitutes the first
improvement over Gaussian elimination-based methods for
computing these fundamental invariants.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comp. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1110 (Algebra); C1120 (Analysis); C4130
(Interpolation and function approximation); C4150
(Nonlinear and functional equations); C4240
(Programming and algorithm theory)",
keywords = "Algebraic closure; algorithms; Coefficient field;
Computational algebra; Computational complexity; Linear
space; Nonlinear polynomial equations; Quadratic time;
Resultants; theory; U-resultants",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.5}
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Systems of equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf G.1.1} Mathematics of
Computing, NUMERICAL ANALYSIS, Interpolation.",
thesaurus = "Computational complexity; Nonlinear equations;
Polynomials; Symbol manipulation",
}
@InProceedings{Cantone:1989:DPE,
author = "D. Cantone and V. Cutello and A. Ferro",
title = "Decision procedures for elementary sublanguages of set
theory. {XIV}. {Three} languages involving rank related
constructs",
crossref = "Gianni:1989:SAC",
pages = "407--422",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present three decidability results for
some quantifier-free and quantified theories of sets
involving rank related constructs.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Courant Inst. of Math. Sci.,
New York Univ., NY, USA",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic)",
keywords = "Decidability results; Decision procedures; Elementary
sublanguages; Quantified theories; Quantifier-free;
Rank related constructs; Set theory",
thesaurus = "Decidability; Formal logic; Set theory",
}
@InProceedings{Caprasse:1989:CEB,
author = "H. Caprasse and J. Demaret and E. Schrufer",
title = "Can {EXCALC} be used to investigate high-dimensional
cosmological models with nonlinear {Lagrangians}?",
crossref = "Gianni:1989:SAC",
pages = "116--124",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Recent work in cosmology is characterized by the
extension of the traditional four-dimensional general
relativity models in two directions: Kaluza--Klein type
models which have more than four dimensions, and models
with Lagrangians containing nonlinear terms in the
Riemann curvature tensor and its contractions. The
package EXCALC 2 seems particularly well suited to
investigate these models further. The implementation of
all operations of EXTERIOR CALCULUS opens the way to
perform these calculations efficiently. The article
presents the current stage of investigation in this
direction.",
acknowledgement = ack-nhfb,
affiliation = "Inst. de Phys., Liege Univ., Belgium",
classification = "A9575P (Mathematical and computer techniques);
A9880D (Theoretical cosmology); C7350 (Astronomy and
astrophysics)",
keywords = "Contractions; Cosmology; EXCALC 2; Four-dimensional
general relativity models; High-dimensional
cosmological models; Kaluza--Klein type models;
Nonlinear Lagrangians; Package; Riemann curvature
tensor",
thesaurus = "Astronomy computing; Astrophysics computing;
Cosmology; Software packages",
}
@InProceedings{ChaffyCamus:1989:ARA,
author = "C. Chaffy-Camus",
title = "An application of {REDUCE} to the approximation of
$f(x,y)$",
crossref = "Gianni:1989:SAC",
pages = "73--84",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Pad{\'e} approximants are an important tool in
numerical analysis, to evaluate $f(x)$ from its power
series even outside the disk of convergence, or to
locate its singularities. The paper generalizes this
process to the multivariate case and presents two
applications of this method: the approximation of
implicit curves and the approximation of double power
series. Computations are carried out on a computer
algebra system REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "TIM3-INPG, Grenoble, France",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Approximation; Computer algebra system; Convergence;
Double power series; Implicit curves; Multivariate
case; Numerical analysis; Pad{\'e} approximants;
Reduce; Singularities",
thesaurus = "Approximation theory; Convergence of numerical
methods; Mathematics computing; Software packages",
}
@InProceedings{Char:1989:ARA,
author = "B. W. Char",
title = "Automatic reasoning about numerical stability of
rational expressions",
crossref = "Gonnet:1989:PAI",
pages = "234--241",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p234-char/",
abstract = "While numerical (e.g. Fortran) code generation from
computer algebra is nowadays relatively easy to do, the
expressions as they are produced via computer algebra
typically benefit from nontrivial reformulation for
efficiency and numerical stability. To assist in
automatic `expert reformulation', we desire good
automated tools to assess the stability of a particular
form of an expression. The author discusses an approach
to proofs of numerical stability (with respect to
roundoff error) of rational expressions. The proof
technique is based upon the ability to propagate
properties such as sign, exact representability, or a
certain kind of numerical stability, to floating point
results from properties of their antecedents. The
qualitative approach to numerical stability lends
itself to implementation as a backwards-chaining
theorem prover. While it is not a replacement for
alternative forms of stability analysis, it can
sometimes discover stability and explain it
straightforwardly.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
keywords = "algorithms; Backwards-chaining theorem prover; Code
generation; Computer algebra; Floating point; Numerical
stability; Rational expressions; Roundoff error;
theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Code generation.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
thesaurus = "Automatic programming; Convergence of numerical
methods; Mathematics computing; Symbol manipulation",
}
@InProceedings{Char:1989:DIC,
author = "B. W. Char and A. R. Macnaughton and P. A. Strooper",
title = "Discovering inequality conditions in the analytical
solutions of optimization problems",
crossref = "Gianni:1989:SAC",
pages = "109--115",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Kuhn--Tucker conditions can provide an analytic
solution to the problem of maximizing or minimizing a
function subject to inequality constraints, if the
artificial variables known as Lagrange multipliers can
be eliminated. The paper describes an automated
reasoning program that assists in the solution process.
The program may also be useful for other problems
involving algebraic reasoning with inequalities.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C1180 (Optimisation techniques); C1230 (Artificial
intelligence); C7310 (Mathematics)",
keywords = "Algebraic reasoning; Analytic solution; Artificial
variables; Automated reasoning program; Function
maximization; Function minimization; Inequality
conditions; Inequality constraints; Kuhn--Tucker
conditions; Lagrange multipliers; Optimization
problems",
thesaurus = "Inference mechanisms; Mathematics computing;
Optimisation",
}
@InProceedings{Chen:1989:CNF,
author = "Guoting Chen",
title = "Computing the normal forms of matrices depending on
parameters",
crossref = "Gonnet:1989:PAI",
pages = "242--249",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p242-chen/",
abstract = "The author considers an algorithm for the exact
computation of the Frobenius, Jordan and Arnold's form
of matrices depending holomorphically on parameters.
The problem originates from the problem of formal
resolution of a first order system of differential
equations depending on parameter. This algorithm has
been implemented in Macsyma.",
acknowledgement = ack-nhfb,
affiliation = "Equipe de Calcul Formel et Algorithmique Parallele,
Laboratoire TIM3-IMAG, Grenoble, France",
classification = "C1110 (Algebra); C1120 (Analysis); C4140 (Linear
algebra); C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; design; Differential equations; Formal
resolution; Macsyma; Matrices; Normal forms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations.",
thesaurus = "Differential equations; Mathematics computing; Matrix
algebra; Symbol manipulation",
}
@InProceedings{Collins:1989:PRP,
author = "G. E. Collins and J. R. Johnson",
title = "The probability of relative primality of {Gaussian}
integers",
crossref = "Gianni:1989:SAC",
pages = "252--258",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors generalize, to an arbitrary number field,
the theorem which gives the probability that two
integers are relatively prime. The probability that two
integers are relatively prime is $ 1/ \zeta (2)$, where
$\zeta$ is the Riemann $\zeta$ function and
$1/\zeta(2)=6/\pi^2$. The theorem for an arbitrary
number field states that the probability that two
ideals are relatively prime is the reciprocal of the
$\zeta$ function of the number field evaluated at two.
In particular, since the Gaussian integers are a unique
factorization domain, the authors get the probability
that two Gaussian integers are relatively prime is
$1/\zeta_G(2)$ where $\zeta_G$ is the $\zeta$ function
associated with the Gaussian integers. In order to
calculate the Gaussian probability, they use a theorem
that enables them to factor the $\zeta$ function into a
product of the Riemann $\zeta$ function and a Dirichlet
series called an L-series.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C1140 (Probability and statistics); C1160
(Combinatorial mathematics)",
keywords = "Arbitrary number field; Dirichlet series; Gaussian
integers; L-series; Probability; Relative primality;
Riemann $\zeta$ function",
thesaurus = "Number theory; Probability",
}
@InProceedings{Collins:1989:QES,
author = "G. E. Collins and J. R. Johnson",
title = "Quantifier elimination and the sign variation method
for real root isolation",
crossref = "Gonnet:1989:PAI",
pages = "264--271",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p264-collins/",
abstract = "An important aspect of the construction of a
cylindrical algebraic decomposition (CAD) is real root
isolation. Root isolation involves finding disjoint
intervals, each containing a single root, for all of
the real roots of a given polynomial. Root isolation is
used to construct a CAD of the real line, which serves
as the base case in the construction of higher
dimensional CAD's. It is also an essential part of the
extension phase, which lifts an induced CAD to the next
higher dimension. The authors reexamine the sign
variation method of root isolation devised by Collins
and Akritas (1976). A new proof of termination is
given, which more accurately describes the behavior of
the algorithm. This theorem is then sharpened for the
special case of cubic polynomials. The result for cubic
polynomials is obtained with the aid of Collins's CAD
based quantifier elimination algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation)",
keywords = "algorithms; Cubic polynomials; Cylindrical algebraic
decomposition; design; Disjoint intervals; Polynomial;
Quantifier elimination; Real root isolation; Sign
variation method; Symbol manipulation; theory",
subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED
ENGINEERING. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Cooperman:1989:RGC,
author = "G. Cooperman and L. Finkelstein and E. Luks",
title = "Reduction of group constructions to point
stabilizers",
crossref = "Gonnet:1989:PAI",
pages = "351--356",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p351-cooperman/",
abstract = "The construction of point stabilizer subgroups is a
problem which has been studied intensively. This work
describes a general reduction of certain group
constructions to the point stabilizer problem. Examples
are given for the centralizer, the normal closure, and
a restricted group intersection problem. For the normal
closure problem, this work provides an alternative to
current algorithms, which are limited by the need for
repeated closures under conjugation. For the
centralizer and restricted group intersection problems,
one can use an existing point stabilizer sequence along
with a recent base change algorithm to avoid generating
a new point stabilizer sequence. This reduces the time
complexity by at least an order of magnitude.
Algorithms and theoretical time estimates for the
special case of a small base are also summarized. An
implementation is in progress.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Base change algorithm; Centralizer; Group
constructions; Group intersection; Group theory; Normal
closure; Point stabilizers; theory; Time complexity",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Number-theoretic
computations. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Computational complexity; Group theory; Symbol
manipulation",
}
@InProceedings{Deprit:1989:MPS,
author = "A. Deprit and E. Deprit",
title = "Massively parallel symbolic computation",
crossref = "Gonnet:1989:PAI",
pages = "308--316",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p308-deprit/",
abstract = "A massively parallel processor proves to be a powerful
tool for manipulating the very large Poisson series
encountered in nonlinear dynamics. Exploiting the
algebraic structure of Poisson series leads quite
naturally to parallel data structures and algorithms
for symbolic manipulation. Exercising the parallel
symbolic processor on the solution of Kepler's equation
reveals the need to reexamine the serial computational
methods traditionally applied to problems in
dynamics.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
USA",
classification = "C1120 (Analysis); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Algebraic structure; algorithms; design; Massively
parallel processor; Nonlinear dynamics; Parallel data
structures; Symbolic manipulation; theory; Very large
Poisson series",
subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf E.1} Data, DATA STRUCTURES. {\bf
G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations. {\bf C.1.3} Computer
Systems Organization, PROCESSOR ARCHITECTURES, Other
Architecture Styles, Stack-oriented processors**.",
thesaurus = "Data structures; Mathematics computing; Nonlinear
equations; Parallel algorithms; Series [mathematics];
Symbol manipulation",
}
@InProceedings{Devitt:1989:UCA,
author = "J. S. Devitt",
title = "Unleashing computer algebra on the mathematics
curriculum",
crossref = "Gonnet:1989:PAI",
pages = "218--227",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author presents examples of the actual use of a
computer algebra system in the mathematics classroom.
These methods and observations are based on the daily
use of symbolic algebra during lectures. The potential
for focusing student energies on the concepts and ideas
of mathematical instead of just mimicking routine
computations is enormous. Considerable work remains to
make such tools widely accessible but the observations
presented will help to make others aware of the great
potential which exists for these and similar methods.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Saskatchewan Univ., Saskatoon, Sask.,
Canada",
classification = "C7310 (Mathematics); C7810C (Computer-aided
instruction)",
keywords = "Computer algebra; Educational computing; Mathematics
curriculum; Symbolic algebra",
thesaurus = "Educational computing; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Dewar:1989:IIS,
author = "M. C. Dewar",
title = "{IRENA}: an integrated symbolic and numerical
computation environment",
crossref = "Gonnet:1989:PAI",
pages = "171--179",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Computer algebra systems provide an extremely
user-friendly and natural problem-solving environment,
but are comparatively slow and limited in the scope of
problems they can treat. Programs which call routines
from numerical software libraries are fast, but require
longer development and testing time, as well as forcing
potential users to describe their problems in what is,
to them, an unnatural form. Both approaches have
advantages and disadvantages, but until now it has been
rather difficult to mix the two. The author describes
IRENA, an interface between the computer algebra system
REDUCE and the NAG numerical subroutine library, which
provides the NAG user with the advantages of a computer
algebra system and the REDUCE user with the facilities
of an extensive library of numerical software. He
discusses how the two methods could be used
side-by-side to solve problems in definite
integration.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics)",
keywords = "Computer algebra system; Definite integration; IRENA;
NAG; Numerical software; Numerical subroutine library;
REDUCE",
thesaurus = "Integration; Mathematics computing; Symbol
manipulation; User interfaces",
}
@InProceedings{Dicrescenzo:1989:AEA,
author = "C. Dicrescenzo and D. Duval",
title = "Algebraic extensions and algebraic closure in
{Scratchpad II}",
crossref = "Gianni:1989:SAC",
pages = "440--446",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Many problems in computer algebra, as well as in
high-school exercises, are such that their statement
only involves integers but their solution involves
complex numbers. For example, the complex numbers
$\sqrt{2}$ and $-\sqrt{2}$ appear in the solutions of
elementary problems in various domains. The authors
describe an implementation of an algebraic closure
domain constructor in the language Scratchpad II. In
the first part they analyze the problem, and in the
second part they describe a solution based on the D5
system.",
acknowledgement = ack-nhfb,
affiliation = "TIM3, INPG, Grenoble, France",
classification = "C7310 (Mathematics)",
keywords = "Algebraic closure domain constructor; D5 system;
Language Scratchpad II",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Edelsbrunner:1989:TPS,
author = "H. Edelsbrunner and F. P. Preparata and D. B. West",
title = "Tetrahedrizing point sets in three dimensions",
crossref = "Gianni:1989:SAC",
pages = "315--331",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper offers combinatorial results on extremum
problems concerning the number of tetrahedra in a
tetrahedrization of $n$ points in general position in
three dimensions, i.e. such that no four points are
coplanar. It also presents an algorithm that in
$O(n\log{}n)$ time constructs a tetrahedrization of a
set of $n$ points consisting of at most $3n-11$
tetrahedra.",
acknowledgement = ack-nhfb,
affiliation = "Illinois Univ., Urbana, IL, USA",
classification = "C4190 (Other numerical methods)",
keywords = "Combinatorial results; Extremum problems; Tetrahedra;
Tetrahedrization",
thesaurus = "Computational geometry",
}
@InProceedings{Einwohner:1989:MPG,
author = "T. H. Einwohner and R. J. Fateman",
title = "A {MACSYMA} package for the generation and
manipulation of {Chebyshev} series",
crossref = "Gonnet:1989:PAI",
pages = "180--185",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p180-einwohner/",
abstract = "Techniques for a MACSYMA package for expanding an
arbitrary univariate expression as a truncated series
in Chebyshev polynomials and manipulating such
expansions are described. A data structure is
introduced to represent a truncated expansion in a set
of orthogonal polynomials which contains the
independent variable, the name of the orthogonal
polynomial set, the number of terms retained, and a
list of the expansion coefficients. The package
converts a given expression into the aforementioned
data structure. Special cases are the conversion of
sums, products, the ratio, or the composition of
truncated Chebyshev expansions. Another special case is
converting an expression free of truncated Chebyshev
expansions. The package generates exact expansion
coefficients whenever possible. In addition to
well-known Chebyshev expansions, such as for
polynomials, the authors provide new methods for
getting exact Chebyshev expansions for reciprocals of
polynomials of degree one or two, meromorphic
functions, arbitrary powers of a first-degree
polynomial, the error-function, and generalized
hypergeometric functions.",
acknowledgement = ack-nhfb,
affiliation = "Lawrence Livermore Lab., California Univ., CA, USA",
classification = "C4130 (Interpolation and function approximation);
C6120 (File organisation); C6130 (Data handling
techniques); C7310 (Mathematics)",
keywords = "algorithms; Chebyshev polynomials; Chebyshev series;
Data structure; MACSYMA; Orthogonal polynomials;
theory; Univariate expression",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
E.1} Data, DATA STRUCTURES. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Chebyshev approximation; Data structures; Mathematics
computing; Polynomials; Series [mathematics]; Software
packages; Symbol manipulation",
}
@InProceedings{Fateman:1989:LTR,
author = "R. J. Fateman",
title = "Lookup tables, recurrences and complexity",
crossref = "Gonnet:1989:PAI",
pages = "68--73",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p68-fateman/",
abstract = "The use of lookup tables can reduce the complexity of
calculation of functions defined typically by
mathematical recurrence relations. Although this
technique has been adopted by several algebraic
manipulation systems, it has not been examined
critically in the literature. While the use of
tabulation or `memoization' seems to be particularly
simple and worthwhile technique in some areas, there
are some negative consequences. Furthermore, the
expansion of this technique to other areas (other than
recurrences) has not been subjected to analysis. The
paper examines some of the assumptions.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic manipulation; algorithms; Complexity;
Functions; Lookup tables; Mathematical recurrence
relations; theory",
subject = "{\bf F.1.3} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Complexity Measures and Classes. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Computational complexity; Number theory; Recursive
functions; Symbol manipulation; Table lookup",
}
@InProceedings{Fateman:1989:SSA,
author = "R. J. Fateman",
title = "Series solutions of algebraic and differential
equations: a comparison of linear and quadratic
algebraic convergence",
crossref = "Gonnet:1989:PAI",
pages = "11--16",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p11-fateman/",
abstract = "Speed of convergence of Newton-like iterations in an
algebraic domain can be affected heavily by the
increasing cost of each step, so much so that a
quadratically convergent algorithm with complex steps
may be comparable to a slower one with simple steps.
The author gives two examples: solving algebraic and
first-order ordinary differential equations using the
MACSYMA algebraic manipulation system, demonstrating
this phenomenon. The relevant programs are exhibited in
the hope that they might give rise to more widespread
application of these techniques.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations); C7310 (Mathematics)",
keywords = "Algebraic equations; Algebraic manipulation system;
algorithms; Convergence; Differential equations; Linear
algebraic convergence; MACSYMA; Newton-like iterations;
Polynomials; Quadratic algebraic convergence; Series
solutions; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Iterative methods. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Convergence of numerical methods; Differential
equations; Iterative methods; Mathematics computing;
Polynomials; Series [mathematics]; Symbol
manipulation",
}
@InProceedings{Fitch:1989:CRB,
author = "J. Fitch",
title = "Can {REDUCE} be run in parallel?",
crossref = "Gonnet:1989:PAI",
pages = "155--162",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p155-fitch/",
abstract = "In order to make a substantial improvement in the
performance of algebra systems it will eventually be
necessary to use a parallel execution system. This
paper considers one approach to detecting parallelism,
an automatic method related to compilation, and applies
it to REDUCE, and to the factoriser in particular.",
acknowledgement = ack-nhfb,
classification = "C6130 (Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310
(Mathematics)",
keywords = "Algebra systems; algorithms; Automatic method;
Compilation; Factoriser; measurement; Parallel
execution system; Parallelism; REDUCE",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf F.3.2} Theory of Computation, LOGICS
AND MEANINGS OF PROGRAMS, Semantics of Programming
Languages.",
thesaurus = "Mathematics computing; Parallel programming; Program
compilers; Symbol manipulation",
}
@InProceedings{Freire:1989:ASC,
author = "E. Freire and E. Gamero and E. Ponce and L. G.
Franquelo",
title = "An algorithm for symbolic computation of center
manifolds",
crossref = "Gianni:1989:SAC",
pages = "218--230",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A useful technique for the study of local bifurcations
is part of the center manifold theory because a
dimensional reduction is achieved. The computation of
Taylor series approximations of center manifolds gives
rise to several difficulties regarding the operational
complexity and the computational effort. Previous works
proceed in such a way that the computational effort is
not optimized. In the paper an algorithm for center
manifolds well suited to symbolic computation is
presented. The algorithm is organized according to an
iterative scheme making good use of the previous steps,
thereby minimizing the number of operations. The
results of two examples obtained through a REDUCE 3.2
implementation of the algorithm are included.",
acknowledgement = ack-nhfb,
affiliation = "Escuela Superior Ingenieros Ind., Sevilla, Spain",
classification = "C1120 (Analysis); C4130 (Interpolation and function
approximation); C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algorithm; Center manifold theory; Computational
effort; Dimensional reduction; Iterative scheme; Local
bifurcations; Operational complexity; REDUCE 3.2;
Symbolic computation; Taylor series approximations",
thesaurus = "Approximation theory; Differential equations;
Mathematics computing; Symbol manipulation",
}
@InProceedings{Galligo:1989:GEC,
author = "Andr\'e Galligo and Lo{\"\i}c Pottier and Carlo
Traverso",
title = "Greater easy common divisor and standard basis
completion algorithms",
crossref = "Gianni:1989:SAC",
pages = "162--176",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The paper considers arithmetic complexity problems;
the main problem is how to limit the growth of the
coefficients in the algorithms and the complexity of
the field operations involved. The problem is important
with every ground field, with the obvious exception of
finite fields.",
acknowledgement = ack-nhfb,
affiliation = "Nice Univ., France",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algorithms; Arithmetic complexity problems;
Coefficients; Field operations; Greater easy common
divisor; Standard basis completion algorithms",
thesaurus = "Computational complexity; Rewriting systems",
}
@InProceedings{Gaonzalez:1989:SS,
author = "L. Gaonzalez and H. Lombardi and T. Recio and M.-F.
Roy",
title = "{Sturm--Habicht} sequence",
crossref = "Gonnet:1989:PAI",
pages = "136--146",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p136-gaonzalez/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic.",
}
@InProceedings{Geddes:1989:HMO,
author = "K. O. Geddes and G. H. Gonnet and T. J. Smedley",
title = "Heuristic methods for operations with algebraic
numbers",
crossref = "Gianni:1989:SAC",
pages = "475--480",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algorithms for doing computations involving algebraic
numbers have been known for quite some time and
implementations now exist in many computer algebra
systems. Many of these algorithms have been analysed
and shown to run in polynomial time and space, but in
spite of this many real problems take large amounts of
time and space to solve. The authors describe a
heuristic method which can be used for many operations
involving algebraic numbers. They give specifics for
doing algebraic number inverses, and algebraic number
polynomial exact division and greatest common divisor
calculation. The heuristic will not solve all instances
of these problems, but it returns either the correct
result or with failure very quickly, and succeeds for a
very large number of problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic numbers; Heuristic methods; Polynomial",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Geddes:1989:NAC,
author = "K. O. Geddes and G. H. Gonnet",
title = "A new algorithm for computing symbolic limits using
hierarchical series",
crossref = "Gianni:1989:SAC",
pages = "490--495",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors describe an algorithm for computing
symbolic limits, i.e. limits of expressions in symbolic
form, using hierarchical series. A hierarchical series
consists of two levels: an inner level which uses a
simple generalization of Laurent series with finite
principal part and which captures the behaviour of
subexpressions without essential singularities, and an
outer level which captures the essential singularities.
Once such a series has been computed for an expression
at a given point, the limit of the expression at the
point is determined by looking at the most significant
term of the series. This algorithm solves the limit
problem for a large class of expressions.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
keywords = "Algorithm; Finite principal part; Hierarchical series;
Laurent series; Limit problem; Singularities; Symbolic
form; Symbolic limits",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Geddes:1989:RIM,
author = "K. O. Geddes and L. Y. Stefanus",
title = "On the {Risch--Norman} integration method and its
implementation in {MAPLE}",
crossref = "Gonnet:1989:PAI",
pages = "212--217",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p212-geddes/",
abstract = "Unlike the recursive Risch algorithm for the
integration of transcendental elementary functions, the
Risch--Norman method processes the tower of field
extensions directly in one step. In addition to
logarithmic and exponential field extensions, this
method can handle extensions in terms of tangents.
Consequently, it allows trigonometric functions to be
treated without converting them to complex exponential
form. The authors review this method and describe its
implementation in MAPLE. A heuristic enhancement to
this method is also presented.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C1120 (Analysis); C4160 (Numerical
integration and differentiation); C7310 (Mathematics)",
keywords = "algorithms; Exponential field extensions; Logarithmic
field extensions; MAPLE; Risch--Norman integration;
Tangents; theory; Transcendental elementary functions;
Trigonometric functions",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Functions; Integration; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Gianni:1989:DA,
author = "P. Gianni and V. Miller and B. Trager",
title = "Decomposition of algebras",
crossref = "Gianni:1989:SAC",
pages = "300--308",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors deal with the problem of decomposing
finite commutative Q-algebras as a direct product of
local Q-algebras. They solve this problem by reducing
it to the problem of finding a decomposition of finite
algebras over finite field. They show that it is
possible to define a lifting process that allows to
reconstruct the answer over the rational numbers. This
lifting appears to be very efficient since it is a
quadratic lifting that doesn't require stepwise
inversions. It is easy to see that the
Berlekamp--Hensel algorithm for the factorization of
polynomials is a special case of this argument.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1110 (Algebra); C4190 (Other numerical methods)",
keywords = "Berlekamp--Hensel algorithm; Decomposing finite
commutative Q-algebras; Lifting process",
thesaurus = "Algebra; Computational geometry",
}
@InProceedings{Giusti:1989:ATP,
author = "M. Giusti and D. Lazard and A. Valibouze",
title = "Algebraic transformations of polynomial equations,
symmetric polynomials and elimination",
crossref = "Gianni:1989:SAC",
pages = "309--314",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors define a general transformation of
polynomials and study the following concrete problem:
how to perform such a transformation using a standard
system of computer algebra, providing the usual
algebraic tools.",
acknowledgement = ack-nhfb,
affiliation = "Centre de Math., Ecole Polytech., Palaiseau, France",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C7310 (Mathematics)",
keywords = "Algebraic tools; Algebraic transformations of
polynomial equations; Computer algebra; Elimination;
Symmetric polynomials",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Giusti:1989:CRC,
author = "M. Giusti",
title = "On the {Castelnuovo} regularity for curves",
crossref = "Gonnet:1989:PAI",
pages = "250--253",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p250-giusti/",
abstract = "Let $k$ be a field of characteristic zero; let us
consider an algebraic subvariety of the projective
space $P_k^n$, defined by a homogeneous ideal I of the
polynomial algebra $R=k(x_o,\ldots{},x_n)$. There
exists different objects measuring the complexity of
this subvariety. Some invariants are naturally
intrinsic: the dimension and the degree of the
subvariety, the Hilbert function and its regularity,
and the Castelnuovo regularity. A natural question is
to study the relationships between the integers, at
least when the dimension is small (less or equal to
one). The author gives a slightly different version of
the Castelnuovo--Gruson--Lazarsfeld--Peskine theorem
(1983), which relates the Castelnuovo regularity and
the degree in the case of curves with more general
hypotheses but unfortunately slightly weaker
conclusion.",
acknowledgement = ack-nhfb,
affiliation = "Centre de Mathematiques, CNRS, Ecole Polytechnique,
Palaiseau, France",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation)",
keywords = "algorithms; Castelnuovo regularity; Complexity;
Curves; design; Hilbert function; measurement;
Polynomial algebra; Polynomials; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Complexity Measures and Classes.",
thesaurus = "Computational complexity; Curve fitting; Polynomials",
}
@InProceedings{Gonzalez:1989:SS,
author = "L. Gonzalez and H. Lombardi and T. Recio and M.-F.
Roy",
title = "{Sturm--Habicht} sequence",
crossref = "Gonnet:1989:PAI",
pages = "136--146",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Formal computations with inequalities is a subject of
general interest in computer algebra. In particular it
is fundamental in the parallelisation of basic
algorithms and quantifier elimination for real closed
fields. The authors give a generalisation of the Sturm
theorem essentially due to Sylvester, which is the key
for formal computations with inequalities. They study
the subresultant sequence, precise some of the
classical definitions in order to avoid problems and
study specialisation properties. They introduce the
Sturm--Habicht sequence, which generalizes Habicht's
work (1948). This new sequence, obtained automatically
from a subresultant sequence, has some remarkable
properties: it gives the same information as the Sturm
sequence, recovered by looking only at its principal
coefficients; it can be computed by ring operations and
exact divisions only, in polynomial time in case of
integer coefficients, eventually by modular methods; it
has good specialisation properties. Some information
about applications and implementation of the
Sturm--Habicht sequence is given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Matematicas, Cantabria Univ., Spain",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "Computational complexity; Computer algebra;
Inequalities; Integer coefficients; Modular methods;
Parallelisation; Polynomial time; Quantifier
elimination; Ring operations; Sturm theorem;
Sturm--Habicht sequence",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials; Series [mathematics]; Symbol
manipulation",
}
@InProceedings{Grigorev:1989:CCC,
author = "D. Yu. Grigor'ev",
title = "Complexity of computing the characters and the genre
of a system of exterior differential equations",
crossref = "Gianni:1989:SAC",
pages = "534--543",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let a system
$(\sum_JA_{J,i}(dX_{j1},\ldots{},dX_{jm})=0)_{m,i}$ of
exterior differential equations be given, where
$A_{J,i}$ are polynomials in $n$ variables
$X_1,\ldots{}, X_n$ of degrees less than $d$ and
skew-symmetric relatively to multiindices
$J=(j_1,\ldots{}, j_m)$, the square brackets denote the
exterior product of the differentials
$dX_{j1},\ldots{}, dX_{jm}$. E. Cartan (1945)
introduced the characters and the genre $h$ of the
system. Cauchy--Kovalevski theorem guarantees the
existence of an integral manifold (and even of the
general form) with the dimension less or equal to $h$
satisfying the given system. An algorithm for computing
the characters and the genre is designed with the
running time polynomial in $L$, $(dn)^n$, herein $L$
denotes the bit-size of the system. The algorithm
involves the subexponential-time procedures for finding
the irreducible components of an algebraic variety.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
Leningrad, USSR",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
keywords = "Algebraic variety; Cauchy--Kovalevski theorem;
Characters; Exterior differential equations; Integral
manifold; Irreducible components; Polynomials",
thesaurus = "Differential equations; Polynomials",
}
@InProceedings{Grossman:1989:LTE,
author = "R. Grossman and R. G. Larson",
title = "Labeled trees and the efficient computation of
derivations",
crossref = "Gonnet:1989:PAI",
pages = "74--80",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p74-grossman/",
abstract = "The paper is concerned with the effective parallel
symbolic computation of operators under composition.
Examples include differential operators under
composition and vector fields under the Lie bracket. In
general, such operators do not commute. An important
problem is to find efficient algorithms to write
expressions involving noncommuting operators in terms
of operators which do commute. If the original
expression enjoys a certain symmetry, then naive
rewriting requires the computation of terms which in
the end cancel. Previously, the authors gave an
algorithm which in some cases is exponentially faster
than the naive expansion of the noncommutating
operators (1989). In this paper they show how that
algorithm can be naturally parallelized.",
acknowledgement = ack-nhfb,
affiliation = "Illinois Univ., Chicago, IL, USA",
classification = "C1120 (Analysis); C1160 (Combinatorial mathematics);
C4210 (Formal logic); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Computational complexity; Data structures;
Derivations; Differential operators; Labeled trees; Lie
bracket; Noncommuting operators; Operators; Parallel
algorithms; Parallel symbolic computation; theory;
Vector fields",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.2} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Modes of Computation,
Parallelism and concurrency.",
thesaurus = "Computational complexity; Data structures;
Differentiation; Parallel algorithms; Symbol
manipulation; Trees [mathematics]",
}
@InProceedings{Hentzel:1989:VNA,
author = "I. R. Hentzel and D. J. Pokrass",
title = "Verification of non-identities in algebras",
crossref = "Gianni:1989:SAC",
pages = "496--507",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present a computer assisted algorithm
which establishes whether or not a proposed identity is
a consequence of the defining identities of a variety
of nonassociative algebras. When the nonassociative
polynomial is not an identity, the algorithm produces a
proof called a characteristic function. Like an
ordinary counterexample, the characteristic function
can be used to convince a verifier that the polynomial
is not identically zero. However the characteristic
function appears to be computationally easier to
verify. Also, it reduces or eliminates problems with
characteristic. The authors used this method to obtain
and verify a new result in the theory of nonassociative
algebras. Namely, in a free right alternative algebra
$(a,a,b)^3 \ne 0$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
classification = "C7310 (Mathematics)",
keywords = "Algebras; Characteristic function; Computer assisted
algorithm; Nonassociative polynomial; Nonidentities
verification",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Juozapavicius:1989:SCW,
author = "A. Juozapavicius",
title = "Symbolic computation for {Witt} rings",
crossref = "Gianni:1989:SAC",
pages = "271--273",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author considers bilinear and quadratic forms over
polynomial rings, such that they can carry linear
discrete orderings. The author defines the notion of
reduced form and presents theorems concerning
equivalence of forms to their reduced presentation. The
proofs of these statements are based on the
Buchberger's algorithms and their modifications to
Gr{\"o}bner bases.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Vilnius State Univ., Lithuanian SSR,
USSR",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Bilinear forms; Symbolic computation; Witt rings;
Quadratic forms; Polynomial rings; Linear discrete
orderings; Reduced form; Gr{\"o}bner bases",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Kaltofen:1989:ISM,
author = "E. Kaltofen and L. Yagati",
title = "Improved sparse multivariate polynomial interpolation
algorithms",
crossref = "Gianni:1989:SAC",
pages = "467--474",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors consider the problem of interpolating
sparse multivariate polynomials from their values. They
discuss two algorithms for sparse interpolation, one
due to Ben-Or and Tiwari (1988) and the other due to
Zippel (1988). They present efficient algorithms for
finding the rank of certain special Toeplitz systems
arising in the Ben-Or and Tiwari algorithm and for
solving transposed Vandermonde systems of equations,
the use of which greatly improves the time complexities
of the two interpolation algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Sparse multivariate polynomial interpolation
algorithms; Time complexities; Toeplitz systems;
Transposed Vandermonde systems of equations",
thesaurus = "Interpolation; Polynomials",
}
@InProceedings{Kaltofen:1989:IVP,
author = "E. Kaltofen and T. Valente and N. Yui",
title = "An improved {Las Vegas} primality test",
crossref = "Gonnet:1989:PAI",
pages = "26--33",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p26-kaltofen/",
abstract = "The authors present a modification of the
Goldwasser--Kilian--Atkin primality test, which, when
given an input $n$, outputs either prime or composite,
along with a certificate of correctness which may be
verified in polynomial time. Atkin's method computes
the order of an elliptic curve whose endomorphism ring
is isomorphic to the ring of integers of a given
imaginary quadratic field $Q(\sqrt{-D})$. Once an
appropriate order is found, the parameters of the curve
are computed as a function of a root modulo $n$ of the
Hilbert class equation for the Hilbert class field of
$Q(\sqrt{-D})$. The modification proposed determines
instead a root of the Watson class equation for
$Q(\sqrt{-D})$ and applies a transformation to get a
root of the corresponding Hilbert equation. This is a
substantial improvement, in that the Watson equations
have much smaller coefficients than do the Hilbert
equations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Certificate of correctness; Elliptic
curve; Endomorphism ring; Goldwasser--Kilian--Atkin
primality test; Hilbert equation; Imaginary quadratic
field; Las Vegas primality test; Number theory;
Polynomial time; Prime number; Programming theory;
theory; Watson class equation",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Hyperbolic
equations. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation.",
thesaurus = "Computational complexity; Mathematics computing;
Number theory; Program verification; Programming
theory",
}
@InProceedings{Kirchner:1989:CER,
author = "C. Kirchner and H. Kirchner",
title = "Constrained equational reasoning",
crossref = "Gonnet:1989:PAI",
pages = "382--389",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p382-kirchner/",
abstract = "The theory of constrained equational reasoning is
outlined. Many questions and prolongations of this work
arise.",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic)",
keywords = "algorithms; Constrained equational reasoning; Formal
logic; Theorem proving; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Formal logic; Theorem proving",
}
@InProceedings{Kobayashi:1989:SSA,
author = "H. Kobayashi and S. Moritsugu and R. W. Hogan",
title = "Solving systems of algebraic equations",
crossref = "Gianni:1989:SAC",
pages = "139--149",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Shows an algorithm for computing all the solutions
with their multiplicities of a system of algebraic
equations. The algorithm previously proposed by the
authors for the case where the ideal is
zero-dimensional and radical seems to have practical
efficiency. The authors present a new method for
solving systems which are not necessarily radical. The
set of all solutions is partitioned into subsets each
of which consists of mutually conjugate solutions
having the same multiplicity.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Coll. of Sci. and Technol., Nihon
Univ., Tokyo, Japan",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "Algebraic equations; Algorithm; Ideal; Multiplicities;
Mutually conjugate solutions; Radical; Subsets;
Zero-dimensional",
thesaurus = "Algebra; Problem solving; Theorem proving",
}
@InProceedings{Kredel:1989:SDC,
author = "H. Kredel",
title = "Software development for computer algebra or from
{ALDES\slash SAC-2} to {WEB\slash Modula-2}",
crossref = "Gianni:1989:SAC",
pages = "447--455",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author defines a new concept for developing
computer algebra software. The development system will
integrate a documentation system, a programming
language, algorithm libraries, and an interactive
calculation facility. The author exemplifies the
workability of this concept by applying it to the well
known ALDES/SAC-2 system. The ALDES Translator is
modified to help in converting ALDES/SAC-2 Code to
Modula-2. The implementation and module setup of the
SAC-2 basic system, list processing system and
arithmetic system in Modula-2 are discussed. An example
gives a first idea of the performance of the system.
The WEB System of Structured Documentation is used to
generate documentation with {\TeX}.",
acknowledgement = ack-nhfb,
affiliation = "Passau Univ., West Germany",
classification = "C6110B (Software engineering techniques); C7310
(Mathematics)",
keywords = "ALDES/SAC-2 system; Algorithm libraries; Computer
algebra software; Documentation system; Interactive
calculation facility; Performance; Programming
language; WEB/Modula-2",
thesaurus = "Mathematics computing; Software engineering; Symbol
manipulation",
}
@InProceedings{Kuhn:1989:MEC,
author = "N. Kuhn and K. Madlener",
title = "A method for enumerating cosets of a group presented
by a canonical system",
crossref = "Gonnet:1989:PAI",
pages = "338--350",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p338-kuhn/",
abstract = "The application of rewriting techniques to enumerate
cosets of subgroups in groups is investigated. Given a
class of groups $G$ having canonical string rewriting
presentations the authors consider the GWP for this
class which is defined by $GWP(w,U)$ iff $w$ in $<U>$
for $w$ in finite $U$ contained in $G$, $G \in G$,
where $<U>$ is the subgroup of $G$ generated by $U$.
They show how to associate to $U$ two rewriting
relations to $-{}_U$ and implies $-{}_U$ on strings
such that $w$ in $<U>$ iff $w$ from $*$ to
$-{}_U\lambda$ iff $w$ implied by
$*\mbox{implies}-_U\lambda$ ($\lambda$ the empty word),
both representing the left congruence generated by
$<U>$. They derive general critical pair criteria for
confluence and $\lambda$-confluence for these
relations. Using these criteria completion procedures
can be constructed which enumerate cosets like the
Todd--Coxeter algorithm without explicit definition of
all cosets. The procedures are shown to be terminating
if the index of the subgroup is finite or for groups
with finite canonical monadic group presentations. If
the completion procedure terminates it returns a prefix
rewriting system which is confluent on $\Sigma *$, thus
deciding the GWP and the index problem for this class
of groups. The normal forms of the rewriting relations
form a minimal Schreier-representative system of $<U>$
in $G$.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "$\Lambda$-confluence; algorithms; Canonical string
rewriting presentations; Completion procedures;
Confluence; Cosets; Critical pair criteria;
Decidability; Finite canonical monadic group
presentations; Generalized word problem; Group theory;
Minimal Schreier-representative system; Rewriting
relations; Rewriting techniques; Subgroups; theory;
Todd--Coxeter algorithm",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf F.4.2} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
Other Rewriting Systems, Decision problems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Decidability; Group theory; Rewriting systems; Symbol
manipulation",
}
@InProceedings{Kutzler:1989:CAT,
author = "B. Kutzler",
title = "Careful algebraic translations of geometry theorems",
crossref = "Gonnet:1989:PAI",
pages = "254--263",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p254-kutzler/",
abstract = "Modern application areas like computer-aided design
and robotics have revived interest in geometry. The
algorithmic techniques of computer algebra are
important tools for solving large classes of nonlinear
geometric problems. However, their application requires
a translation of geometric problems into algebraic
form. So far, this algebraization process has not
gained special attention, since it was considered
`obvious'. In the context of automated geometry theorem
proving, the use of algebraic deduction techniques led
to very promising results, but it seemed to change the
nature of proof problems from deciding the validity of
a theorem to finding nondegeneracy conditions under
which the theorem holds. A careful analysis shows, that
this is mainly due to the `careless' translation
method. A careful translation technique is presented
that resolves this defect. The usefulness of the new
algebraization method is demonstrated on concrete
examples. A practical comparison with the former
`careless' translation is done.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C4210 (Formal logic); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "Algebraic deduction; algorithms; Automated geometry
theorem proving; Computer algebra; experimentation;
Geometry theorems; Nonlinear geometric problems;
theory",
subject = "{\bf I.2.0} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, General. {\bf G.2.1} Mathematics of
Computing, DISCRETE MATHEMATICS, Combinatorics.",
thesaurus = "Computational geometry; Symbol manipulation; Theorem
proving",
}
@InProceedings{MacCallum:1989:ODE,
author = "M. A. H. MacCallum",
title = "An ordinary differential equation solver for
{REDUCE}",
crossref = "Gianni:1989:SAC",
pages = "196--205",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Progress and plans for the implementation of an
ordinary differential equation solver in REDUCE 3.3 are
reported; the aim is to incorporate the best available
methods for obtaining closed-form solutions, and to aim
at the `best possible' alternative when this fails. It
is hoped that this will become a part of the standard
REDUCE program library. Elementary capabilities have
already been implemented, i.e. methods for first order
differential equations of simple types and linear
equations of any order with constant coefficients. The
further methods to be used include: for first-order
equations, an adaptation of Shtokhamer's MACSYMA
program; for higher-order linear equations,
factorisation of the operator where possible; and for
nonlinear equations, the exploitation of Lie
symmetries.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Queen Mary Coll., London, UK",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Closed-form solutions; Factorisation; First-order
equations; Lie symmetries; MACSYMA program; Nonlinear
equations; Ordinary differential equation solver;
REDUCE 3.3; REDUCE program library",
thesaurus = "Differential equations; Mathematics computing;
Software packages; Subroutines",
}
@InProceedings{Menezes:1989:SCA,
author = "A. J. Menezes and P. C. {van Oorschot} and S. A.
Vanstone",
title = "Some computational aspects of root finding in
${GF}(q^m)$",
crossref = "Gianni:1989:SAC",
pages = "259--270",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper is an implementation report comparing
several variations of a deterministic algorithm for
finding roots of polynomials in finite extension
fields. Running times for problem instances in fields
$\mbox{GF}(2^m)$, including $m>1000$, are given.
Comparisons are made between the variations, and
improvements achieved in running times are discussed.",
acknowledgement = ack-nhfb,
affiliation = "Waterloo Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Computational aspects; Root finding; Roots of
polynomials",
thesaurus = "Polynomials",
}
@InProceedings{Miller:1989:PGE,
author = "B. R. Miller",
title = "A program generator for efficient evaluation of
{Fourier} series",
crossref = "Gonnet:1989:PAI",
pages = "199--206",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p199-miller/",
abstract = "Many fields require the evaluation of large
multi-variate Fourier series, but the naive method of
calling sine and cosine for each term can be
prohibitive where computing resources are constrained
or the series are extremely large (30000 terms).
Although the number of such calls can be reduced by
using trigonometric identities, such a reduction is
usually not possible by hand. Indeed, even when it is
carried out by computer, care must be taken to generate
compact programs and avoid generating large numbers of
intermediate terms. The author describes an algorithm
for automatically generating very efficient Fortran
programs directly from the mathematical description of
the series to be evaluated. The resulting Fortran
programs are 5-7 times faster than the naive version
and sometimes significantly more compact.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersbury, MD,
USA",
classification = "C6115 (Programming support); C7310 (Mathematics)",
keywords = "algorithms; design; Fortran programs; Fourier series;
languages; Program generator",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computability
theory. {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation. {\bf D.3.3} Software,
PROGRAMMING LANGUAGES, Language Constructs and
Features, Procedures, functions, and subroutines.",
thesaurus = "Automatic programming; Mathematics computing; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Mora:1989:GBN,
author = "T. Mora",
title = "{Gr{\"o}bner} bases in noncommutative algebras",
crossref = "Gianni:1989:SAC",
pages = "150--161",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author has studied, in 1988, the concept of
standard and Gr{\"o}bner bases and algorithms for their
computation in a very wide algebraic context (graded
structures). It is easy to show that if
$R=k<X_1,\ldots{}, X_n>/H$, where $H$ is the ideal
generated by $(X_jX_j-c_{ij}X_iX_j-p_{ij})$ and
$\deg(p_{ij})<\deg(X_iX_j)$ for each $i,j$, then $R$ is
such a graded structure; so his previous techniques can
be applied to it in order to define a concept of
Gr{\"o}bner basis and to produce an algorithm for their
computation, provided that if $J$ is the ideal
generated by $(X_jX_i-c_{ij}X_iX_j:i<j)$, it holds
that: (1) Each ideal in $k<X_1, \ldots{}, X_n>$,
homogeneous for the graduation defined above and
containing J, is finitely generated; (2) For each
homogeneous ideal $(h_1, \ldots{}, h_s)$ in
$k<X_1,\ldots{},X_n>/J$, it is possible to compute a
finite set of syzygies, which together with the trivial
ones, generate the module of syzygies; and (3) For each
homogeneous ideal $(h_1, \ldots{}, h_s)$ and each
homogeneous element $h$ in $k<X_1,\ldots{}, X_n>/J$, it
is possible to decide whether $h$ in
$(h_1,\ldots{},h_s)$, in which case it is possible to
compute a representation of $h$ in terms of
$(h_1,\ldots{},h_s)$. It turns out that the above
conditions hold whenever for no
$i<j<k,c_{ij}=c_{jk}=0$. The author shows how to solve
problems (2) and (3) in case for no
$i<j<k,C_{ij}=c_{jk}=0$.",
acknowledgement = ack-nhfb,
affiliation = "Genova Univ., Italy",
classification = "C4210 (Formal logic)",
keywords = "Gr{\"o}bner bases; Noncommutative algebras; Graded
structures; Ideal; Homogeneous; Set of syzygies;
Decide",
thesaurus = "Algebra; Decidability; Theorem proving",
}
@InProceedings{Murray:1989:EPD,
author = "N. V. Murray and E. Rosenthal",
title = "Employing path dissolution to shorten tableaux
proofs",
crossref = "Gonnet:1989:PAI",
pages = "373--381",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p373-murray/",
abstract = "Path dissolution is an inferencing mechanism that
generalizes the method of analytic tableaux. The main
result presented is that every nontrivial step in any
tableau proof can be speeded up with the application of
dissolution techniques.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
intelligence); C4210 (Formal logic)",
keywords = "algorithms; Analytic tableaux; Formal logic; Graph
theory; Inferencing mechanism; Path dissolution;
Rewrite operations; Tableau proof; Tableaux proofs;
theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic.",
thesaurus = "Graph theory; Inference mechanisms; Rewriting systems;
Theorem proving",
}
@InProceedings{Musser:1989:GP,
author = "D. R. Musser and A. A. Stepanov",
title = "Generic programming",
crossref = "Gianni:1989:SAC",
pages = "13--25",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Generic programming centers around the idea of
abstracting from concrete, efficient algorithms to
obtain generic algorithms that can be combined with
different data representations to produce a wide
variety of useful software. Four kinds of
abstraction-data, algorithmic, structural, and
representational-are discussed, with examples of their
use in building an Ada library of software components.
The main topic discussed is generic algorithms and an
approach to their formal specification and
verification, with illustration in terms of a
partitioning algorithm such as is used in the quicksort
algorithm. It is argued that generically programmed
software component libraries offer important advantages
for achieving software productivity and reliability.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C6110 (Systems analysis and programming); C6120
(File organisation)",
keywords = "Abstracting; Ada library; Algorithmic abstraction;
Data abstraction; Data representations; Formal
specification; Formal verification; Generic algorithms;
Generic programming; Generically programmed software
component libraries; Partitioning algorithm; Quicksort
algorithm; Representational abstraction; Software
productivity; Software reliability; Structural
abstraction",
thesaurus = "Data structures; Programming",
}
@InProceedings{OHearn:1989:NTP,
author = "P. O'Hearn and Z. Stachniak",
title = "Note on theorem proving strategies for resolution
counterparts of nonclassical logics",
crossref = "Gonnet:1989:PAI",
pages = "364--372",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p364-o_hearn/",
abstract = "The paper shows that two of the more powerful speed-up
techniques available for the classical first-order
logic, namely the set of support and the polarity
strategies, can be formulated and applied to resolution
proof systems for nonclassical logics. The authors
review background information on propositional logics
and propositional resolution proof systems. They
introduce the set of support and polarity strategies.
They show that resolution counterparts of most
structural propositional logics admit both strategies
preserving their refutational completeness.",
acknowledgement = ack-nhfb,
affiliation = "Queen's Univ., Kingston, Ont., Canada",
classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
intelligence); C4210 (Formal logic)",
keywords = "algorithms; Deductive systems; First-order logic;
Inference rules; Nonclassical logics; Polarity;
Propositional logics; Propositional resolution proof
systems; Resolution counterparts; Resolution proof
systems; Speed-up techniques; Support; Theorem proving;
theory; Trees",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory.",
thesaurus = "Formal logic; Inference mechanisms; Theorem proving;
Trees [mathematics]",
}
@InProceedings{Okada:1989:SNC,
author = "M. Okada",
title = "Strong normalizability for the combined system of the
typed $\lambda$ calculus and an arbitrary convergent
term rewrite system",
crossref = "Gonnet:1989:PAI",
pages = "357--363",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p357-okada/",
abstract = "The author gives a proof of strong normalizability of
the typed $\lambda$-calculus extended by an arbitrary
convergent term rewriting system, which provides the
affirmative answer to the open problem proposed in
Breazu-Tannen (1988). Klop (1980) showed that a
combined system of the untyped $\lambda$-calculus and
convergent term rewriting system is not Church--Rosser
in general, though both are Church--Rosser. It is
well-known that the typed $\lambda$-calculus is
convergent (Church--Rosser and terminating).
Breazu-Tannen showed that a combined system of the
typed $\lambda$-calculus and an arbitrary
Church--Rosser term rewriting system is again
Church--Rosser. The strong normalization result in this
paper shows that the combined system of the typed
$\lambda$-calculus and an arbitrary convergent term
rewriting system is again convergent. The strong
normalizability proof is easily extended to the case of
the second order (polymorphically) typed $\lambda$
calculus and the case in which $\mu$-reduction rule is
added.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Concordia Univ., Montreal,
Que., Canada",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Church--Rosser; Convergent term rewrite
system; design; Polymorphically; Rewriting system;
Strong normalizability; theory; Typed $\lambda$
calculus; Typed $\lambda$-calculus",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Lambda
calculus and related systems. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Convergence; Rewriting systems; Symbol manipulation",
}
@InProceedings{Ollivier:1989:IRM,
author = "F. Ollivier",
title = "Inversibility of rational mappings and structural
identifiability in automatics",
crossref = "Gonnet:1989:PAI",
pages = "43--54",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p43-ollivier/",
abstract = "The author investigates different methods for testing
whether a rational mapping $f$ from $k^n$ to $k^m$
admits a rational inverse, or whether a polynomial
mapping admits a polynomial one. He gives a new
solution, which seems much more efficient in practice
than previously known ones using `tag' variables and
standard basis, and a majoration for the degree of the
standard basis calculations which is valid for both
methods in the case of a polynomial map which is
birational. He shows that a better bound can be given
for the method, under some assumption on the form of
$f$. The method can also extend to check whether a
given polynomial belongs to the subfield generated by a
finite set of fractions. The author illustrates the
algorithm with an application to structural
identifiability. The implementation has been done in
the IBM computer algebra system Scratchpad II.",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau,
France",
classification = "C1110 (Algebra); C1120 (Analysis); C7310
(Mathematics)",
keywords = "algorithms; Computer algebra system; experimentation;
Fractions; IBM; Inversibility; Polynomial inverse;
Polynomial mapping; Rational inverse; Rational
mappings; Scratchpad II; Structural identifiability;
theory",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Inverse problems; Mathematics computing; Polynomials;
Set theory; Symbol manipulation",
}
@InProceedings{Pan:1989:SCD,
author = "Victor Pan",
title = "On some computations with dense structured matrices",
crossref = "Gonnet:1989:PAI",
pages = "34--42",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p34-pan/",
abstract = "The author reduces several computations with Hilbert
and Vandermonde type matrices to matrix computations of
the Hankel--Toeplitz type (and vice versa). This
unifies various known algorithms for computations with
dense structured matrices and allows the extension of
any progress in computations with matrices of one class
to the computations with other classes. This allows the
computation of the inverses and the determinants of
$n*n$ matrices of Vandermonde and Hilbert types for the
cost of $O(n \log^2n)$ arithmetic operations.
Previously, such results were only known for the more
narrow class of Vandermonde and generalized Hilbert
matrices.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Univ. of New York, Bronx, NY,
USA",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Computational complexity; Dense structured
matrices; Determinants; Hankel--Toeplitz type; Hilbert;
Inverses; theory; Vandermonde",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Matrix inversion.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Inverse
problems; Mathematics computing; Matrix algebra",
}
@InProceedings{Porter:1989:DRA,
author = "S. C. Porter",
title = "Dense representation of affine coordinate rings of
curves with one point at infinity",
crossref = "Gonnet:1989:PAI",
pages = "287--297",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p287-porter/",
abstract = "Traditional methods of representing rational functions
on curves are unwieldy and unsuitable for solution of
many problems. This paper describes a simple and
elegant representation of elements of the affine
coordinate ring of an algebraic curve and describes
efficient, easy to implement algorithms to perform
addition, subtraction, multiplication and polynomial
evaluation. This data structure overcomes many of the
disadvantages of more unwieldy traditional
representations. Elements are represented as vectors of
elements of the ground field in a manner similar to the
representation of polynomials of one variable as an
array of coefficients. This data structure is a
fundamental ingredient in the author's decoding method
for algebraic geometry codes. The rational function
approximation techniques used for decoding could not
have been described with multivariate polynomials or
truncated infinite series.",
acknowledgement = ack-nhfb,
affiliation = "Baise State Univ., ID, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Affine coordinate rings; Algebraic curve; Algebraic
geometry codes; algorithms; Curves; Data structure;
Decoding; Polynomial; Rational function approximation;
Rational functions; theory; Vectors",
subject = "{\bf E.1} Data, DATA STRUCTURES. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation. {\bf E.4}
Data, CODING AND INFORMATION THEORY.",
thesaurus = "Computational geometry; Data structures; Functions;
Mathematics computing; Polynomials; Programming theory;
Symbol manipulation; Vectors",
xxpages = "288--297",
}
@InProceedings{Purtilo:1989:MEO,
author = "J. M. Purtilo",
title = "Minion: an environment to organize mathematical
problem solving",
crossref = "Gonnet:1989:PAI",
pages = "147--154",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p147-purtilo/",
abstract = "Maryland University are constructing a management
assistant that works in conjunction with existing
symbolic computation systems. Called Minion, it allows
users to express simple plans for solving large
problems in the interactive environment, and then
guides the user's interaction according to that plan.
Key features are that plans are easy to construct; the
assistant helps a user visualize progress towards
solving the global problem; and individual steps within
a plan can be executed by arbitrary software tools,
whether symbolic-, numeric- or logic-based in their
implementation. The author briefly portrays the
organizational problem that must be treated, and
motivates the need for structure management tools in
mathematical problem solving environments. He details
features of the Minion prototype. After a brief update
on the status of the existing Polylith system, he
describes how Minion is implemented using an
interconnection resource.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
classification = "C6130 (Data handling techniques); C6180 (User
interfaces); C7310 (Mathematics)",
keywords = "algorithms; Interactive environment; Interconnection
resource; Management assistant; Maryland University;
Mathematical problem solving; Minion; Polylith;
Structure management tools; Symbolic computation
systems; theory; User interfaces",
subject = "{\bf I.3.1} Computing Methodologies, COMPUTER
GRAPHICS, Hardware Architecture. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Interactive systems; Mathematics computing; Symbol
manipulation; User interfaces",
}
@InProceedings{Rabinowitz:1989:CSS,
author = "S. Rabinowitz",
title = "On the computer solution of symmetric homogeneous
triangle inequalities",
crossref = "Gonnet:1989:PAI",
pages = "272--286",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p272-rabinowitz/",
abstract = "The article presents an effective systematic algorithm
that one can use to prove inequalities. A computer
algorithm that can prove many inequalities is
presented.",
acknowledgement = ack-nhfb,
affiliation = "Alliant Comput. Syst. Corp., Littleton, MA, USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Computer algorithm; Symmetric homogeneous
triangle inequalities; theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Equations; Mathematics computing; Programming theory;
Symbol manipulation",
}
@InProceedings{Ravenscroft:1989:SSG,
author = "R. A. {Ravenscroft, Jr.} and E. A. Lamagna",
title = "Symbolic summation with generating functions",
crossref = "Gonnet:1989:PAI",
pages = "228--233",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The generating function technique presented is an
important addition to the area of summation algorithms.
With it, many summations that cannot be evaluated by
existing algorithms can be solved. Among these are
hybrid sums and sums involving special classes of
functions including binomial coefficients, Fibonacci
numbers, and harmonic numbers. However, the method is
not viable for hand calculation since the algebraic
manipulation gets very complex. Fortunately, the steps
used in the procedure are consistent regardless of the
particular generating functions that are involved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Brown Univ., Providence, RI,
USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Generating functions; Hybrid sums; Summation
algorithms; Symbolic summation",
thesaurus = "Computation theory; Functions; Series [mathematics];
Symbol manipulation",
}
@InProceedings{Roch:1989:CAM,
author = "J.-L. Roch and P. Senechaud and F. Siebert-Roch and G.
Villard",
title = "Computer algebra on {MIMD} machine",
crossref = "Gianni:1989:SAC",
pages = "423--439",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "PAC is a computer algebra system, based on MIMD type
parallelism. It uses parallelism as a tool for
processing problems which are too complex for a
sequential treatment. Basic fundamentals of the system
are firstly discussed. Then, different problems are
studied, particularly the implementation of
infinite-precision arithmetic, the solution of linear
systems and of Diophantine equations, the
parallelization of Buchberger's algorithm for
Gr{\"o}bner bases. A prototype of PAC is implemented on
the Floating Point System hypercube Tesseract 20 (16
nodes), and different timing results obtained on this
machine are given.",
acknowledgement = ack-nhfb,
affiliation = "TIM3, INPG, Grenoble, France",
classification = "C7310 (Mathematics)",
keywords = "MIMD machine; PAC; Computer algebra system;
Infinite-precision arithmetic; Solution of linear
systems; Diophantine equations; Parallelization;
Gr{\"o}bner bases; Floating Point System hypercube
Tesseract 20; Timing results",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Rolletschek:1989:SDC,
author = "H. Rolletschek",
title = "Shortest division chains in imaginary quadratic number
fields",
crossref = "Gianni:1989:SAC",
pages = "231--243",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $O_d$ be the set of algebraic integers in an
imaginary quadratic number field $Q(\sqrt{d})$, $d<0$,
where $d$ is the discriminant of $O_d$. Consider the
Euclidean Algorithm (EA), applied to algebraic integers
$\xi$, $\eta$ in $O_d$. It consists in computing a
sequence of remainders
$\rho_0=\xi,\rho_1=\eta,\rho_2,\ldots{},\rho_{n+1}=0$,
where $\rho_{i+1}=\rho_{i-1}-\gamma_i\rho_i$ for
algebraic integers $\gamma _i \in K, i=1, \ldots{}, n$.
It is shown that except for $d=-11$ the number of
divisions to be carried out is always minimized by
choosing each $\gamma_i$ such that
$N(\rho_{i-1}-\gamma_i\rho_i)$, the norm of
$\rho_{i-1}-\gamma_i\rho_i$, is minimal. This result
has been proven previously in special cases. It also
applies to those imaginary quadratic number rings which
are not Euclidean; in this case the division chains may
be infinite. For $d=-7,-8$ the methods applied so far
must be modified somewhat, and for $d=-11$ a
counterexample is provided and a theorem which
partially answers the question, how shortest division
chains can be obtained.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kent State Univ., OH, USA",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Algebraic integers; Discriminant; Divisions; EA;
Euclidean Algorithm; Imaginary quadratic number fields;
Norm; Remainders; Set; Shortest division chains",
thesaurus = "Number theory",
}
@InProceedings{Saunders:1989:PIC,
author = "B. D. Saunders and H. R. Lee and S. K. Abdali",
title = "A parallel implementation of the cylindrical algebraic
decomposition algorithm",
crossref = "Gonnet:1989:PAI",
pages = "298--307",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p298-saunders/",
abstract = "The authors describe a parallelization scheme for
Collins's cylindrical algebraic decomposition algorithm
for quantifier elimination in the theory of real closed
fields. They discuss a parallel implementation of the
computer algebra system SAC2 in which a complete
sequential implementation of Collins's algorithm
already exists. They report some initial results on the
speedup obtained, drawing on a suite of examples
previously given by Arnon.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Delaware Univ.,
Newark, DE, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Cylindrical
algebraic decomposition algorithm; Parallel
implementation; Parallelization; Polynomials;
Quantifier elimination; Real closed fields; SAC2;
theory",
subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Mathematics computing; Parallel algorithms;
Polynomials; Programming theory; Symbol manipulation",
}
@InProceedings{Schwarz:1989:FAL,
author = "F. Schwarz",
title = "A factorization algorithm for linear ordinary
differential equations",
crossref = "Gonnet:1989:PAI",
pages = "17--25",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p17-schwarz/",
abstract = "The reducibility and factorization of linear
homogeneous differential equations are of great
theoretical and practical importance in mathematics.
Although it has been known for a long time that
factorization is in principle a decision procedure, its
use in an automatic differential equation solver
requires a more detailed analysis of the various steps
involved. Especially important are certain auxiliary
equations, the so-called associated equations. An upper
bound for the degree of its coefficients is derived.
Another important ingredient is the computation of
optimal estimates for the size of polynomial and
rational solutions of certain differential equations
with rotational coefficients. Applying these results,
the design of the factorization algorithm LODEF and its
implementation in the Scratchpad II Computer Algebra
System is described.",
acknowledgement = ack-nhfb,
affiliation = "GMD, Inst. F1, St. Augustin, West Germany",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "algorithms; Associated equations; Automatic
differential equation solver; Factorization algorithm;
Linear ordinary differential equations; LODEF; Optimal
estimates; Polynomial solutions; Rational solutions;
Rotational coefficients; Scratchpad II Computer Algebra
System; theory; Upper bound",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods). {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
thesaurus = "Linear differential equations; Mathematics computing;
Polynomials; Symbol manipulation",
}
@InProceedings{Sergeraert:1989:NRN,
author = "F. Sergeraert",
title = "From a noncomputability result to new interesting
definitions and computability results",
crossref = "Gianni:1989:SAC",
pages = "26--32",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Examines the strange situation encountered in
algebraic topology: on one hand no general algorithm is
able to decide whether some topological space is simply
connected; this is an easy consequence of the
undecidability of the word problem. On the other hand
most of the important results in algebraic topology
assume that the spaces under consideration are simply
connected. So that one can ask for algorithms that use
some method or other, and always compute something, in
such a way that if the space given is simply connected,
then the result obtained is the good one. The problem
is to explain what is something in general. The paper
explains that a solution can be found for the computing
problems of the homotopy groups. Then something is a
K-theory group. It obtains in this way a new
understanding of the algebraic K-theory groups and
positive results about their computability.",
acknowledgement = ack-nhfb,
affiliation = "Inst. Fourier, St. Martin d'Heres, France",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "Algebraic K-theory groups; Algebraic topology;
Computability; Homotopy groups; Simply connected;
Topological space; Undecidability; Word problem",
thesaurus = "Group theory; Topology",
}
@InProceedings{Shackell:1989:AEO,
author = "J. Shackell",
title = "Asymptotic estimation of oscillating functions using
an interval calculus",
crossref = "Gianni:1989:SAC",
pages = "481--489",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author considers the problem of estimating the
asymptotic growth of functions defined by expressions
involving exponentials, logarithms, algebraic
operations and also sine functions. Modulo the
assumption that zero-equivalence can be decided on the
set of constant terms, an algorithm exists for the case
when there are no trigonometric functions in the
expression.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Math., Kent Univ., Canterbury, UK",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic operations; Asymptotic estimation;
Asymptotic growth; Exponentials; Interval calculus;
Logarithms; Oscillating functions; Sine functions;
Zero-equivalence",
thesaurus = "Approximation theory; Estimation theory; Symbol
manipulation",
}
@InProceedings{Shackell:1989:DAF,
author = "J. Shackell",
title = "A differential-equations approach to functional
equivalence",
crossref = "Gonnet:1989:PAI",
pages = "7--10",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "To seek algebraic dependencies between functions is to
ask whether there exists a polynomial in them which is
functionally equivalent to zero. The methods outlined
work directly with the given expression, which is
regarded as a polynomial in a top-level basic function
with coefficients in a function field containing the
other basic functions. The top-level function is
defined by a differential equation over the coefficient
field. The techniques are entirely elementary and
involve differentiation, substitution and calculation
of GCDs. The methods decide zero-equivalence in fields
built using arithmetic operations and functional
composition with functions defined as solutions of
algebraic differential equations. The paper treats only
first-order, first-degree equations.",
acknowledgement = ack-nhfb,
affiliation = "Kent Univ., Canterbury, UK",
classification = "C1110 (Algebra); C1120 (Analysis); C4130
(Interpolation and function approximation); C4170
(Differential equations)",
keywords = "Algebraic dependencies; Differential-equations;
Differentiation; Functional equivalence; Functions;
Polynomial; Substitution; Zero-equivalence",
thesaurus = "Differential equations; Functions; Polynomials",
}
@InProceedings{Shackle:1989:DAF,
author = "J. Shackle",
title = "A differential-equations approach to functional
equivalence",
crossref = "Gonnet:1989:PAI",
pages = "7--10",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p7-shackle/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
}
@InProceedings{Sharma:1989:SDA,
author = "N. Sharma and P. S. Wang",
title = "Symbolic derivation and automatic generation of
parallel routines for finite element analysis",
crossref = "Gianni:1989:SAC",
pages = "33--56",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Describes some initial results of a joint research
project involving engineering and computer science.
Based on earlier work on the automatic derivation and
generation of numeric code for finite element analysis,
the authors are conducting research into the mapping of
finite element computations on parallel architectures.
Software is being developed to automatically derive and
generate parallel code that can be used with existing
sequential code to improve speed. They are developing
techniques to derive parallel procedures, based on
high-level user input, to exploit parallel computer
architectures. An experimental software system called
P-FINGER is under development to derive key finite
element routines for the Warp systolic array computer.
A separate parallel code generation package is used to
render the symbolically derived parallel procedures
into code for the Warp parallel computer.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA",
classification = "C4100 (Numerical analysis); C7400 (Engineering)",
keywords = "Automatic derivation; Automatic generation; Computer
science; Engineering; Experimental software system;
Finite element analysis; Finite element computations;
Finite element routines; P-FINGER; Parallel
architectures; Parallel code; Parallel code generation
package; Parallel computer architectures; Parallel
procedures; Parallel routines; Symbolic derivation;
Symbolically derived parallel procedures; Warp parallel
computer; Warp systolic array computer",
thesaurus = "Engineering computing; Finite element analysis;
Parallel processing",
}
@InProceedings{Siebert-Roch:1989:PAH,
author = "F. Siebert-Roch",
title = "Parallel algorithms for {Hermite} normal form of an
integer matrix",
crossref = "Gonnet:1989:PAI",
pages = "317--321",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p317-siebert-roch/",
abstract = "The main problem in integral matrices
triangularization is the `intermediate coefficients
swell'. This aspect limits the dimension of treated
matrices. The lliopoulos algorithm computes the Hermite
normal form of an integer matrix controlling the
coefficients growth by means of the determinant. The
author presents two parallelizations of this algorithm
and their implementations on a MIMD machine, with 16
processors.",
acknowledgement = ack-nhfb,
affiliation = "Laboratoire TIM3-IMAG, Grenoble, France",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Determinant; Hermite normal form; Integer
matrix; Integral matrices triangularization;
Intermediate coefficients swell; Lliopoulos algorithm;
MIMD; Parallel algorithms; Parallelizations; theory",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Mathematics
computing; Matrix algebra; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Singer:1989:LFI,
author = "M. F. Singer",
title = "{Liouvillian} first integrals of differential
equations",
crossref = "Gianni:1989:SAC",
pages = "57--63",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The system of differential equations
$x=P(x,y),y=Q(x,y)$ has a Liouvillian first integral if
and only if the differential form $Q(x,y)dx-P(x,y)dy$
has an integrating factor of the form
$R(x,y)=exp(\int{}U(x,y)dx+V(x,y)dy)$ where $U$ and $V$
are rational functions and $U_y=V_x$. This theorem
shows that if a Liouvillian first integral exists, then
there is a Liouvillian first integral of a very special
form, but it does not show how to find one. Before
turning to this latter question, the author discusses
how this theorem is placed in the setting of
differential algebra and the tools used to prove it.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
classification = "C1120 (Analysis); C4170 (Differential equations);
C4180 (Integral equations)",
keywords = "Differential algebra; Differential equations;
Differential form; Integrating factor; Liouvillian
first integrals; Rational functions",
thesaurus = "Differential equations; Integral equations",
}
@InProceedings{Smedley:1989:NMA,
author = "T. J. Smedley",
title = "A new modular algorithm for computation of algebraic
number polynomial gcds",
crossref = "Gonnet:1989:PAI",
pages = "91--94",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p91-smedley/",
abstract = "Euclid's algorithm for finding the greatest common
divisor of two polynominals when applied to polynomials
over an algebraic extension field, tends to be very
slow. In the case of polynomials with integer
coefficients, one approach to solving this problem is
to use a modular algorithm. This approach has been
extended to algebraic number fields by Langemyr and
McCallum (1987). Another approach for algebraic numbers
is to use a heuristic method (Geddes, Gonnett and
Smedley, 1988). The paper shows that this heuristic
method can be made into an algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci. Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "Algebraic number polynomial gcds; algorithms; Euclid;
Heuristic method; Integer coefficients; Modular
algorithm; Symbol manipulation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Computation theory; Polynomials; Symbol manipulation",
}
@InProceedings{Stifter:1989:GRM,
author = "S. Stifter",
title = "A generalization of the {Roider} method to solve the
robot collision problem in {3D}",
crossref = "Gianni:1989:SAC",
pages = "332--343",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Roider method is a method to test by means of
computational geometry whether two convex, compact
objects, say $A$ and $B$, in two dimensions intersect.
Roughly, this iterative method constructs a witness to
disjointness (a wedge formed by a pair of
touching-lines from some $P(\in A)$ to $B$ that
separates $A$ and $B$) if the objects are disjoint. If
the objects intersect then a witness to intersection,
i.e. a point in common to both objects, is constructed.
The author generalizes the Roider method in two
aspects: Firstly, he generalizes the algorithm such
that it is also applicable to convex, compact objects
in three dimensions. Secondly, he generalizes the
method such that it can be used to test whether a
non-moving object A collides with a moving object
$B$.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Keples
Univ., Linz, Austria",
classification = "C3120C (Spatial variables); C4190 (Other numerical
methods)",
keywords = "3D; Computational geometry; Disjointness; Iterative
method; Robot collision problem; Roider method",
thesaurus = "Computational geometry; Position control",
}
@InProceedings{Teitelbaum:1989:CCR,
author = "J. Teitelbaum",
title = "On the computational complexity of the resolution of
plane curve singularities",
crossref = "Gianni:1989:SAC",
pages = "285--292",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes an algorithm which computes the
resolution of a plane curve singularity-that is, a
singularity at the origin defined by a formal power
series $F$ in two variables $x$ and $y$ over a field
$k$. The algorithm requires that $k$ be of
characteristic zero (or at least of `large'
characteristic) but this hypothesis can certainly be
removed at the expense of some complications. The
algorithm obtains explicit equations for the blowing-up
of the singularity, and therefore yields all of the
interesting invariants of the singularity, such as its
conductor and its Milnor number. The author also
provides upper bounds for the number of $k$-operations
needed for the operation of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Michigan Univ., Ann Arbor, MI, USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Computational complexity; Formal power series;
Resolution of plane curve singularities",
thesaurus = "Computational complexity; Series [mathematics]",
}
@InProceedings{Todd:1989:SAP,
author = "P. H. Todd and G. W. Cherry",
title = "Symbolic analysis of planar drawings",
crossref = "Gianni:1989:SAC",
pages = "344--355",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A method is described for performing a symbolic
analysis of planar drawings. The method takes input in
the form of a dimensioned (i.e. labeled) drawing and
determines whether the coordinates of all of the points
in the drawing can be uniquely written in terms of the
specified labels. If it is possible to determine the
coordinates of the points (i.e. the drawing is
consistently dimensioned), then they are calculated.
Otherwise the algorithm returns a flag specifying
whether the drawing is underdimensioned or
overdimensioned. The method employs standard
constructions from geometry such as the construction of
a line from two distinct points or the construction of
a line from a given line, a point and an angle. In
order to determine whether some sequence of given
constructions can be used to calculate the coordinates
of each point the authors construct and analyse an
undirected graph called the dimension graph of the
drawing. If such a sequence exists, then the
calculations are performed by calling symbolic routines
which correspond to the various constructions. An
implementation is described and examples are given.",
acknowledgement = ack-nhfb,
affiliation = "Tektronix Labs., Beaverton, OR, USA",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C6130 (Data handling techniques)",
keywords = "Coordinates; Dimension graph; Geometry; Labeled
drawing; Planar drawings; Symbolic analysis; Symbolic
routines; Undirected graph",
thesaurus = "Computational geometry; Graph theory; Symbol
manipulation",
}
@InProceedings{Traverso:1989:EGB,
author = "C. Traverso and L. Donati",
title = "Experimenting the {Gr{\"o}bner} basis algorithm with
the {A1PI} system",
crossref = "Gonnet:1989:PAI",
pages = "192--198",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p192-traverso/",
abstract = "The AlPI (Algoritmi Pisa) system is a small polynomial
algebra system. It was designed and implemented by the
first author in MuLISP-86. It is now (almost) ported by
the second author in lucid COMMON-LISP, in such a way
that only a few macros are needed to transport it in
any COMMON-LISP dialect (MuLISP included). Its main aim
is the experimentation on the Buchberger Gr{\"o}bner
basis completion algorithm with its different versions,
and on the Mora tangent cone algorithm. It is driven by
a menu, and has a series of facilities to manipulate
lists of polynomials. After a description of the system
and of the versions of the algorithms presently
implemented, the authors give a series of experimental
results (for the MuLISP version). These results, and
results of the same kind to obtain with further
experimentation, can give suggestions on the versions
of the algorithm to choose as default for other
implementations of the algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dipartmento di Matematica, Pisa Univ., Italy",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "algorithms; experimentation; theory; User interfaces;
Gr{\"o}bner basis algorithm; AlPI system; Algoritmi
Pisa; Polynomial algebra system; MuLISP-86; Macros;
Buchberger Gr{\"o}bner basis; Completion algorithm;
Mora tangent cone algorithm",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Mathematics computing; Polynomials; Symbol
manipulation",
xxtitle = "Experimenting the {Gr{\"o}bner} basis algorithm with
the {AlPI} system",
}
@InProceedings{Traverso:1989:GTA,
author = "C. Traverso",
title = "{Gr{\"o}bner} trace algorithms",
crossref = "Gianni:1989:SAC",
pages = "125--138",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Practical computing experience on Gr{\"o}bner bases
has shown that computing with rational numbers or
integers, very frequently one has very large
coefficients in the intermediate computations, and that
often the final result is of more moderate size.
Sometimes it happens that the size of these numbers,
which have to be kept up to the end, is such that
memory overflow or excessive paging occurs. The
author's approach gives a series of algorithms, based
on the concept of Gr{\"o}bner trace; these algorithms
are mainly probabilistic (Monte Carlo); they include a
series of tests (still probabilistic) to check the
probable correctness; he also describes deterministic
tests that unfortunately are sometimes as costly as a
direct Gr{\"o}bner basis computation, but sometimes
instead very rapid.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Pisa Univ., Italy",
classification = "C1140G (Monte Carlo methods); C4210 (Formal logic)",
keywords = "Gr{\"o}bner trace algorithms; Gr{\"o}bner bases;
Rational numbers; Integers; Probabilistic; Monte Carlo;
Probable correctness; Deterministic tests",
thesaurus = "Monte Carlo methods; Rewriting systems",
}
@InProceedings{Valibouze:1989:RSF,
author = "A. Valibouze",
title = "Resolvents and symmetric functions",
crossref = "Gonnet:1989:PAI",
pages = "390--399",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p390-valibouze/",
abstract = "A model of transformations of polynomial equations
(direct image model) is studied. The model expresses
some minimal polynomials and some resolvents relative
to the Galois group of a polynomial in order to use a
general algorithm of resolution. This algorithm can be
effectively computed in MACSYMA with the extension SYM
that manipulates symmetric polynomials. Examples
obtained by specializing the general algorithm for the
Galois resolvent are given.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Pierre et Marie Curie, Paris, France",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C7310 (Mathematics)",
keywords = "algorithms; Direct image model; Galois group; MACSYMA;
Minimal polynomials; Polynomial equations; Resolution;
Resolvents; SYM; Symmetric polynomials; theory;
Transformations",
language = "French",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Functions; Mathematics computing; Polynomials; Symbol
manipulation",
}
@InProceedings{vanHulzen:1989:COP,
author = "J. A. {van Hulzen} and B. J. A. Hulshof and B. L.
Gates and M. C. {van Heerwaarden}",
title = "A code optimization package for {REDUCE}",
crossref = "Gonnet:1989:PAI",
pages = "163--170",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p163-van_hulzen/",
abstract = "A survey of the strategy behind and the facilities of
a code optimization package for REDUCE are given. The
authors avoid a detailed discussion of the different
algorithms and concentrate on the user aspects of the
package. Examples of straightforward and more advanced
usage are shown.",
acknowledgement = ack-nhfb,
affiliation = "Twente Univ., Dept. of Comput. Sci., Enschede,
Netherlands",
classification = "C6130 (Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310
(Mathematics)",
keywords = "algorithms; Code optimization package; Compilers;
REDUCE; theory; User aspects",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.2.2} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Automatic Programming. {\bf D.3.4}
Software, PROGRAMMING LANGUAGES, Processors,
Compilers.",
thesaurus = "Mathematics computing; Optimisation; Program
compilers; Symbol manipulation",
}
@InProceedings{Vinette:1989:USC,
author = "F. Vinette and J. Cizek",
title = "The use of symbolic computation in solving some
nonrelativistic quantum mechanical problems",
crossref = "Gianni:1989:SAC",
pages = "85--95",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Stresses the importance of symbolic computation
languages as a new research tool in applied
mathematics. The treatment of some non-relativistic
quantum mechanical problems are presented as
illustrations of the use of the symbolic computation
language MAPLE developed at the University of Waterloo.
Emphasis is given on the possibility to manipulate
expressions symbolically, to perform rapidly tedious
operations as well as to work in rational arithmetic.
Another important feature will consist in the interface
of MAPLE and FORTRAN.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Waterloo Univ., Ont., Canada",
classification = "A0365D (Functional analytical methods); C7320
(Physics and Chemistry)",
keywords = "Applied mathematics; Expression manipulation; FORTRAN;
Interface; MAPLE; Nonrelativistic quantum mechanical
problems; Symbolic computation languages; Symbolic
manipulation",
thesaurus = "High level languages; Physics computing; Quantum
theory; Symbol manipulation",
}
@InProceedings{Watt:1989:FPM,
author = "S. M. Watt",
title = "A fixed point method for power series computation",
crossref = "Gianni:1989:SAC",
pages = "206--217",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a novel technique for manipulating structures
which represent infinite power series. The technique
described allows a power series to be defined in a very
natural but computationally inefficient way and
transforms it to an equivalent, efficient form. This is
achieved by using a fixed point operator on the delayed
part to remove redundant calculations. The paper
describes this fixed point method and the class of
problems to which it is applicable. It has been used in
Scratchpad II to improve the performance of a number of
operations on infinite series, including division,
reversion, special functions and the solution of linear
and non-linear ordinary differential equations. A few
examples are given of the method and of the speed up
obtained. To illustrate, the computation of the first
$n$ terms of $\exp(u)$ for a dense, infinite series $u$
is reduced from $O(n^4)$ to $O(n^2)$ coefficient
operations, the same as required by the standard
on-line algorithms.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Delayed part; Fixed point method; Fixed point
operator; Infinite power series; Power series
computation; Redundant calculations; Scratchpad II",
thesaurus = "Computational complexity; Mathematics computing",
}
@InProceedings{Weerawarana:1989:GPC,
author = "S. Weerawarana and P. S. Wang",
title = "{GENCRAY}: a portable code generator for {Cray}
{Fortran}",
crossref = "Gonnet:1989:PAI",
pages = "186--191",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p186-weerawarana/",
abstract = "The authors have applied these concepts to finite
element analysis. Their research resulted in the
software systems FINGER and GENTRAN, both written in
Franz LISP. FINGER, derives element strain-displacement
matrices and stiffness matrices based on user-supplied
parameters. The derived codes involve declarations,
expressions, arrays, functions and subroutines. These
quantities are represented by LISP internal data
structures that must be generated into numerical code
by a code translation process. This is the function of
GENTRAN which can translate MACSYMA representations
into f77, ratfor, or C. GENCRAY is a code generation
package similar to GENTRAN but different in many
respects. The output of GENCRAY is f77 or Cray
Fortran-77 (CFT77) code. CFT77 is a superset of f77 and
is the standard Fortran used on Cray supercomputers.
The authors present the design of GENCRAY, the steps of
code translation, its implementation, features for
generating vectorizable and parallel code for the Cray,
and how a user can customize GENCRAY to suite different
purposes.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA",
classification = "C6115 (Programming support); C6130 (Data handling
techniques); C6150C (Compilers, interpreters and other
processors); C7310 (Mathematics)",
keywords = "algorithms; Code generation package; Code translation;
Cray Fortran; Data structures; FINGER; Finite element
analysis; GENCRAY; GENTRAN; Portable code generator;
Supercomputers; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Finite
element methods. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Code generation. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Automatic programming; Finite element analysis;
Mathematics computing; Parallel programming; Program
interpreters; Software portability; Symbol
manipulation",
}
@InProceedings{Weispfenning:1989:EDP,
author = "V. Weispfenning",
title = "Efficient decision procedures for locally finite
theories. {II}",
crossref = "Gianni:1989:SAC",
pages = "262--273",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "For pt. I, see AECC-3, Grenoble, Springer LNCS, vol.
229.",
abstract = "Let $T$ be a finitely axiomatized, universal theory in
a finite, first-order language $L$, and suppose $T$ has
a model companion $T'$ with only finitely many
countable models. $T$ is uniformly locally finite, say
with generating function $g: N$ to $N$. The author
shows the existence of a further function $am: N$ to
$N$ measuring the extent to which $\mbox{Mod(T)}$ fails
to satisfy the amalgamation property. The main result
is as follows: There exist explicitly described uniform
decision and quantifier elimination procedures for
$T'$, whose asymptotic complexity can be bounded from
above by an elementary recursive function in $g$ and
am, without any further reference to $T$ or $T'$. A
corresponding result (with $g$ replaced by $d$) holds,
if $T$ is not finitely axiomatized, provided there is a
function $d: N$ to $N$ bounding the size of suitable
descriptions of $n$-generated $T$-models.",
acknowledgement = ack-nhfb,
affiliation = "Lehrstuhl fur Math., Passau Univ., West Germany",
classification = "C1140E (Game theory); C4210 (Formal logic)",
keywords = "Asymptotic complexity; Decision procedures;
First-order language; Generating function; Locally
finite theories; Quantifier elimination procedures",
thesaurus = "Decision theory; Formal logic",
}
@InProceedings{White:1989:CF,
author = "N. L. White and T. McMillan",
title = "{Cayley} factorization",
crossref = "Gianni:1989:SAC",
pages = "521--533",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An important problem in computer-aided geometric
reasoning is to automatically find geometric
interpretations for algebraic expressions. For
projective geometry this question can be reduced to the
Cayley factorization problem. A Cayley factorization of
a homogeneous bracket polynomial $P$ is a Cayley
algebra expression (using only the join and meet
operations) which evaluates to P. The authors give an
introduction to both Cayley algebra and bracket
algebra. The main result of the paper is an algorithm
which solves the Cayley factorization problem in the
important special case that $P$ is multilinear.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Florida Univ., Gainesville, FL, USA",
classification = "C4210 (Formal logic); C7310 (Mathematics)",
keywords = "Algebraic expressions; Bracket algebra; Cayley
factorization; Computer-aided geometric reasoning;
Homogeneous bracket polynomial; Projective geometry",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Winkler:1989:GDA,
author = "F. Winkler",
title = "A geometrical decision algorithm based on the
{Gr{\"o}bner} bases algorithm",
crossref = "Gianni:1989:SAC",
pages = "356--363",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Gr{\"o}bner bases have been used in various ways for
dealing with the problem of geometry theorem proving as
posed by Wu (1978). Kutzler and Stifter (1986) have
proposed a procedure centered around the computation of
a basis for the module of syzygies of the geometrical
hypotheses. The author elaborates this approach and
extends it to a complete decision procedure. Also, in
geometry theorem proving the problem of constructing
subsidiary (or degeneracy) conditions arises. Such
subsidiary conditions usually are not uniquely
determined and obviously one wants to keep them as
simple as possible. This problem, however, has not
received enough attention in the geometry theorem
proving literature. The author's algorithm is able to
construct the simplest subsidiary conditions with
respect to certain predefined criteria, such as lowest
degree or dependence on a given set of variables.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C4190 (Other numerical methods); C4210 (Formal
logic)",
keywords = "Geometrical decision algorithm; Gr{\"o}bner bases
algorithm; Geometry theorem proving; Complete decision
procedure; Subsidiary conditions",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Winkler:1989:KPB,
author = "F. Winkler",
title = "{Knuth--Bendix} procedure and {Buchberger} algorithm
--- a synthesis",
crossref = "Gonnet:1989:PAI",
pages = "55--67",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p55-winkler/",
abstract = "The Knuth--Bendix procedure for the completion of a
rewrite rule system and the Buchberger algorithm for
computing a Gr{\"o}bner basis of a polynomial ideal are
very similar in two respects: they both start with an
arbitrary specification of an algebraic structure
(axioms for an equational theory and a basis for a
polynomial ideal, respectively) which is transformed to
a very special specification of this algebraic
structure (a complete rewrite rule system and a
Gr{\"o}bner basis of the polynomial ideal,
respectively). This special specification allows many
problems concerning the given algebraic structure to be
decided. Moreover, both algorithms achieve their goals
by employing the same basic concepts: formation of
critical pairs and completion. Although the two methods
are obviously related, the exact nature of this
relation remains to be clarified. The author shows how
the Knuth--Bendix procedure and the Buchberger
algorithm can be seen as special cases of a more
general completion procedure.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4210 (Formal logic); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; theory; Decidability; Programming theory;
Knuth--Bendix procedure; Rewrite rule system;
Buchberger algorithm; Gr{\"o}bner basis; Polynomial;
Algebraic structure; Equational theory",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Decidability; Polynomials; Programming theory;
Rewriting systems; Set theory",
}
@InProceedings{Wissmann:1989:ART,
author = "D. Wissmann",
title = "Applying rewriting techniques to groups with
power-commutation-presentations",
crossref = "Gianni:1989:SAC",
pages = "378--389",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author applies rewriting techniques to certain
types of string-rewriting systems related to
power-commutation-presentations for finitely generated
(f.g.) abelian groups, f.g. nilpotent groups, f.g.
supersolvable groups and f.g. polycyclic groups. The
author develops a modified version of the Knuth--Bendix
completion procedure which transforms such a
string-rewriting system into an equivalent canonical
system of the same type. This completion procedure
terminates on all admissible inputs and works with a
fixed reduction ordering on strings. Since canonical
string-rewriting systems have decidable word problem
this procedure shows that the systems above have
uniformly decidable word problem. In addition, this
result yields a new purely combinatorial proof for the
well-known uniform decidability of the work problem for
the corresponding groups.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Kaiserslautern Univ., West
Germany",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic)",
keywords = "Abelian groups; Combinatorial proof; Decidable word
problem; Knuth--Bendix completion; Nilpotent groups;
Polycyclic groups; Power-commutation-presentations;
Rewriting techniques; String-rewriting systems;
Supersolvable groups; Uniform decidability",
thesaurus = "Decidability; Group theory; Rewriting systems",
}
@InProceedings{Aberer:1990:NFF,
author = "K. Aberer",
title = "Normal forms in function fields",
crossref = "Watanabe:1990:IPI",
pages = "1--7",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p1-aberer/",
abstract = "Considers function fields of functions of one variable
augmented by the binary operation of composition of
functions. It is shown that the straightforward
axiomatization of this concept allows the introduction
of a normal form for expressions denoting elements in
such fields. While the description of this normal form
seems relatively intuitive, it is surprisingly
difficult to prove this fact. The author presents an
algorithm for the normalization of expressions,
formulated in the symbolic computer algebra language
Mathematica. This allows us to effectively decide
compositional identities in such fields. Examples are
given.",
acknowledgement = ack-nhfb,
affiliation = "ETH, Zurich, Switzerland",
classification = "C1100 (Mathematical techniques); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "algorithms; Axiomatization; Binary operation;
Compositional identities; Function fields; languages;
Mathematica; Symbolic computer algebra language",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Functions; Symbol manipulation",
}
@InProceedings{Adamchik:1990:ACI,
author = "V. S. Adamchik and O. I. Marichev",
title = "The algorithm for calculating integrals of
hypergeometric type functions and its realization in
{REDUCE} system",
crossref = "Watanabe:1990:IPI",
pages = "212--224",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p212-adamchik/",
abstract = "The most effective and the simplest algorithm for
analytical integration was made by O. I. Marichev
(1983). This algorithm allows one to calculate definite
and indefinite integrals of the products of elementary
and special functions of hypergeometric type. It
embraces about 70 per cent of integrals which are
included in the world reference-literature. It allows
one to calculate many other integrals too. The article
contains a short description of this algorithm and its
realization in the REDUCE system during the process of
creation of the INTEGRATOR system.",
acknowledgement = ack-nhfb,
affiliation = "Byelorussian Univ., Minsk, Byelorussian SSR, USSR",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Analytical integration; Convergence;
Hypergeometric type functions; INTEGRATOR system;
languages; Pascal; REDUCE system; Residue number
theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Pascal.",
thesaurus = "Convergence of numerical methods; Integration",
}
@InProceedings{Baaz:1990:SPR,
author = "M. Baaz and A. Leitsch",
title = "A strong problem reduction method based on function
introduction",
crossref = "Watanabe:1990:IPI",
pages = "30--37",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p30-baaz/",
abstract = "Although problem reduction is a very important tool in
mathematical practice, relatively little attention has
been paid to problem reduction in automated theorem
proving. The authors propose problem reduction based on
a splitting rule of the form $C$ implies $C'$, where
$C\approx{}C_1vC_2,C'\approx{}C_1vC_2',C_2'\approx{}C_2$
$(x\mbox{from}f(y_1,\ldots{},y_n)),(x,y_1,\ldots{},y_n)$
is the set of variables both in $C_1$ and $C_2$ and $f$
is a new function symbol up to this point not occurring
in any clause. Finally the authors construct a sequence
of clause sets $C_n$ having resolution proofs
exponential in $n$ only, but application of the new
reduction rule reduces the problem to two problems
linear in $n$. Thus it turns out that the introduction
of (elementary) quantificational rules into clause
logic can strongly influence the structure of proofs
and the performance of theorem provers",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algebra und Diskrete Math., Tech. Univ.
Wien, Austria",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Automated theorem proving; Clause logic;
Problem reduction; Quantificational rules; Theorem
provers; theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic. {\bf I.2.3}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Deduction and Theorem Proving. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Functions; Theorem proving",
xxauthor = "M. Baaz and A. Leitsh",
}
@InProceedings{Belmesk:1990:EME,
author = "M. Belmesk",
title = "An execution model for exploiting and-or parallelism
in logic programs (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "288--288",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p288-belmesk/",
abstract = "Several models have been developed for parallel
execution of logic programming languages. Most of them
involve variations of two basic mechanisms: and
parallelism and or parallelism. The model developed
exploits both the and -and or- parallelism using a
compile-time program-level and clause-level data
dependence analysis to generate an execution graph that
embodies the possible parallel executions. The
execution graph is a directed acyclic graph, containing
one node per atom of the clause body and two nodes for
the head clause. Simple tests on the terms provided at
run-time determine which of the different possible
executions graph is to be used.",
acknowledgement = ack-nhfb,
affiliation = "Lifia-Inst. IMAG, Grenoble, France",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; And-or parallelism; Execution graph;
Execution model; Logic programming languages; Parallel
execution",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf F.1.2} Theory
of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes
of Computation, Parallelism and concurrency.",
thesaurus = "Logic programming; Parallel programming",
}
@InProceedings{Bini:1990:PPC,
author = "D. Bini and V. Pan",
title = "Parallel polynomial computations by recursive
processes",
crossref = "Watanabe:1990:IPI",
pages = "294--294",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p294-bini/",
abstract = "Let $\lg$ stand for $\log_2$, $\lg^{(0)}n=n$,
$\lg^{(h)}n=\lg\lg^{(h-1)}n,h=1,\ldots{},\lg*n,\lg*n=\min(h,\lg^{(h)}n<=1)$.
Given natural $N$, $h$, $1<=h<=\lg*N$, and polynomial
$p(x), p(0) \ne 0$, the authors compute
$r(x)=p(x)^{-1}\bmod{}x^N$ for the cost
$O_A(t,P),t=h\lg{}N, P=(N/h)\lg^{(h)}N$, under the PRAM
arithmetic model, that is, the authors need $O(t)$
steps and $O(P)$ processors (with $t$ and $P$ as
above), provided $DFT(m)$ costs $O_A(\lg{}m,m)$. For
$h=\lg*N$, the cost bounds turn into
$O_A(\lg{}N\lg*N,N/\lg*N)$. The results apply to
various related computations.",
acknowledgement = ack-nhfb,
affiliation = "Pisa Univ., Italy",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Computational complexity; Parallel
computations; Polynomial computations; PRAM arithmetic
model; Recursive processes",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials; Recursive functions",
}
@InProceedings{Bradford:1990:PBA,
author = "R. Bradford",
title = "A parallelization of the {Buchberger} algorithm",
crossref = "Watanabe:1990:IPI",
pages = "296--296",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p296-bradford/",
abstract = "Describes experiments with a little elementary
parallelism applied to Buchberger's algorithm. This is
in contrast to Ponder (1988) and Vidal (1990) as gains
can be achieved by using the method even on a single
processor.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Buchberger's algorithm; experimentation;
languages; Parallelism",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Parallel algorithms; Polynomials; Symbol
manipulation",
}
@InProceedings{Cantone:1990:DFE,
author = "D. Cantone and V. Cutello",
title = "A decidable fragment of the elementary theory of
relations and some applications",
crossref = "Watanabe:1990:IPI",
pages = "24--29",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p24-cantone/",
abstract = "The class of purely universal formulae of the
elementary theory of relations with equality is shown
to have an NP-complete satisfiability problem, under
the assumption that there is an a priori bound on the
length of quantifier prefixes and the arities of
relation variables. In the second part of the paper the
authors discuss possible applications in the field of
theorem proving in set and graph theory and of
consistency checking for queries in relational
databases.",
acknowledgement = ack-nhfb,
affiliation = "Archimedes SRL, Catania, Italy",
classification = "C4210 (Formal logic); C4250 (Database theory)",
keywords = "algorithms; Consistency checking; Decidable;
Elementary theory of relations; Graph theory;
Relational databases; Satisfiability; Theorem proving;
theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computability
theory. {\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Database theory; Decidability; Relational databases;
Theorem proving",
}
@InProceedings{Char:1990:PRS,
author = "B. W. Char",
title = "Progress report on a system for general-purpose
parallel symbolic algebraic computation",
crossref = "Watanabe:1990:IPI",
pages = "96--103",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p96-char/",
abstract = "Discusses on-going work on large-grained parallel
symbolic computation using a system based on Maple and
Linda. The prototype runs on a Sequent Balance. The
approach can be used with most existing algebra/symbol
manipulation systems and provides the potential to
deliver of parallel symbolic computation on a variety
of architectures (e.g. shared memory, hypercubes,
networked workstations). Parallel speedup was achieved
on a variety of algebraic problems, although many
significant improvements in efficiency remain to be
achieved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algebraic computation; design; languages;
Large-grained; Linda; Maple; Parallel symbolic
computation; performance; Sequent Balance; Symbol
manipulation systems",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Linda. {\bf D.1.3} Software,
PROGRAMMING TECHNIQUES, Concurrent Programming.",
thesaurus = "Parallel processing; Symbol manipulation",
}
@InProceedings{Chen:1990:ACF,
author = "Guoting Chen",
title = "An algorithm for computing the formal solutions of
differential systems in the neighborhood of an
irregular singular point",
crossref = "Watanabe:1990:IPI",
pages = "231--235",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p231-chen/",
abstract = "Discusses an algorithm for the computation of the
formal solutions of differential systems in the
neighborhood of an irregular singular point. In the
reduction of the differential systems, the author uses
its Arnold--Wasow's canonical form. He discusses also
an algorithm for the reduction of the differential
system to its Arnold--Wasow's canonical form. Then he
discusses the results of a shearing transformation on
this canonical form and gets the convergence of the
algorithm. This paper consists of a complete study of
the problem of computations of the formal solutions of
differential systems in the neighborhood of a singular
point (regular or irregular).",
acknowledgement = ack-nhfb,
affiliation = "LMC, IMAG INPC CNRS, Grenoble, France",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Computation; Convergence; Differential
systems; Formal solutions; Irregular singular point;
languages; Shearing transformation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Convergence of numerical methods; Differential
equations; Symbol manipulation",
}
@InProceedings{Chen:1990:IAM,
author = "G. Chen and I. Gil",
title = "The implementation of an algorithm in {Macsyma}:
computing the formal solutions of differential systems
in the neighborhood of regular singular point",
crossref = "Watanabe:1990:IPI",
pages = "307--307",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p307-chen/",
abstract = "Discusses the problems arising in the implementation
in Macsyma of a direct algorithm for computing the
formal solutions of differential systems in the
neighborhood of regular singular point. The
differential system to be considered is of the form
$x^h dy/dx=A(x)y$ with $A(x)=A_0+A_1x+\ldots{}$ is an
$n$ by $n$ matrices of formal series.",
acknowledgement = ack-nhfb,
affiliation = "Equipe de Calcul Parallele et Calcul Formel, Grenoble,
France",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Differential systems; Formal solutions;
Macsyma; Regular singular point",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Cherief:1990:AMP,
author = "F. Cherief",
title = "An algebraic model for the parallel interpretation of
equationally defined functions (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "285--285",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p285-cherief/",
abstract = "Summary form only given. Algebraic Languages are well
suited for rapid prototyping. Their operational
semantics is given by means of term rewriting systems.
Here, the author proposes a new approach for the
parallel interpretation of term rewriting systems by
mapping every defined function into parallel processes.
The target language is HAL, a new process algebra where
parallel computations are described as a set of
interconnected processes which communicate through the
explicit sending and receiving of messages. HAL is
derived from LOTOS, FP2 and CCS. In HAL an event is a
set of simultaneous communications. Each communication
within an event transports one term along one
connector. When two connectors are linked, the
corresponding communication unifies the two terms. This
essential feature makes it possible to perform all
computations via communications
(computation=communication). In the case considered
here unification reduces to matching.",
acknowledgement = ack-nhfb,
affiliation = "LIFIA-IMAG, Grenoble, France",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic model; algorithms; HAL; Interconnected
processes; languages; Operational semantics; Parallel
interpretation; Prototyping; Simultaneous
communications; Target language; Term rewriting
systems",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Grammars and Other Rewriting Systems.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.3.2} Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
of Programming Languages, Algebraic approaches to
semantics.",
thesaurus = "Formal languages; Parallel languages; Rewriting
systems",
}
@InProceedings{Chou:1990:ARG,
author = "Shang-Ching Chou",
title = "Automated reasoning in geometries using the
characteristic set method and {Gr{\"o}bner} basis
method",
crossref = "Watanabe:1990:IPI",
pages = "255--260",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p255-chou/",
abstract = "Presents an overview of the applications of the
characteristic set method and the Gr{\"o}bner basis
method to automated reasoning in elementary geometries,
differential geometries, and mechanics.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
classification = "C4190 (Other numerical methods); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "Characteristic set method; Gr{\"o}bner basis method;
Automated reasoning; Elementary geometries;
Differential geometries; algorithms; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving.",
thesaurus = "Computational geometry; Inference mechanisms; Symbol
manipulation",
}
@InProceedings{Chou:1990:MMG,
author = "Shang-Ching Chou and Xiao-Shan Gao",
title = "Methods for mechanical geometry formula deriving",
crossref = "Watanabe:1990:IPI",
pages = "265--270",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p265-chou/",
abstract = "A precise formulation for the relations among certain
variables under a set of polynomial equations and a set
of polynomial inequations (to exclude certain special
cases which cannot be excluded by the selection of
parameters alone) is given. Several methods are
presented to find such relations. The methods have been
implemented and used to find geometry formulas, to
discover geometry theorems, and to find geometry locus
equations. About 120 non-trivial problems have been
solved using the methods.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
classification = "C1120 (Analysis); C7310 (Mathematics)",
keywords = "algorithms; Geometry formulas; Geometry locus
equations; Geometry theorems; Mechanical geometry;
Polynomial equations; Polynomial inequations",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Codognet:1990:EDU,
author = "P. Codognet",
title = "Equations, disequations and unsolvable subsets
(abstract)",
crossref = "Watanabe:1990:IPI",
pages = "289--289",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p289-codognet/",
abstract = "Presents a framework for solving a system of equations
and disequations that allow to determine, upon
unsolvability, the `cause' of the failure, i.e. the
minimal unsolvable subsets of equations and
disequations responsible of it.",
acknowledgement = ack-nhfb,
affiliation = "INRIA, Le Chesnay, France",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Disequations; Equations; Failure;
Unsolvability; Unsolvable subsets",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computational
logic. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Computability theory.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Cooperman:1990:RBC,
author = "G. Cooperman and L. Finkelstein and N. Sarawagi",
title = "A random base change algorithm for permutation
groups",
crossref = "Watanabe:1990:IPI",
pages = "161--168",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p161-cooperman/",
abstract = "A new random base change algorithm is presented for a
permutation group $G$ acting on $n$ points whose worst
case asymptotic running time is better for groups with
a small to moderate size base than any known
deterministic algorithm. To achieve this time bound,
the algorithm requires a \mbox{Rand}om generator
$\mbox{Rand}(G)$ producing a Random element of $G$ with
the uniform distribution and so that each call to
$\mbox{Rand}(G)$ takes time
$O(\log(\bmod{}G\bmod{})n)$. The random base change
algorithm has probability $1-1/\bmod{}G\bmod{}^2$ of
completing in time $ O(\log^2(\bmod{}G\bmod{})n)$ and
outputting a data structure for representing the point
stabilizer sequence relative to the new ordering which
requires $O(\log(\bmod{}g\bmod{})n)$ space and which
can be used to test group membership in time
$O(\log(\bmod{}G\bmod{})n)$. The time to build a data
structure for computing a $\mbox{Rand}(G)$ with the
above properties from a strong generating set for $G$
is dominated by the time to construct the strong
generating set of from the original set of
generators.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Asymptotic running time; Data structure;
Deterministic algorithm; Permutation groups; Point
stabilizer sequence; Random base change algorithm;
Random generator; Space complexity; Time complexity",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Computations on
discrete structures.",
thesaurus = "Algorithm theory; Computational complexity; Data
structures; Group theory; Random functions",
}
@InProceedings{Doleh:1990:SSI,
author = "Y. Doleh and P. S. Wang",
title = "{SUI}: a system independent user interface for an
integrated scientific computing environment",
crossref = "Watanabe:1990:IPI",
pages = "88--95",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p88-doleh/",
abstract = "The design and implementation of a Scientific User
Interface is presented. Written in the C language, SUI
is a window-menu-mouse oriented graphical user
interface that is designed to provide a modern and
integrated computing environment for scientific work.
SUI can serve multiple client systems in parallel
including symbolic, numeric, graphics and document
formatting systems. SUI achieves hardware and operating
system independence as well as network transparency by
employing the X11 protocols and achieves client system
independence by defining a client-SUI protocol that is
simple and effective. Features of SUI includes input
editing, history, 2-D mathematical expression display,
interactive selection of subexpressions, interactive
display and manipulation of 2-D and 3-D plots of
mathematical functions, cut and paste with syntax
translation, command templates, incremental 2-D display
of mathematical input, and interactive configuration.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C6180 (User interfaces)",
keywords = "2-D display; 3-D plots; C language; Command templates;
Cut and paste; Document formatting; Graphical user
interface; Graphics; History; Input editing; Integrated
computing environment; Integrated scientific computing
environment; Interactive display; languages;
Mathematical expression display; Mathematical
functions; Network transparency; Numeric; Scientific
User Interface; SUI; Symbolic; Syntax translation;
Window-menu-mouse oriented",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf I.3.6} Computing
Methodologies, COMPUTER GRAPHICS, Methodology and
Techniques, Interaction techniques. {\bf I.3.1}
Computing Methodologies, COMPUTER GRAPHICS, Hardware
Architecture, Input devices. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Graphical user interfaces; Symbol manipulation",
}
@InProceedings{Fateman:1990:ATD,
author = "R. J. Fateman",
title = "Advances and trends in the design and construction of
algebraic manipulation systems",
crossref = "Watanabe:1990:IPI",
pages = "60--67",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p60-fateman/",
abstract = "Compares and contrast several techniques for the
implementation of components of an algebraic
manipulation system. On one hand is the mathematical
algebraic approach which characterizes (for example)
IBM's Scratchpad II. On the other hand is the more ad
hoc approach which characterizes many other popular
systems (for example, Macsyma, Reduce, Maple, and
Mathematica). While the algebraic approach has
generally positive results, careful examination
suggests that there are significant remaining problems,
especially in the representation and manipulation of
analytical, as opposed to algebraic mathematics. The
author describes some of these problems, and some
general approaches for solutions.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Algebraic manipulation systems; Algebraic mathematics;
design; languages; Macsyma; Maple; Mathematica;
Mathematical algebraic; Reduce; Scratchpad II",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Faure:1990:MS,
author = "C. Faure",
title = "A {Meta} simplifier",
crossref = "Watanabe:1990:IPI",
pages = "290--290",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p290-faure/",
abstract = "The simplification process is a key point in computer
algebra systems. The author presents a model of a
simplifier based on two ideas: homogenizing the
computation over numerical and formal expressions, and
building a simplifier completely reachable by the user.
In order to evaluate numerical expressions, the
simplifier calls functions which compute the result or
raise a runtime type error. Formal expressions are
transformed modulo the properties of the operators. For
homogenizing those two processes, three basic
mechanisms come out: simplification by properties, type
checking, evaluation. Moreover a fourth mechanism using
rewriting rules is necessary to compute nonstandard
transformations needed by the user.",
acknowledgement = ack-nhfb,
affiliation = "INRIA, Centre de Sophia-Antipolis, Valbonne, France",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Computer algebra systems; design; Evaluation;
Homogenization; Meta amplifier; Nonstandard
transformations; Rewriting rules; Run-time error;
Runtime type error; Simplification; Type checking",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions.",
thesaurus = "Algebra; Rewriting systems; Symbol manipulation",
}
@InProceedings{Fee:1990:CCC,
author = "G. J. Fee",
title = "Computation of {Catalan}'s constant using
{Ramanujan}'s formula",
crossref = "Watanabe:1990:IPI",
pages = "157--160",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p157-fee/",
abstract = "The author uses some formulas due to Ramanujan for the
multiple precision computation of Catalan's constant
$C=0.915\ldots{}$. The algorithm has been implemented
in Maple and $C$ has been computed to 20000 decimal
places. The resulting program is very simple yet
efficient. It computes $N$ digits of $C$ in $O(N^2)$
time and $O(N)$ space.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "B0290D (Functional analysis); C4120 (Functional
analysis); C4240 (Programming and algorithm theory)",
keywords = "algorithms; C; Catalan constant; Function evaluation;
languages; Maple; Ramanujan formula",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications, C.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Computational complexity; Function evaluation",
}
@InProceedings{Fitch:1990:DSR,
author = "J. Fitch",
title = "A delivery system for {REDUCE}",
crossref = "Watanabe:1990:IPI",
pages = "76--81",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p76-fitch/",
abstract = "A nonLISP delivery system for REDUCE is described and
compared with other implementations of REDUCE for speed
and size, as well as ease of porting. The mechanism for
this delivery system is direct compilation of the
REDUCE sources into ANSI C, which is then compiled and
linked together with some support code for arithmetic
and space administration. The resulting system is
compared with a number of other implementations of true
REDUCE, and is shown to be similar in size, but faster.
The time to port the system is measured in hours. Also
considered are the difficulties in this method of
delivering LISP code, and an assessment of the loss of
flexibility.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Delivery system; languages; LISP code;
REDUCE",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications, LISP.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Compilers.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Franova:1990:PIC,
author = "M. Franov{\'a}",
title = "{PRECOMAS}. {An} implementation of constructive
matching methodology",
crossref = "Watanabe:1990:IPI",
pages = "16--23",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p16-franova/",
abstract = "The system PRECOMAS (PRoofs Educed by COnstructive
MATching of Synthesis) implements the Constructive
Matching methodology for automatic constructions of
programs from formal specifications. The author
describes briefly the goal of PRECOMAS, its logical
background and the CM method applied to proving atomic
formulae. She shows how the user of the system is
involved in solving a program synthesis problem. She
shows that this interaction does not concern the
problem of guiding the program synthesis process, this
being solved by CM. The experimental version serves to
confirm that the system is worth being developed.",
acknowledgement = ack-nhfb,
affiliation = "CNRS, Univ. Paris Sud, Orsay, France",
classification = "C4240 (Programming and algorithm theory); C6115
(Programming support)",
keywords = "algorithms; Atomic formulae; Constructive Matching;
design; Formal specifications; PRECOMAS; Program
synthesis; theory",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf D.1.2}
Software, PROGRAMMING TECHNIQUES, Automatic
Programming.",
thesaurus = "Formal logic; Programming environments",
}
@InProceedings{Ganzha:1990:ARS,
author = "V. G. Ganzha and S. V. Meleshko and V. P. Shelest",
title = "Application of {REDUCE} system for analyzing
consistency of systems of {PDE}'s",
crossref = "Watanabe:1990:IPI",
pages = "301--301",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p301-ganzha/",
abstract = "Summary form only given. A consistency analysis of
differential equation systems involves a sequence of
differential-algebraic operations. At present there are
known two methods: the Cartan's and the
Riquier--Janet--Kuranishi (RJK) method which are
equivalent. The implementation of the both of the
methods with the purpose of their practical application
leads to large symbolic computations which often cannot
be performed without a computer.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "algorithms; Consistency; Consistency analysis;
Differential equation systems; Partial differential
equations; Riquier--Janet--Kuranishi method; RJK
method",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Computational complexity; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Ganzha:1990:LAS,
author = "V. G. Ganzha and M. Yu. Shashkov",
title = "Local approximation study of difference operators by
means of {REDUCE} system",
crossref = "Watanabe:1990:IPI",
pages = "185--192",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p185-ganzha/",
abstract = "Describes new algorithms and programs in the REDUCE
system for the automated study of a local order of the
approximation of difference operator written on
non-orthogonal meshes. The performance of the program
is demonstrated by local approximation of several
difference operators in one and two-dimensional
cases.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C4170
(Differential equations)",
keywords = "algorithms; Approximation; Difference operators;
languages; Local order; Nonorthogonal meshes; Numerical
methods; performance; REDUCE system",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Difference equations; Function approximation",
}
@InProceedings{Gatemann:1990:SSP,
author = "K. Gatemann",
title = "Symbolic solution polynomial equation systems with
symmetry",
crossref = "Watanabe:1990:IPI",
pages = "112--119",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p112-gatemann/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Gatermann:1990:SSP,
author = "K. Gatermann",
title = "Symbolic solution of polynomial equation systems with
symmetry",
crossref = "Watanabe:1990:IPI",
pages = "112--119",
year = "1990",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Systems of polynomial equations often have symmetry.
The Buchberger algorithm which may be used for the
solution ignores this symmetry. It is restricted to
moderate problems unless factorizing polynomials are
found leading to several smaller systems. Therefore two
methods are presented which use the symmetry to find
factorizing polynomials, decompose the ideal and thus
decrease the complexity of the system a lot. In a first
approach projections determine factorizing polynomials
as input for the solution process, if the group
contains reflections with respect to a hyperplane. Two
different ways are described for the symmetric group
$S_m$ and the dihedral group $D_m$. While for $S_m$
subsystems are ignored if they have the same zeros
modulo $G$ as another subsystem, for the dihedral group
$D_m$ polynomials with more than two factors are
generated with the help of the theory of linear
representations and restrictions are used as well.
These decomposition algorithms are independent of the
finally used solution technique. The author uses the
REDUCE package Gr{\"o}bner to solve examples which
illustrate the efficiency of the REDUCE program. A
short introduction to the theory of linear
representations is given. In a second approach problems
of another class are transformed such that more factors
are found during the computation; these transformations
are based on the theory of linear representations.
Examples illustrate these approaches. The range of
solvable problems is enlarged significantly.",
acknowledgement = ack-nhfb,
affiliation = "Konrad Zuse Zentrum fur Inf. Berlin, Germany",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "Symbolic solution; Polynomial equation systems;
Buchberger algorithm; Factorizing polynomials;
Symmetry; Complexity; Symmetric group; Dihedral group;
Linear representations; REDUCE package; Gr{\"o}bner;
Solvable problems",
thesaurus = "Computational complexity; Polynomials; Symbol
manipulation",
}
@InProceedings{Gerdt:1990:CGN,
author = "V. P. Gerdt and A. Yu. Zharkov",
title = "Computer generation of necessary integrability
conditions for polynomial nonlinear evolution systems",
crossref = "Watanabe:1990:IPI",
pages = "250--254",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p250-gerdt/",
abstract = "Uses the symmetry approach to establish an efficient
program in REDUCE for verifying necessary integrability
conditions for polynomial-nonlinear evolution equations
and systems in one-spatial and one-temporal dimensions.
These conditions follow from the existence of higher
infinitesimal symmetries and conservation law
densities. The authors briefly consider the
mathematical background of the symmetry approach to the
problem of integrability. In the description of the
algorithms and their implementation in REDUCE they
present in particular the basic algorithm for reversing
the operator of the total derivative with respect to
the spatial variable. One of the most interesting
applications of the present program is the problem of
classification when the complete list of integrable
equations from a given multiparametric family is
needed. In this case the program generates necessary
integrability conditions in form of a system of
nonlinear algebraic equations in the parameters present
in the initial equations. In spite of their often
complicated structure, there are systems for which the
solution can be found in exact form by applying the
technique of Gr{\"o}bner basis. The authors present
three examples of evolution equations for which this
system can in fact be solved.",
acknowledgement = ack-nhfb,
affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Integrability; Polynomial nonlinear evolution systems;
REDUCE; Symmetry approach; Spatial variable; Nonlinear
algebraic equations; Gr{\"o}bner basis; algorithms;
languages; verification",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Gerdt:1990:SAS,
author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
title = "Solving algebraic systems which arise as necessary
integrability conditions for polynomial-nonlinear
evolution equations",
crossref = "Watanabe:1990:IPI",
pages = "299--299",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p299-gerdt/",
abstract = "The investigation of the problem of integrability of
polynomial-nonlinear evolution equations in particular,
verifying the existence of the higher symmetries and
conservation laws can often be reduced to the problem
of finding the exact solution of a complicated system
of nonlinear algebraic equations. It is remarkable that
these algebraic equations can be not only obtained
completely automatically by computer but also often not
only completely solved by computer, in spite of their
complicated structure and often infinitely many
solutions. The authors demonstrate this fact using the
Gr{\"o}bner basis method and obtain all (infinitely
many) solutions of the systems of algebraic equations
which are equivalent to integrability of three
different multiparametric families of NLEEs: the
seventh order scalar KdV-like equations, the seventh
order MKdV-like equations, and the third order coupled
KdV-like systems.",
acknowledgement = ack-nhfb,
affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "Algebraic systems; Integrability; Polynomial-nonlinear
evolution equations; Nonlinear algebraic equations;
Gr{\"o}bner basis; Algebraic equations; NLEEs;
verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf K.8} Computing
Milieux, PERSONAL COMPUTING, IBM PC.",
thesaurus = "Differential equations; Nonlinear equations;
Polynomials; Symbol manipulation",
}
@InProceedings{Glueck:1990:AMT,
author = "R. Glueck and V. F. Turchin",
title = "Application of metasystem transition to function
inversion and transformation",
crossref = "Watanabe:1990:IPI",
pages = "286--287",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p286-glueck/",
abstract = "The authors prove by construction an application
considered theoretically by Turchin (1972) that
self-application of metacomputation will allow the
automatic construction of inverse algorithms, in
particular the algorithm of binary subtraction from the
algorithm of binary addition. Further, they present
results concerning the algorithmic construction of an
efficient pattern matcher, which leads to the Knuth,
Morris and Pratt algorithm. These results were achieved
with the first working model of a self-applicable
supercompiler system, implementing the concept of
metacomputation.",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Technol. Vienna, Austria",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algorithmic construction; algorithms; Function
inversion; Inverse algorithms; Metacomputation;
Metasystem transition; Pattern matcher; theory;
Transformation; verification",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors. {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Pattern matching.",
thesaurus = "Algorithm theory; Computation theory; Symbol
manipulation",
}
@InProceedings{Grigoriev:1990:CIT,
author = "D. Yu. Grigoriev",
title = "Complexity of irreducibility testing for a system of
linear ordinary differential equations",
crossref = "Watanabe:1990:IPI",
pages = "225--230",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p225-grigoriev/",
abstract = "Let a system of linear ordinary differential equations
of the first order $Y'=AY$ be given, where $A$ is $n*n$
matrix over a field $F(X)$, assume that the degree
$deg_X(A)<d$ and the size of any coefficient occurring
in $A$ is at most $M$. The system $Y'=AY$ is called
reducible if it is equivalent (over the field $F(X)$)
to a system $Y'_1=A_1Y_1$. An algorithm is described
for testing irreducibility of the system, with an
expression for the time complexity.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
Leningrad, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory)",
keywords = "algorithms; Irreducibility; Irreducibility testing;
Linear ordinary differential equations; Time
complexity",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Differential equations",
}
@InProceedings{Grigoriev:1990:HTS,
author = "D. Yu. Grigoriev",
title = "How to test in subexponential time whether two points
can be connected by a curve in a semialgebraic set",
crossref = "Watanabe:1990:IPI",
pages = "104--105",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p104-grigoriev/",
abstract = "A subexponential-time algorithm is designed which
finds the number of connected components of a
semialgebraic set given by a quantifier-free formula of
the first-order theory of real closed fields. Moreover,
the algorithm allows for any two points from the
semialgebraic set to test, whether they belong to the
same connected component. Decidability of the mentioned
problems follows from the quantifier elimination method
in the first-order theory of real closed fields.
However, complexity bound of this method is
nonelementary, in particular, one cannot estimate it by
any finite iteration of the exponential function. G.
Collins (1975) has proposed a construction of
cylindrical algebraic decomposition which allows to
solve these problems in exponential time.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. V.A Steklov, Inst. of Acad. of Sci.,
Leningrad, USSR",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "algorithms; Complexity; Connected components;
Cylindrical algebraic decomposition; Decidability; Real
closed fields; Semialgebraic set; Subexponential time;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Computational complexity; Computational geometry;
Decidability; Symbol manipulation",
}
@InProceedings{Hong:1990:IPO,
author = "Hooh Hong",
title = "An improvement of the projection operator in
cylindrical algebraic decomposition",
crossref = "Watanabe:1990:IPI",
pages = "261--264",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p261-hong/",
abstract = "The Cylindrical Algebraic Decomposition (CAD) method
of Collins (1975) decomposes $r$-dimensional Euclidean
space into regions over which a given set of
polynomials have constant signs. An important component
of the CAD method is the projection operation: given a
set A of $r$-variate polynomials, the projection
operation produces a set $P$ of $(r-1)$-variate
polynomials such that a CAD of $r$-dimensional space
for $A$ can be constructed from a CAD of
$(r-1)$-dimensional space for $P$. The author presents
an improvement to the projection operation. By
generalizing a lemma on which the proof of the original
projection operation is based, he is able to find
another projection operation which produces a smaller
number of polynomials.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Ohio State Univ., Columbus, OH,
USA",
classification = "C4190 (Other numerical methods); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "algorithms; CAD; Cylindrical Algebraic Decomposition;
Euclidean space; Polynomials; Projection operator",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Kalkbrener:1990:SSB,
author = "M. Kalkbrener",
title = "Solving systems of bivariate algebraic equations by
using primitive polynomial remainder sequences",
crossref = "Watanabe:1990:IPI",
pages = "295--295",
year = "1990",
bibdate = "Sat Apr 25 12:58:10 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p295-kalkbrener/",
abstract = "Let $K$ be a field, $K$ the algebraic closure of $K$
and $f=q_m(x)y^m+ \cdots{} +q_o(x)$ a polynomial in
$K(x,y)$ with $q_m \ne 0$. The polynomial $q_m$ is
called the leading coefficient of $f$, abbreviated
$lc(f)$. The degree of $f$ in $y$ is denoted by
$\deg(f)$. Let $f_1, f_2,\ldots{}, f_k$ be the
primitive polynomial remainder sequence of the
primitive polynomials $f_1$ and $f_2$ in $K(x,y)$,
abbreviated $pprs(f_1,f_2)$. For every $i$ in
$(2,\ldots{},k-1)$ let $c_i$ be the content of the
pseudoremainder of $f_{i-}1$ and
$f_i,l_i:=lc(f_i)^{deg(fi-1)-deg(fi)+1},M_i:=(p\in{}K(x)-K\bmod{}p)$
is irreducible, monic and there exists a $j$ in $N$
such that $p^j$ divides $c_2\ldots{}c_i$ but not
$l_2\ldots{}l_i$,
$(\pi,1,\ldots{},\pi,s_i):=(p\in{}Mi\bmod{}p\in{}M_r
{\rm for } r=2,\ldots{},i-1)$ and
$e_i:=\pi,1\ldots{}pis_i.e_2,\ldots{},e_k-1$ is called
the elimination sequence of $f_1$ and $f_2$,
abbreviated $\mbox{elimseq}(f_1, f_2)$. Theorem 1 Let
$a=(a_1,a_2)$ be an element of $K^2$. $f_1(a)=f_2(a)=0$
iff $f_k(a)=0$ or there exists an $i$ in
$(2,\ldots{},k-1)$ with $(f_i/f_k)(a)=e_i(a)=0$. The
correctness of bsolve is based on this result. By using
this algorithm arbitrary systems of bivariate algebraic
equations can be solved.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Algebraic closure; Algorithm correctness; algorithms;
Bivariate algebraic equations; Bsolve; Primitive
polynomial remainder sequences",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Algebra; Program verification; Symbol manipulation",
}
@InProceedings{Kaltofen:1990:MRS,
author = "E. Kaltofen and {Lakshman Y. N.} and J.-M. Wiley",
title = "Modular rational sparse multivariate polynomial
interpolation",
crossref = "Watanabe:1990:IPI",
pages = "135--139",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p135-kaltofen/",
abstract = "The problem of interpolating multivariate polynomials
whose coefficient domain is the rational numbers is
considered. The effect of intermediate number growth on
a speeded Ben-Or and Tiwari algorithm (1988) is
studied. Then the newly developed modular algorithm is
presented. The computing times for the speeded Ben-Or
and Tiwari and the modular algorithm are compared, and
it is shown that the modular algorithm is markedly
superior.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Computing times; Modular algorithm;
Multivariate polynomials; Polynomial interpolation;
Rational numbers; Rational sparse polynomials; Symbolic
expressions; Time complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Interpolation; Polynomials",
}
@InProceedings{Kapur:1990:RPG,
author = "D. Kapur and H. K. Wan",
title = "Refutational proofs of geometry theorems via
characteristic set computation",
crossref = "Watanabe:1990:IPI",
pages = "277--284",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p277-kapur/",
abstract = "A refutational approach to geometry theorem proving
using Ritt--Wu's algorithm for computing a
characteristic set is discussed. A geometry problem is
specified as a quantifier-free formula consisting of a
finite set of hypotheses implying a conclusion, where
each hypothesis is either a geometry relation or a
subsidiary condition ruling out degenerate cases, and
the conclusion is another geometry relation. The
conclusion is negated, and each of the hypotheses
(including the subsidiary conditions) and the negated
conclusion is converted to a polynomial equation.
Characteristic set computation is used for checking the
inconsistency of a finite set of polynomial equations
over an algebraic closed field. The method is
contrasted with a related refutational method that used
Buchberger's Gr{\"o}bner basis algorithm for the
inconsistency check.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1110 (Algebra); C4210 (Formal logic); C7310
(Mathematics)",
keywords = "Algebraic closed field; algorithms; Characteristic set
computation; Geometry theorem proving; Polynomial
equations; Refutational approach; Ritt--Wu's algorithm;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf I.1.4} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Applications.",
thesaurus = "Computational geometry; Polynomials; Theorem proving",
}
@InProceedings{Kohno:1990:RPT,
author = "M. Kohno",
title = "Reduction problems in the theory of differential
equations",
crossref = "Watanabe:1990:IPI",
pages = "244--249",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p244-kohno/",
abstract = "In studying the theory of differential equations, it
seems to be better to treat systems of differential
equations rather than single differential equations,
since the latter are included in a class of the former
and the theory can be made clear through full use of
matrix calculus. Even some specialists of numerical
analysis of differential equations recommend to deal
with systems rather than single equations in practical
calculation of approximate solutions. The objective of
this report is to show an attempt to solve the
reduction problems, illustrating some algorithms to be
applied by algebraic manipulation system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kumamoto Univ., Japan",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Algebraic manipulation system; algorithms;
Differential equations; Matrix calculus; Reduction
problems; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Kolyada:1990:SSC,
author = "S. V. Kolyada",
title = "Systems for symbolic computations in {Boolean}
algebra",
crossref = "Watanabe:1990:IPI",
pages = "291--291",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p291-kolyada/",
abstract = "Boolean algebra as scientific discipline has a few
features. It is a pure mathematical theory and, on the
other hand, an applied mathematical theory too. Boolean
algebra is applied, for instance, to improve
intelligence of software, to automate integrated
circuit design and theorem proving as it can be used to
model situation analysis and decision making. Computer
algebra system for boolean algebra (APAL-PC) allows one
to write and process logical formulae in usual manner.
The system APAL-PC is developed for IBM PC personal
computers on the basis of the programming language C
and universal formula processing tools implemented at
Glushkov Institute of Cybernetics. The experience of
development of a similar system APAL-ES (implemented in
OS/360 environment) is taken into consideration in
designing of the APAL-PC.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybernetics, Kiev, USSR",
classification = "C4210 (Formal logic); C7310 (Mathematics)",
keywords = "APAL-PC; Boolean algebra; design; IBM PC; languages;
Symbolic computations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic.",
thesaurus = "Boolean algebra; IBM computers; Symbol manipulation",
}
@InProceedings{Kuhn:1990:TLC,
author = "N. Kuhn and K. Madlener and F. Otto",
title = "A test for $\lambda$-confluence for certain prefix
rewriting systems with applications to the generalized
word problem",
crossref = "Watanabe:1990:IPI",
pages = "8--15",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p8-kuhn/",
abstract = "Applies rewriting techniques to the generalized word
problem for groups. Let $R$ be a finite
string-rewriting system on an alphabet $\Sigma$ such
that the monoid $M_R$ presented by $(\Sigma:R)$ is a
group, and let $U$ contained in $\Sigma ^+$ be a finite
set. The generalized word problem GWP is defined by
$GWP(w,U)$ iff $w \in (U)$, where $(U)$ is the subgroup
of $M_R$ generated by $U$. With $U$ we associate a
prefix rewriting relation $\mbox{implies}_P$ on
$\Sigma*$ such that $w$ implies/implied by $-{}_P$
$\lambda$ iff $GWP(w,U)$ holds. If $\mbox{implies} _P$
is $\lambda$-confluent then $w\mbox{implies}_P\lambda$
iff $w \in (U)$. Then $\mbox{implies} _P$ yields a
decision procedure for GWP. For groups given through
confluent string-rewriting systems $R$ the authors
develop a necessary and sufficient condition for
$\mbox{implies}_P$ being $\lambda$-confluent and show
that this condition becomes decidable in case of $R$
being length-reducing, in addition.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., Germany",
classification = "C4210 (Formal logic)",
keywords = "$\Lambda$-confluence; algorithms; Decidable;
Generalized word problem; languages; Length-reducing;
Prefix rewriting systems; Rewriting; String-rewriting
system; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems.",
thesaurus = "Decidability; Rewriting systems",
}
@InProceedings{Letichevsky:1990:APA,
author = "A. A. Letichevsky and J. V. Kapitonova",
title = "Algebraic programming in the {APS} system",
crossref = "Watanabe:1990:IPI",
pages = "68--75",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p68-letichevsky/",
abstract = "System APS (algebraic programming system) which was
developed in the Glushkov Institute of Cybernetics of
the Ukrainian Acadamy of Sciences is an instrumental
tool for designing applied systems by means of
algebraic programming. Systems of rewriting rules may
be interpreted in APS by means of different
computational strategies. This approach allows the use
of not only canonical (confluent and noetherian) but
any other systems of equalities, and algebraic programs
may be designed by combining rewriting rules with
different strategies of their applications. Another
peculiarity of APS is the possibility to combine
procedural and algebraic methods of programming.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybernetics, Acad. of Sci., Kiev,
Ukrainian SSR, USSR",
classification = "C6115 (Programming support)",
keywords = "Algebraic programming; algorithms; APS system;
Computational strategies; languages; Rewriting rules",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.3.2}
Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Semantics of Programming Languages, Algebraic
approaches to semantics.",
thesaurus = "Programming environments; Symbol manipulation",
}
@InProceedings{Liska:1990:FRP,
author = "R. Liska and L. Drska",
title = "{FIDE}: a {REDUCE} package for automation of {FInite}
difference method for solving {pDE}",
crossref = "Watanabe:1990:IPI",
pages = "169--176",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p169-liska/",
abstract = "Discusses the automation of the process of numerical
solving of partial differential equations systems
(PDES) by means of computer algebra. For solving PDES
the finite difference method is applied. The computer
algebra system REDUCE and the numerical programming
language FORTRAN are used in the methodology presented,
its main aim being to speed up the process of preparing
numerical programs for solving PDES. Quite often,
especially for complicated systems, this process is a
tedious and time consuming task. In the process several
stages can be found in which computer algebra can be
used for performing routine analytical calculations,
namely: transformation of differential equations into
different coordinate systems, discretization of
differential equations, analysis of difference schemes,
and generation of numerical programs. The FIDE package
is applied to two physical problems. The first one is
the nonlinear Schr{\"o}dinger equation. The second one
is the Fokker--Planck equation. The numerical programs
have been tested and compared with similar published
calculations.",
acknowledgement = ack-nhfb,
affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Tech. Univ. of
Prague, Czechoslovakia",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Computer algebra; Coordinate systems;
Discretization; FIDE; FInite difference method;
Fokker--Planck equation; FORTRAN;
Integro-interpolation; languages; Nonlinear
Schr{\"o}dinger equation; Numerical solving; Partial
differential equations; PDE; REDUCE package",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Finite
difference methods. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, FORTRAN.",
thesaurus = "Difference equations; Partial differential equations;
Software packages; Symbol manipulation",
xxauthor = "R. Liska and L. Drsda",
}
@InProceedings{Liu:1990:AFA,
author = "Zhuo-jun Liu",
title = "An algorithm for finding all isolated zeros of
polynomial systems",
crossref = "Watanabe:1990:IPI",
pages = "300--300",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p300-liu/",
abstract = "Solving algebraic equations is desired for many
problems appearing in applied science. Sometimes,
finding all isolated solutions is enough. Suppose a set
of polynomials (abbr. polset), denoted by PS, to be
given. As a usual convention, by Zero(PS) and
ISZero(PS), we respectively denote the zeros and
isolated zeros defined by PS. Recently, the homotopy
continuation method was widely used to find all
isolated zeros of polset. However, that method is not
good enough to find the isolated zeros of any polset.
Here, based on Wu's method, the author introduces a new
algorithm to solve this problem.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Algorithm; algorithms; Isolated zeros; Polset;
Polynomial systems; Polynomials; Wu's method",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Poles and zeros; Polynomials; Symbol manipulation",
}
@InProceedings{Llovet:1990:MAC,
author = "J. Llovet and J. R. Sendra",
title = "A modular approach to the computation of the number of
real roots",
crossref = "Watanabe:1990:IPI",
pages = "298--298",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p298-llovet/",
abstract = "The problem of computing the number of distinct real
roots of a real polynomial can be solved analyzing the
sign variations of the sequence of principal minors of
the Hankel matrix associated with the given polynomial.
In this paper, the authors present a modular algorithm
to achieve this goal. In this approach, the principal
minors sequence of the associated Hankel matrix is
computed using modular methods. The computing time
analysis shows that the maximum computing time function
of the modular algorithm is $O(n^5l^2)$, where $n$ is
the degree of the polynomial and $l$ its length.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Alcala Univ., Madrid, Spain",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Associated Hankel matrix; Computing time;
Distinct real roots; Hankel matrix; Modular algorithm;
Principal minors; Real polynomial",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Polynomials; Symbol
manipulation",
}
@InProceedings{Manocha:1990:RCP,
author = "D. Manocha",
title = "Regular curves and proper parametrizations",
crossref = "Watanabe:1990:IPI",
pages = "271--276",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p271-manocha/",
abstract = "Presents an algorithm for determining whether a given
rational parametric curve, defined as vector valued
function over a finite domain, has a regular
parametrization. A curve has a regular parametrization
if it has no cusps in its defining interval. It has
been known that the vanishing of the derivative vector
is a necessary condition for the existence of cusps.
The author shows that if a curve is properly
parametrized, then the vanishing of the derivative
vector is a necessary and sufficient condition for the
existence of cusps. If a curve has no cusps in its
defining interval, its proper parametrization is a
regular parametrization. He presents a simple algorithm
to compute the proper parametrization of a polynomial
parametric curve which is used to analyze for cusps and
later on reduce the problem of detecting cusps in a
rational curve to that of a polynomial curve.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Cusps; Polynomial curve; Polynomial
parametric curve; Proper parametrization; Rational
parametric curve; Vector valued function",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.3.5} Computing
Methodologies, COMPUTER GRAPHICS, Computational
Geometry and Object Modeling, Geometric algorithms,
languages, and systems.",
thesaurus = "Computational geometry; Symbol manipulation",
}
@InProceedings{Mazurik:1990:SCS,
author = "S. I. Mazurik and E. V. Vorozhtsov",
title = "Symbolic-numerical computations in the stability
analyses of difference schemes",
crossref = "Watanabe:1990:IPI",
pages = "177--184",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p177-mazurik/",
abstract = "The authors propose a number of symbolic-numeric
approaches to the computer-aided construction of the
stability domains of difference schemes approximating
the partial differential equations with constant
coefficients. They use the Fourier method, the
algebraic methods of the Routh--Hurwitz and Schur--Cohn
theories for the localization of the polynomial zeros,
the methods of optimization theory as well as the means
of computer algebra, digital image processing and
computer graphics. The efficiency of the approaches is
demonstrated at the practical examples of difference
schemes for fluid dynamics problems.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, USSR",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algebraic methods; algorithms; Computer algebra;
Computer graphics; Difference schemes; Digital image
processing; Fluid dynamics problems; Fourier method;
Optimization theory; Partial differential equations;
Polynomial zeros; Routh--Hurwitz; Schur--Cohn theories;
Stability analyses; Symbolic-numeric approaches;
theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.8}
Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Finite difference methods. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Convergence of numerical methods; Difference
equations; Mathematics computing; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Mishra:1990:ARA,
author = "B. Mishra and P. Pedersen",
title = "Arithmetic with real algebraic numbers is in {NC}",
crossref = "Watanabe:1990:IPI",
pages = "120--126",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p120-mishra/",
abstract = "The authors describe NC algorithms for doing exact
arithmetic with real algebraic numbers in the
sign-coded representation introduced by Coste and Roy
(1988). They present polynomial sized circuits of depth
$O(\log^3N)$ for the monadic operations
$-\alpha,1/\alpha$, as well as $\alpha +r$,
$\alpha\cdot{}r$, and $\mbox{sgn} (\alpha -r)$, where
$r$ is rational and $\alpha$ is real algebraic. They
also present polynomial sized circuits of depth
$O(\log^7N)$ for the dyadic operations $\alpha+\beta$,
$\alpha\cdot\beta$, and $\mbox{sgn}(\alpha-\beta)$,
where $\alpha$ and $\beta$ are both real algebraic. The
algorithms employ a strengthened form of the NC
polynomial-consistency algorithm of Ben-Or, Kozen, and
Reif (1986).",
acknowledgement = ack-nhfb,
affiliation = "New York Univ., NY, USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "algorithms; Dyadic operations; Exact arithmetic; Fast
parallel algorithms; Monadic operations; NC algorithms;
NC polynomial-consistency algorithm; Polynomial sized
circuits; Real algebraic numbers; Sign-coded
representation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General.",
thesaurus = "Parallel algorithms; Polynomials",
}
@InProceedings{Murray:1990:RIT,
author = "N. V. Murray and E. Rosenthal",
title = "Reexamining intractability of tableau methods",
crossref = "Watanabe:1990:IPI",
pages = "52--59",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p52-murray/",
abstract = "Considers the class of formulas on which the method of
analytic tableaux was first shown to be intractable,
and shows that the applications of the ordinary
distributive law tableau methods admit linear time
proofs for this class. The authors introduce a new
class of formulas that are intractable for tableaux
(even with the distributive law), and demonstrate that
path dissolution admits linear proofs of these
formulas. Modifications of the tableau method are
described that would render this class tractable. Since
dissolution is linear on this class, these results
demonstrate that dissolution cannot be $p$-simulated by
the method of analytic tableau.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Analytic tableaux; Dissolution; Linear
proofs; Linear time proofs; Path dissolution; Tableau
methods; theory; verification",
subject = "{\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Graph algorithms. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving,
Deduction.",
thesaurus = "Formal logic",
}
@InProceedings{Noda:1990:SHI,
author = "Matu-Tarow T. Noda and E. Miyahiro",
title = "On the symbolic\slash numeric hybrid integration",
crossref = "Watanabe:1990:IPI",
pages = "304--304",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p304-noda/",
abstract = "Integrating a given function is one of the most
important areas in the mathematical computing. Both
numerical and symbolic integration methods have been
developed and widely used. Numerical methods, however,
have some defects such as (1) formal integrals are not
obtained, (2) wrong answers are given for pathological
integrand and (3) error estimates depend on types of
integrands. Symbolic methods have also difficulties on
(1) restrictions on an integrand and (2) uses of
wasteful big-number computation. To avoid difficulties,
some attempts in which both methods are combined have
been proposed, called hybrid methods. The authors
propose new hybrid integration method for a rational
function, (say $q/r$, $q$ and $r$ are polynomials) with
floating point but real coefficients.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Ehime Univ., Matsuyama, Japan",
classification = "C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Floating point; Hybrid integration;
Numerical; Numerical integration; Rational function;
Symbolic integration",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Nonalgebraic algorithms. {\bf G.1.4}
Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation.",
thesaurus = "Integration; Numerical methods; Symbol manipulation",
}
@InProceedings{Norman:1990:CBI,
author = "A. C. Norman",
title = "A critical-pair\slash completion based integration
algorithm",
crossref = "Watanabe:1990:IPI",
pages = "201--205",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p201-norman/",
abstract = "The presentation re-expresses the 1976 Risch method in
terms of rewrite rules, and thus exposes the major
problem it suffers from as a manifestation of the fact
that in certain circumstances the set of rewrites
generated is not confluent. This difficulty is then
attacked using a critical-pair/completion (CPC)
approach. For very many integrands it is then easy to
see that the initial set of rewrites used in the early
implementations do not need any extension, and this
fact explains the high level of competence of the
programs involved despite their shaky theoretical
foundations. For a further large collection of problems
even a simple CPC scheme converges rapidly; when the
techniques are applied to the REDUCE integration test
suite in all applicable cases a short computation
succeeds in completing the set of rewrites and hence
gives a secure basis for testing for integrability.
This paper describes the implementation of the CPC
process and discusses current limitations to and
possible future extended applications of it.",
acknowledgement = ack-nhfb,
affiliation = "Trinity Coll., Cambridge, UK",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Convergence; CPC scheme;
Critical-pair/completion based integration algorithm;
experimentation; Integrability; REDUCE integration test
suite; Rewrite rules; Transcendental functions",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Computations on
discrete structures.",
thesaurus = "Convergence of numerical methods; Integration;
Rewriting systems",
}
@InProceedings{Okubo:1990:GTO,
author = "K. Okubo",
title = "Global theory of ordinary differential equations and
formula manipulation",
crossref = "Watanabe:1990:IPI",
pages = "193--200",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p193-okubo/",
abstract = "The author discusses the fundamental domain of the
monodromy group for hypergeometric equations. One can
classify these triangles formed by circular arcs with
the sum of inner angles greater, equal or less than
$\pi$. The domains have been classified into three
classes, those on the unit sphere, those on the open
complex plane and those on the unit disk. Any
algebraically integrable solution of a hypergeometric
equation is expressed by invariants of the groups of
five platonic solids or dipyramids. One can express the
key in terms of non-Euclidean expression by the sum of
inner angles of triangles. The authors rephrases this
into quadratic invariant of definite, degenerate or
indefinite sign. The quadratic invariants may be of
help as the key to the classification in higher
dimensions.",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Electro-Commun., Chofu, Tokyo, Japan",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
keywords = "Algebraically integrable solution; Circular arcs;
Dipyramids; Five platonic solids; Formula manipulation;
Gauss equation; Hypergeometric equations; Inner angles;
Monodromy group; Open complex plane; Ordinary
differential equations; Quadratic invariant; Unit disk;
Unit sphere",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Padget:1990:UPS,
author = "J. Padget and A. Barnes",
title = "Univariate power series expansions in {Reduce}",
crossref = "Watanabe:1990:IPI",
pages = "82--87",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p82-padget/",
abstract = "Describes the development of a formal power series
expansion package for Reduce which takes advantage of
Reduce's domain mechanism to make for a seamless
integration of series values with the rest of the
Reduce system. Consequently, series values may be
manipulated with the same algebraic operators as other
algebraic objects. To create the illusion of infinite
power series a simulated lazy-evaluation mechanism has
been used. The paper reports experience of using the
Reduce domain mechanism and documents the algorithms
and data structures that can be used to implement and
to represent power series.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C7310 (Mathematics)",
keywords = "Algebraic operators; Algorithms; algorithms; Data
structures; Domain mechanism; languages;
Lazy-evaluation mechanism; Power series expansions;
Reduce; Series values",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Scott:1990:SAM,
author = "T. C. Scott and G. J. Fee",
title = "Some applications of {Maple} symbolic computation to
scientific and engineering problems",
crossref = "Watanabe:1990:IPI",
pages = "302--303",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p302-scott/",
abstract = "Presents a survey of use of the Maple symbolic
computation system at the University of Waterloo. This
represents only a sample of what has and can be done
with symbolic computation. However, these examples have
been chosen from a broad spectrum of areas which
includes: Quantum theory, general and special
relativity, audio engineering and asbestos fiber
analysis (an application of fluid and
magneto-dynamics). They represent new avenues of
research and illustrate the large untapped potential of
symbolic computation.",
acknowledgement = ack-nhfb,
affiliation = "Maple Symbolic Comput. Group, Waterloo Univ., Ont.,
Canada",
classification = "C7300 (Natural sciences); C7400 (Engineering)",
keywords = "Asbestos fiber analysis; Audio engineering; design;
General relativity; Maple; Quantum theory; Special
relativity; Symbolic computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple.",
thesaurus = "Engineering computing; Natural sciences computing;
Symbol manipulation",
}
@InProceedings{Shirayanagi:1990:IPF,
author = "K. Shirayanagi",
title = "On the isomorphism problem for finite-dimensional
binomial algebras",
crossref = "Watanabe:1990:IPI",
pages = "106--111",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p106-shirayanagi/",
abstract = "Binomial algebras are finitely presented algebras
defined by monomials or binomials. Given two binomial
algebras, one important problem is to decide whether or
not they are isomorphic as algebras. The author studies
an algorithm for solving this problem, when both
algebras are finite-dimensional over a field. In
particular, when they are monomial algebras (i.e
binomial algebras defined by monomials only), the
problem has already been completely solved by the
presentation uniqueness. The author provides some
necessary conditions in terms of partially ordered sets
for two certain binomial algebras to be isomorphic. In
other words, invariants of the binomial algebras are
presented. These conditions together serve as an
effective procedure for solving the isomorphism
problem.",
acknowledgement = ack-nhfb,
affiliation = "NTT Software Lab., Tokyo, Japan",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Binomial algebras; Binomials; Finitely
presented algebras; Monomials; Partially ordered sets;
Presentation uniqueness; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Algebra; Set theory; Symbol manipulation",
}
@InProceedings{Smedley:1990:DAD,
author = "T. J. Smedley",
title = "Detecting algebraic dependencies between unnested
radicals (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "292--293",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p292-smedley/",
abstract = "There are a number of known methods for checking for
dependencies between unnested radicals. However, these
methods usually have one or both of the following
disadvantages: 1. They rely on integer factorisation,
or 2. They generate an algebraic extension field of
degree higher than is necessary to express the input.
The first disadvantage is not generally too important,
as the integers involved are usually quite small and
can be easily factored. However, the second
disadvantage can cause real problems. Since the degree
of the algebraic extension has a large influence on the
cost of algorithms involving algebraic numbers, the
author wants a method which detects dependencies but
keeps the degree of the extension field as low as
possible.",
acknowledgement = ack-nhfb,
affiliation = "Delaware Univ., Newark, DE, USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algebraic dependencies; Algebraic extension; Algebraic
numbers; Unnested radicals; verification",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Representations (general and
polynomial). {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Symbol manipulation",
}
@InProceedings{Stachniak:1990:RPS,
author = "Z. Stachniak",
title = "Resolution proof systems with weak transformation
rules",
crossref = "Watanabe:1990:IPI",
pages = "38--43",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p38-stachniak/",
abstract = "In previous papers the author defined and explored a
formal methodological framework on the basis of which
resolution proof systems for strongly-finite logics can
be introduced and studied. In the present paper he
extends this approach to a wider class of so-called
resolution logics.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., York Univ., North York, Ont.,
Canada",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Formal methodological framework;
Resolution logics; Resolution proof systems;
Strongly-finite logics; theory; verification; Weak
transformation rules",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computational
logic. {\bf I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving, Deduction.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic.",
thesaurus = "Formal logic",
}
@InProceedings{Takayama:1990:ACI,
author = "N. Takayama",
title = "An algorithm of constructing the integral of a module
--- an infinite dimensional analog of {Gr{\"o}bner}
basis",
crossref = "Watanabe:1990:IPI",
pages = "206--211",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p206-takayama/",
abstract = "Let $U$ be a left ideal of Weyl algebra:
$A_n=K(x_1,\ldots{},x_n,\delta_1,\ldots{},\delta_n)$.
Put $M=A_n/U$. M is a left $A_n$ module. The paper
presents an explicit construction of the left $A_{n-1}$
module by introducing an analog of Gr{\"o}bner basis of
a submodule of a kind of infinite dimensional free
module. The author gives a complete algorithm. The
algorithm is an answer to the research problem of the
paper (AZ).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kobe Univ., Japan",
classification = "B0290R (Integral equations); C4180 (Integral
equations)",
keywords = "algorithms; Integral; Gr{\"o}bner basis; Left ideal;
Weyl algebra",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Integral equations; Symbol manipulation",
}
@InProceedings{Takayama:1990:GBI,
author = "N. Takayama",
title = "{Gr{\"o}bner} basis, integration and transcendental
functions",
crossref = "Watanabe:1990:IPI",
pages = "152--156",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p152-takayama/",
abstract = "It is well known that Gr{\"o}bner basis is a
fundamental and powerful tool to solve problems of
polynomials. One can use the Gr{\"o}bner basis of Weyl
algebra to solve the problems of integration and
formula verification of transcendental functions. The
paper surveys the theory of the Gr{\"o}bner basis of
the ring of differential operators and its applications
to the following problems: computation of differential
equations for a definite integral with parameters; zero
recognition of an expression that contains special
functions or binomial coefficients etc., i.e. formula
verification by a computer; derivations of some of
special function identities; solving a definite
integral or obtaining an asymptotic expansion of a
definite integral with parameters.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kobe Univ., Japan",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "Transcendental functions; Gr{\"o}bner basis;
Polynomials; Weyl algebra; Integration; Formula
verification; Differential operators; Differential
equations; Definite integral; Zero recognition;
Binomial coefficients; Special function identities;
Asymptotic expansion; algorithms; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Differential equations; Function approximation;
Integration; Polynomials; Symbol manipulation",
}
@InProceedings{Tan:1990:OTS,
author = "H. Q. Tan and X. Dong",
title = "Optimization techniques for symbolic equation solver
in engineering applications",
crossref = "Watanabe:1990:IPI",
pages = "305--305",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p305-tan/",
abstract = "In MACSYMA, there are procedures for solving systems
of equations, such as solve and linsolve. Because the
systems of equations we are dealing with are mostly
sparse, the application of Gaussian elimination which
is used in linsolve produces results that are usually
lengthy and inefficient. The authors have implemented a
new derivation procedure to solve the problem of
expression growth and increase the computational
efficiency. The underlying concept is the
identification of the smallest full subsystems
contained within the original and then subsequent
remaining systems, labeling common terms by
intermediate variables. Gaussian elimination is
employed to solve these subsystems independently and
sequentially instead of the complete system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Akron Univ., OH, USA",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Derivation procedure; Gaussian
elimination; Symbolic equation solver",
subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Tao:1990:SAM,
author = "Qingsheng Tao",
title = "Symbolic and algebraic manipulation for formulae of
interpolation and quadrature",
crossref = "Watanabe:1990:IPI",
pages = "306--306",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p306-tao/",
abstract = "Computer algebra has been used for construction and
analysis of algorithms of numerical computation. In the
paper, an attempt has been made to derive the formulae
of interpolation and quadrature with Computer Algebra.
In REDUCE language, the formula manipulation system for
interpolation INTEP and for quadrature QUADRAT are
developed. The two formula manipulators can be used to
derive Lagrange, Hermite and Birkhoff interpolation
formulae with any degree of polynomials and to derive
Newton--Cotes quadrature formulae and the quadrature
formulae involving the derivatives of the integrand.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech., Zhejiang Univ., Hangzhou, China",
classification = "C4130 (Interpolation and function approximation);
C4160 (Numerical integration and differentiation)",
keywords = "Algebraic manipulation; algorithms; Birkhoff; Computer
Algebra; Formula manipulators; Hermite; INTEP;
Interpolation; Interpolation formulae; Lagrange;
languages; Newton--Cotes quadrature formulae; QUADRAT;
Quadrature; Symbolic manipulation",
subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Integration; Interpolation; Symbol manipulation",
}
@InProceedings{Ulmer:1990:LSH,
author = "F. Ulmer and J. Calmet",
title = "On {Liouvillian} solutions of homogeneous linear
differential equations",
crossref = "Watanabe:1990:IPI",
pages = "236--243",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p236-ulmer/",
abstract = "Deals with the problem of finding Liouvillian
solutions of an $n$-th order homogeneous linear
differential equation $L(y)=0$ with coefficients in a
differential field $k$ whose field of constants is $C$.
For second order linear differential equations such an
algorithm has been given by J. Kovacic (1986) and
implemented. A general decision procedure for finding
Liouvillian solutions of $n$-th order equations has
been given by M. F. Singer (1981), but the resulting
algorithm, although constructive, is not in
implementable form even for second order equations. The
algorithm uses the fact that, if $L(y)=0$ has a
Liouvillian solution, then, $L(y)=0$ has a solution $z$
such that $u=z'/z$ is algebraic over $k$, which means
that $L(y)$ has a solution $z$ of the form
$e^{\int{}u}$, where $u$ is algebraic over $k$. Since
the logarithmic derivative $u=z'/z$ of a solution $z$
is a solution of the Riccati equation $R(y)=0$
associated to $L(y)=0$, the problem thus reduces to
find an algebraic solution $u$ of $R(y)=0$. This task
is now split into two parts: (i) to find the set DEG(n)
of possible degrees $N$ for the minimal polynomial
$P(x)=0$ of $u$ over $k$, (ii) to compute, for each
possible degree of $P(x)$, the possible coefficients of
$P(x)$. If we donate $c(ii)$ the complexity of the
second step and Hash DEG($n$) the size of the set
DEG($n$), one sees that the complexity of the whole
procedure is of the form $c(ii)^{Hash DEG(n)}$ and thus
exponential in Hash DEG($n$). This shows that the only
way to make the procedure effective is to get sharp
bounds on the size of the set DEG($n$), which is the
scope of this paper.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algebraic solution; algorithms; Complexity;
Homogeneous; Linear differential equations; Liouvillian
solutions; Sharp bounds",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Computational complexity; Differential equations;
Symbol manipulation",
}
@InProceedings{vonzurGathen:1990:PFF,
author = "J. {von zur Gathen}",
title = "Polynomials over finite fields with large images",
crossref = "Watanabe:1990:IPI",
pages = "140--144",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p140-von_zur_gathen/",
abstract = "A polynomial $f$ in $F_q(x)$, over a finite field
$F_q$ with $q$ elements, is $\rho$-large if its image
in $F_q$ contains at least $q-\rho$ elements. The
article presents an efficient probabilistic test for
this property, using expected time polynomial in
$\deg{}f$, $\log{}q$, and $\rho$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Toronto Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Expected time polynomial; Finite fields;
Large images; Polynomial; Probabilistic test; Time
complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Probabilistic
computation.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Wang:1990:PUP,
author = "P. S. Wang",
title = "Parallel univariate polynomial factorization on
shared-memory multiprocessors",
crossref = "Watanabe:1990:IPI",
pages = "145--151",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p145-wang/",
abstract = "Using parallelism afforded by shared-memory
multiprocessors to speed up systems for polynomial
factorization is discussed. The approach is to take the
fastest known factoring algorithm for practical
purposes and parallelize key parts of it. The
univariate factoring algorithm consists of two major
tasks (a) factoring modulo small integer primes and (b)
EEZ lifting and recovery of true factors. A C coded
system PFACTOR that implements (a) in parallel is
described in detail. PFACTOR is a stand-alone parallel
factorizer that can take input from a file, a pipe or a
socket connection over a network. It can also be used
interactively as a UNIX command. PFACTOR consists of
parallel selection of primes, automatic balancing of
work, parallel Berlekamp algorithm, and parallel
reconciliation of degrees of factors modulo different
primes. Actual timings on the Encore Multimax show the
effectiveness of the approach.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; C coded system; EEZ lifting; Encore
Multimax; Modulo small integer primes; Parallel
Berlekamp algorithm; Parallel reconciliation;
Parallelism; performance; PFACTOR; Polynomial
factorization; Shared-memory multiprocessors; Time
complexity; Univariate factoring algorithm; UNIX
command",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Modes of Computation, Parallelism and
concurrency.",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials",
}
@InProceedings{Yamasaki:1990:DLP,
author = "S. Yamasaki",
title = "Dataflow for logic program as substitution
manipulator",
crossref = "Watanabe:1990:IPI",
pages = "44--51",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p44-yamasaki/",
abstract = "Shows a method of constructing a dataflow, which
denotes the deductions of a logic program, by means of
a sequence domain based on equivalence classes of
substitutions. The dataflow involves fair merge
functions to represent unions of atom subsets over a
sequence domain, as well as functions as manipulations
of unifiers for the deductions of clauses. A continuous
functional is associated with the dataflow on condition
that the dataflow completely and soundly denotes the
atom generation in terms of equivalent substitutions
sets. Its least fixpoint is interpreted as denoting the
whole atom generation based on manipulations of
equivalent substitutions sets.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Technol., Okayama Univ., Japan",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Continuous functional; Dataflow;
Equivalence classes; Fair merge functions; Logic
program; Sequence domain; Substitution manipulator;
theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Logic programming; Programming theory",
}
@InProceedings{Yokoyama:1990:DSP,
author = "K. Yokoyama and M. Noro and T. Takeshima",
title = "On determining the solvability of polynomials",
crossref = "Watanabe:1990:IPI",
pages = "127--134",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p127-yokoyama/",
abstract = "Landau and Miller (1985) presented a method for
determining the solvability of a monic irreducible
polynomial over integers in polynomial time. In their
method, a series of polynomials is constructed so that
the original problem is reduced to determining the
solvability of new polynomials. The authors present an
improved method for finding such a series of
polynomials efficiently. More precisely, they introduce
a new notion on a series of blocks in the set of all
roots of the original polynomial under the action of
its Galois group, and then present an efficient method
for finding such a series of blocks by modifying Landau
and Miller's method for finding minimal imprimitive
blocks.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Ltd., Numazu, Japan",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Galois group; Minimal imprimitive blocks;
Monic irreducible polynomial; Polynomials; Problem
complexity; Solvability; Time complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS,
Graph Theory, Graph algorithms.",
thesaurus = "Computability; Computational complexity; Polynomials",
}
@InProceedings{Yokoyama:1990:FMP,
author = "Kazuhiro Yokoyama and Masayuki Noro and Taku
Takeshima",
title = "On factoring multi-variate polynomials over
algebraically closed fields (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "297--297",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p297-yokoyama/",
abstract = "For a problem how to find an extension field over
which we can obtain an absolutely irreducible factor,
Kaltofen gave an answer in 1983 and explicitly in 1985
by employing analytic argument for showing his answer,
and Chistov and Grigor'ev also gave the same answer in
1983 by algebraic arguments. Here the authors give an
alternative proof for Kaltofen's answer in algebraic
way, independently to Chistov and Grigor'ev, and by the
benefit of new way, they also give several extensions
of his answer and properties of absolutely irreducible
factors. They also discuss usage of their results for
actual computation of absolutely irreducible factors.
They restrict themselves to bi-variate polynomials with
integer (or rational) coefficients.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Ltd., Japan",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Actual computation; Algebraic arguments; Algebraically
closed fields; Bi-variate polynomials; Irreducible
factor; Multi-variate polynomials; theory;
verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Abramov:1991:FAS,
author = "S. A. Abramov and K. Yu. Kvashenko",
title = "Fast algorithms to search for the rational solutions
of linear differential equations with polynomial
coefficients",
crossref = "Watt:1991:IPI",
pages = "267--270",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p267-abramov/",
abstract = "The paper is concerned with some ways for an
improvement with regard to solving the linear ordinary
differential equations of the form
$\sum_0^na_i(x)y^{(i)}(x)=b(x)$ where
$a_0(x),\ldots{},a_n(x),b(x)$ in $K(x)$ ($K$ is the
constant field), $a_n(x) \neq 0$. The authors consider
one after another of the problems of finding all the
polynomial and rational solutions of equation. They
consider the simplest approach and then its
improvement.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Linear differential equations; Polynomial
coefficients; Rational solutions; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Linear differential equations; Symbol manipulation",
}
@InProceedings{Amirkhanov:1991:BOV,
author = "I. V. Amirkhanov and E. P. Zhidkov and I. E.
Zhidkova",
title = "The betatron oscillations in the vicinity of nonlinear
resonance in cyclic accelerator investigation",
crossref = "Watt:1991:IPI",
pages = "452--453",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p452-amirkhanov/",
abstract = "Motion of charged particle in given fields in a cyclic
accelerator has been investigated. The nonlinear
problem of finding stable trajectories in the vicinity
of a resonance has been solved. The equations of motion
for charged particle deviation from ideal orbit or the
betatron oscillations equations (which are lateral to
the closed orbit oscillations with the frequencies
$\nu_x, \nu_z$) are studied using REDUCE-3.2. The study
of the equations formed by computer is applied to two
types of accelerators: (1) the averaged equations in
the vicinity of 19 resonances for a weakly focusing
accelerator (WFA) and (2) those in the vicinity of 24
resonances-for a strong focusing accelerator (SFA).",
acknowledgement = ack-nhfb,
affiliation = "JINR, Moscow, USSR",
classification = "A2920F (Betatrons); B7410 (Accelerators); C7320
(Physics and Chemistry)",
keywords = "algorithms; Betatron oscillations; Charged particle
deviation; Cyclic accelerator; Nonlinear resonance;
REDUCE-3.2; Strong focusing accelerator; Weakly
focusing accelerator",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics.",
thesaurus = "Betatrons; Physics computing",
}
@InProceedings{Apel:1991:FAA,
author = "Joachim Apel and Uwe Klaus",
title = "{FELIX}: an assistant for algebraists",
crossref = "Watt:1991:IPI",
pages = "382--389",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p382-apel/",
abstract = "FELIX is a special computer algebra system designed
for calculations with elements of algebraic structures
as well as with substructures and homomorphisms. It
covers both commutative polynomial rings and modules
and non-commutative structures. Buchberger's algorithm
for the computation of Gr{\"o}bner bases is fundamental
for many of the included operations. The articles
contains a short description of the system FELIX and
illustrates the sensitivity of Buchberger's algorithm
against changes of selection strategies.",
acknowledgement = ack-nhfb,
affiliation = "Leipzig Univ., Germany",
classification = "C7310 (Mathematics)",
keywords = "algorithms; design; FELIX; Computer algebra system;
Algebraic structures; Substructures; Homomorphisms;
Commutative polynomial rings; Modules; Non-commutative
structures; Buchberger's algorithm; Gr{\"o}bner bases",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Astrelin:1991:BDI,
author = "A. V. Astrelin",
title = "A bound of degree of irreducible eigenpolynomial of
some differential operator",
crossref = "Watt:1991:IPI",
pages = "265--266",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p265-astrelin/",
abstract = "Consider the following problem: for the differential
operator $D=P \delta / \delta x+Q \delta / \delta y$
find an integer $K$, such that any irreducible
polynomial $f$ dividing $Df$ has degree $\deg{}f<=K$.
This problem arises when one wants to find the symbolic
solution of a differential equation $dy/dx=R(x,y)$
where $R$ is a rational function. A solution when $P$
and $Q$ are homogeneous polynomials of equal degrees
i.e. $P(x,y)=x^mp(x/y),Q(x,y)=x^mq(x,y)$ for some $m$
is proposed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C1120 (Analysis); C4170
(Differential equations)",
keywords = "algorithms; Differential equation; Differential
operator; Homogeneous polynomials; Irreducible
eigenpolynomial; Irreducible polynomial; Rational
function; Symbolic solution",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Differential equations; Polynomials",
}
@InProceedings{Babai:1991:NLT,
author = "L{\'a}szl{\'o} Babai and Gene Cooperman and Larry
Finkelstein and {\'A}kos Seress",
title = "Nearly linear time algorithms for permutation groups
with a small base",
crossref = "Watt:1991:IPI",
pages = "200--209",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p200-babai/",
abstract = "A base of a permutation group $G$ is a subset $B$ of
the permutation domain such that only the identity of
$G$ fixes $B$ pointwise. The permutation
representations of important classes of groups,
including all finite simple groups other than the
alternating groups, admit $O(\log{}n)$ size bases,
where $n$ is the size of the permutation domain. Groups
with very small bases dominate the work on permutation
groups in much of computational group theory. A series
of new combinatorial results allows us to present Monte
Carlo algorithms achieving $O(n \log^cn)$ ($c$ a
constant) time and space performance for such groups
with respect to the fundamental operations of finding
order and testing membership. (The input is a list of
generators of the group). Previous methods have
achieved similar space performance only at the expense
of increased time performance. Adaptations of a
`cube-doubling' technique (L. Babai, E. Szemeredi,
1984) and a local expansion property of groups (L.
Babai, 1991) are the key to theoretically reducing the
time complexity to $O(n \log^c n)$. The shared
principal novelty of the new ideas is in their ability
to build and manipulate certain chains of subsets of a
group, which are not themselves subgroups, in order to
build the point stabilizer subgroup chain. Further
combinatorial ideas are used to lower the constant $c$.
Comparative timing estimates, based on asymptotic
worst-case analysis, lead us to expect a new
implementation to be faster than previous
implementations for groups of high degree.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comp. Sci. Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Alternating groups; Asymptotic worst-case
analysis; Computational group theory; Cube-doubling;
Finite simple groups; Fundamental operations; Group
order determination; Local expansion property;
Membership testing; Monte Carlo algorithms; Permutation
domain; Permutation group; Point stabilizer subgroup
chain; Shared principal novelty; theory; Time
complexity",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.3} Mathematics
of Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo). {\bf G.2.1}
Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Combinatorial algorithms.",
thesaurus = "Computational complexity; Group theory",
}
@InProceedings{Backelin:1991:HWP,
author = "J{\"o}rgen Backelin and Ralf Fr{\"o}berg",
title = "How we proved that there are exactly 924 cyclic
7-roots",
crossref = "Watt:1991:IPI",
pages = "103--111",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p103-backelin/",
abstract = "The following problem has become some sort of test
problem for Gr{\"o}bner bases techniques: find all
solutions to $Sn=z_1+z_2+\ldots{}+z_{n-1}+z_n=0$,
$z_1z_2+z_2z_3+\ldots{}+z_{n-1}z_n+z_nz_1=0$, \ldots{}
$z_1z_2\ldots{}z_{n-1}+z_2z_3\ldots{}z_n+\ldots{}+z_{n-1}z_n\ldots{}z_{n-3}+z_nz_1\ldots{}z_{n-2}=0$,
$z_1z_2\ldots{}z_n=1$. The solutions are called cyclic
$n$-roots. In order to solve the problem one of the
authors constructed a new characteristic 0 Gr{\"o}bner
basis programme, Bergman. The authors describe some
features of Bergman, in particular its graph component
algorithm. They make some theoretical analysis and
practical tests of the differences in performance
between Bergman and some other Buchberger based
algorithms, mainly the Gebauer--Moller algorithm. With
the help of Bergman and some commutative algebra they
succeeded to prove: there are exactly 924 cyclic
7-roots. Each of them has multiplicity 1.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Stockholm Univ., Sweden",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; verification; Exact proof; Cyclic 7-roots;
Cyclic $n$-roots; Characteristic 0 Gr{\"o}bner basis
programme; Bergman; Graph component algorithm;
Gebauer--Moller algorithm; Multiplicity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Becker:1991:CRP,
author = "Thomas Becker and Volker Weispfenning",
title = "The {Chinese} remainder problem, multivariate
interpolation, and {Gr{\"o}bner} bases",
crossref = "Watt:1991:IPI",
pages = "64--69",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p64-becker/",
abstract = "Let $K(X)$ be a multivariate polynomial ring over a
field $K, I_1, \ldots{}, I_m$ ideals in $K(X)$, $U$
contained in $X$. Using a single Gr{\"o}bner basis in
an extension ring of $K(X)$, the authors solve the
following problems effectively. Given
$f_1,\ldots{},f_m$ in $K(X)$, put
$A_f=\cap_{k=1}^m(I_k+f_k)$. (1) Decide whether
$A_f\cap{}K(U)\ne0$ and if so, construct some element
of $A_f\cap{}K(U)$. (2) For given $g$ in $K(U)$, decide
whether $g\in{}A_f$. (3) Construct all elements of
$A_f\cap{}K(U)$. Taking for $I^k$ a suitable vanishing
ideal of some parametrized hypersurface in
$K^n(1<=k<=m)$, this solves a generalized Hermite and
spline interpolation problem.",
acknowledgement = ack-nhfb,
affiliation = "Fakultat fur Math. und Inf., Passau Univ., Germany",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; theory; Hermite problem; Chinese remainder
problem; Multivariate interpolation; Gr{\"o}bner bases;
Multivariate polynomial ring; Extension ring; Vanishing
ideal; Parametrized hypersurface; Spline
interpolation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.2.m} Mathematics of Computing, DISCRETE
MATHEMATICS, Miscellaneous. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations.",
thesaurus = "Interpolation; Polynomials; Splines [mathematics]",
}
@InProceedings{Belkov:1991:RUC,
author = "Alexander A. Bel'kov and Alexander V. Lanyov",
title = "{REDUCE} usage for calculation of low-energy process
amplitudes in chiral {QCD} model",
crossref = "Watt:1991:IPI",
pages = "454--455",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p454-bel_kov/",
abstract = "Describes the extension of REDUCE capabilities for the
calculations of strong and weak meson processes within
the chiral Lagrangians with higher derivatives. The
main non-trivial difficulty is to obtain the process
amplitude from the Lagrangian, describing these
interactions. Another one is to overcome some REDUCE
deficiencies such as the lack of arguments in the
matrix data type as well as of some physical operations
with the particle operators. This package of procedures
allows one to calculate the amplitudes of the strong
and weak processes by simple specifying the particles
involved and their momenta.",
acknowledgement = ack-nhfb,
affiliation = "Particle Phys. Lab., JINR, Moscow, USSR",
classification = "A0270 (Computational techniques); A1110 (Field
theory); A1130R (Chiral symmetries); A1235C (General
properties of quantum chromodynamics (dynamics,
confinement, etc.)); C7320 (Physics and Chemistry)",
keywords = "algorithms; Chiral Lagrangians; Meson processes;
REDUCE capabilities",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Chiral symmetries; Colour model; Meson field theory;
Physics computing; Symbol manipulation",
}
@InProceedings{Berndt:1991:ACA,
author = "R. Berndt and A. Lock and G. Witte and C. h.
W{\"o}ll",
title = "Application of computer algebra to surface lattice
dynamics",
crossref = "Watt:1991:IPI",
pages = "433--438",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p433-berndt/",
abstract = "Lattice dynamical calculations for surfaces and in
particular for stepped and absorbed covered surfaces
are commonly hampered by the complexity of the
dynamical matrix for these systems. The authors propose
the use of computer algebra programs to set up the
dynamical matrix. In the present implementation the
dynamical matrix is calculated fully analytically
within the framework of a force constant-mode and
partially analytically for other interaction models
such as the shell model or the bond charge model.",
acknowledgement = ack-nhfb,
affiliation = "Max-Planck Inst. fur Stromungsforschung, Gottingen,
Germany",
classification = "A6830 (Dynamics of solid surfaces and interface
vibrations); A6845 (Solid-fluid interface processes);
C4140 (Linear algebra); C7320 (Physics and Chemistry)",
keywords = "Absorbed covered surfaces; algorithms; Bond charge
model; Computer algebra; Dynamical matrix; Force
constant-mode; Interaction models; languages; Shell
model; Surface lattice dynamics",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.2.m} Mathematics of
Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN.",
thesaurus = "Adsorbed layers; Crystal surface and interface
vibrations; Matrix algebra; Phonon dispersion
relations; Physics computing; Symbol manipulation",
}
@InProceedings{Beth:1991:FGN,
author = "T. Beth and W. Geiselmann and F. Meyer",
title = "Finding (good) normal bases in finite fields",
crossref = "Watt:1991:IPI",
pages = "173--178",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p173-beth/",
abstract = "An algorithm to generate low complexity normal bases
in finite fields is presented. This algorithm
generalizes the method of Ash et al. to fields of
arbitrary characteristic. It can be applied to most
finite fields and produces (under certain conditions)
the multiplication matrix for the normal basis
multiplication of $\mbox{GF}(q^n):\mbox{GF}(q)$ in
$O(n^2 \log^2 n \log{}q)$ bit-operations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4240
(Programming and algorithm theory)",
keywords = "algorithms; Finite fields; Low complexity normal
bases; Multiplication matrix; Normal basis
multiplication",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations in finite fields. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Bosma:1991:CFG,
author = "Wieb Bosma and Michael Pohst",
title = "Computations with finitely generated modules over
{Dedekind} rings",
crossref = "Watt:1991:IPI",
pages = "151--156",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p151-bosma/",
abstract = "In computer algebra the use of normal forms for
matrices is of eminent importance. Especially, Hermite
and Smith normal form techniques are frequently used
for various computational problems over Euclidean
rings. The paper discusses a generalization of these
concepts to Dedekind rings. It considers the problem of
normal forms for matrices in the context of basis
transformations for finitely generated modules.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Pure Math., Sydney Univ., NSW, Australia",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; Basis transformations; Computer algebra;
Dedekind rings; Euclidean rings; Finitely generated
modules; Hermite normal form; Matrices; Smith normal
form; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Matrix algebra; Number theory",
}
@InProceedings{Bronstein:1991:RDE,
author = "Manuel Bronstein",
title = "The {Risch} differential equation on an algebraic
curve",
crossref = "Watt:1991:IPI",
pages = "241--246",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p241-bronstein/",
abstract = "The author presents a new rational algorithm for
solving Risch differential equations over algebraic
curves. This algorithm can also be used to solve
$n^{\mbox{th}}$-order linear ordinary differential
equations with coefficients in an algebraic extension
of the rational functions. In the general (`mixed
function') case, this algorithm finds the denominator
of any solution of the equation. The algorithm has been
implemented in the Maple and Scratchpad computer
algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Inf. ETH-Zentrum, Zurich, Switzerland",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "$N^{th}$-order linear ordinary differential equations;
Algebraic curve; algorithms; Computer algebra systems;
Maple; Rational algorithm; Rational functions; Risch
differential equation; Scratchpad",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
systems (direct and iterative methods). {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, SCRATCHPAD. {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Buchmann:1991:CNP,
author = "Johannes Buchmann and Volker M{\"u}ller",
title = "Computing the number of points of elliptic curves over
finite fields",
crossref = "Watt:1991:IPI",
pages = "179--182",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p179-buchmann/",
abstract = "The authors study the problem of counting the points
on an elliptic curve over a prime field. Although
Schoof (1985) proves that the cardinality of an
elliptic curve group over a finite field can be
computed in polynomial time, his algorithm is extremely
inefficient in practice. On the other hand, the
application of Shanks' babystep giantstep idea (1970)
to the problem yields an algorithm which is efficient
for medium size prime numbers but of exponential
complexity. So far no experimental results concerning
those algorithms have been published. The authors
present a practical improvement of the algorithm of
Shanks which is based on the ideas of Schoof. It turns
out to be very efficient.",
acknowledgement = ack-nhfb,
affiliation = "FB 14 Inf., Saarlandes Univ., Saarbrucken, Germany",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Cardinality; Elliptic curves; Finite
fields; Medium size prime numbers; Prime field",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Bundgen:1991:CIP,
author = "Reinhard B{\"u}ndgen",
title = "Completion of integral polynomials by {AC-term}
completion",
crossref = "Watt:1991:IPI",
pages = "70--78",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p70-bundgen/",
abstract = "The article presents a canonical term rewriting system
RX whose ground normal forms can directly be mapped to
integral polynomials in distributive normal form.
Completing RX and a set of ground equations simulates
the Gr{\"o}bner base computation for the ideal
presented by the ground equations. With this approach,
it clearly shows the correspondence of the key features
of algebraic completion procedures for integral
polynomial ideals and their simulation in a term
rewriting environment.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst., Tubingen Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C4210 (Formal logic)",
keywords = "algorithms; AC-term completion; Canonical term
rewriting system; Ground normal forms; Distributive
normal form; Ground equations; Gr{\"o}bner base
computation; Algebraic completion procedures; Integral
polynomial ideals",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials; Rewriting systems",
}
@InProceedings{Burge:1991:SRI,
author = "William H. Burge",
title = "{Scratchpad} and the {Rogers--Ramanujan} identities",
crossref = "Watt:1991:IPI",
pages = "189--190",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p189-burge/",
abstract = "This note sketches the part played by Scratchpad in
obtaining new proofs of Euler's theorem and the
Rogers--Ramanujan Identities.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Euler theorem; Infinite series; Restricted
partition pairs; Rogers--Ramanujan identities;
Scratchpad",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, SCRATCHPAD.",
thesaurus = "Mathematics computing; Number theory; Symbol
manipulation",
}
@InProceedings{Butler:1991:DDG,
author = "Greg Butler and Sridhar S. Iyer and Susan H. Ley",
title = "A deductive database of the groups of order dividing
128",
crossref = "Watt:1991:IPI",
pages = "210--218",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p210-butler/",
abstract = "The paper describes the design and implementation of a
deductive database for the 2668 groups of order $2^n$,
($n<=7$). The system was implemented in NU-Prolog, a
Prolog system with built-in functions for creating and
using deductive databases. In addition to the database,
a simple query language was written. This enables
database users to assess the data using a simpler and
more familiar set-theoretic syntax than that provided
by the Prolog interpreter.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Sydney Univ., NSW, Australia",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C6160Z (Other DBMS); C6170 (Expert systems); C7310
(Mathematics)",
keywords = "Built-in functions; Deductive database; design;
languages; NU-Prolog; Query language; Set-theoretic
syntax",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Special-purpose algebraic
systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, Prolog.",
thesaurus = "Deductive databases; Group theory; Knowledge based
systems; Mathematics computing; Set theory",
}
@InProceedings{Canny:1991:OCD,
author = "John Canny and J. Maurice Rojas",
title = "An optimal condition for determining the exact number
of roots of a polynomial system",
crossref = "Watt:1991:IPI",
pages = "96--102",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p96-canny/",
abstract = "It was shown by Bernshtein (1975) that the number of
roots in $(C*)^n$ of a polynomial system depends only
on the Newton polytopes of the system, for almost all
specializations of the coefficients. This result,
referred to as the BKK bound, gives an upper bound on
the number of roots of a polynomial system. The BKK
bound is often much better than the Bezout bound for
the same system, but the original theorem gives an
exact bound only if all the coefficients corresponding
to Newton polytope boundaries are generically chosen.
The current paper shows that the BKK bound is exact
under much weaker assumptions: only coefficients
corresponding to certain vertices of the Newton
polytopes need be generic. This result allows
application of the BKK bound to many practical
problems.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; BKK bound; Newton polytopes; Optimal
condition; Polynomial system; Roots; theory; Upper
bound; verification; Vertices",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Chen:1991:NNF,
author = "Guoting Chen and Jean Della Dora and Laurent
Stolovitch",
title = "Nilpotent normal form via {Carleman} linearization
(for systems of ordinary differential equations)",
crossref = "Watt:1991:IPI",
pages = "281--288",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p281-chen/",
abstract = "Considers in this paper the normal formal problem for
systems of nonlinear ordinary differential equations
with singularity at the origin. The problem has its
origin in the classical work of Poincare. The authors
define a normal form for differential systems whose
linear part is nilpotent which is called nilpotent
normal form. They give an algorithm for the computation
of the normal form and the transformation that leads a
system to its normal form. The elementary notations and
methods used in the paper are the Carleman
linearizations of differential systems and formal
diffeomorphisms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Math., Univ. Louis Pasteur, Strasbourg,
France",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Carleman linearizations; Formal
diffeomorphisms; Nilpotent normal form; Nonlinear
ordinary differential equations; Normal form;
Singularity; Transformation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Nonlinear differential equations",
}
@InProceedings{Cohen:1991:OES,
author = "Ian Cohen and Karl-Erik E. Thylwe",
title = "Obtaining exact steady-state responses in driven
undamped oscillators",
crossref = "Watt:1991:IPI",
pages = "319--320",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p319-cohen/",
abstract = "Exact solutions are very scarce in non-linear applied
mathematics. However, exact solutions can be an
invaluable aid to understanding how well an approximate
method is working. It can also be used as a `stepping
off' solution into parameter regions where no exact
solutions exist. Most importantly however, each exact
solution is a potential candidate for a new area of
research as it can contain new insights into the
physics of the equation under investigation or may be
used to replace numerical methods in an investigation.
Another important motivation is the synthesis in this
project of Gr{\"o}bner bases with dynamical systems
research, two areas at the forefront of modern
research.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech., R. Inst. of Technol., Stockholm,
Sweden",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Steady-state responses; Undamped
oscillators; Gr{\"o}bner bases; Dynamical systems",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Differential equations; Nonlinear systems",
}
@InProceedings{Crouch:1991:CID,
author = "Peter Crouch and Robert Grossman and Richard Larson",
title = "Computations involving differential operators and
their actions on functions",
crossref = "Watt:1991:IPI",
pages = "301--307",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p301-crouch/",
abstract = "Further develops the authors algorithms for rewriting
expressions involving differential operators. The
differential operators considered arise in the local
analysis of nonlinear dynamical systems. The authors
extend these algorithms in two different directions:
they generalize the algorithms so that they apply to
differential operators on groups and develop the data
structures and algorithms to compute symbolically the
action of differential operators on functions. Both of
these generalizations are needed for applications. The
paper is preliminary: a final paper containing proofs
and a further analysis of the algorithm will appear
elsewhere.",
acknowledgement = ack-nhfb,
affiliation = "Arizona State Univ., Tempe, AZ, USA",
classification = "C6120 (File organisation); C7310 (Mathematics)",
keywords = "algorithms; Data structures; Differential operators;
Nonlinear dynamical systems; Rewriting expressions;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures.",
thesaurus = "Rewriting systems; Symbol manipulation",
}
@InProceedings{Czapor:1991:HSS,
author = "S. R. Czapor",
title = "A heuristic selection strategy for lexicographic
{Gr{\"o}bner} bases?",
crossref = "Watt:1991:IPI",
pages = "39--48",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p39-czapor/",
abstract = "It is well known that the computation of lexicographic
Gr{\"o}bner bases using the Buchberger's algorithm is
more difficult than the computation of Gr{\"o}bner
bases with respect to total degree orderings. The
lexicographic algorithm is particularly susceptible to
the problem of intermediate expression swell; that is,
intermediate polynomials may be far larger than those
which make up the final basis. To some extent, this is
a function of `selection strategy', i.e. the order in
which S-polynomials are used to extend a partial basis.
The paper argues and provides empirical evidence that
for the lexicographic ordering (in direct contrast to
the case of degree orderings), a simple heuristic
strategy will in practice control intermediate growth
more effectively than the normal strategy based on the
lexicographic term ordering alone. The results is
usually a much more efficient computation, even for
nonzero dimension ideals.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Stat. and Comput. Sci., Dalhousie
Univ., Halifax, NS, Canada",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; Heuristic selection strategy;
Lexicographic Gr{\"o}bner bases; Buchberger's
algorithm; Intermediate expression swell; Intermediate
polynomials; S-polynomials; Partial basis;
Lexicographic ordering; Intermediate growth; Nonzero
dimension ideals",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.0} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, General.",
thesaurus = "Polynomials",
}
@InProceedings{Davenport:1991:SVA,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s view of algebra. {II}. {A} categorical
view of factorization",
crossref = "Watt:1991:IPI",
pages = "32--38",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p32-davenport/",
abstract = "For pt.I see Proc. DISCO 1990 (p.40-54). The paper
explains how Scratchpad solves the problem of
presenting a categorical view of factorization in
unique factorization domains, i.e. a view which can be
propagated by functors such as
SparseUnivariatePolynomial or Fraction. This is not
easy, as the constructive version of the classical
concept of UniqueFactorizationdomain cannot be so
propagated. The solution adopted is based largely on
the Seidenberg conditions ($F$) and ($P$), but there
are several additional points that have to be borne in
mind to produce reasonably efficient algorithms in the
required generality. The consequence of the algorithms
and interfaces presented is that Scratchpad can
factorize in any extension of the integers or finite
fields by any combination of polynomial, fraction and
algebraic extensions: a capability far more general
than any other computer algebra system possesses.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Bath Univ., Claverton Down, UK",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic extensions; algorithms; Categorical view;
Computer algebra system; Factorization; Finite fields;
Fraction; Integers; Polynomial; Scratchpad; Seidenberg
conditions",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations in finite fields.",
thesaurus = "Mathematics computing; Polynomials; Symbol
manipulation",
}
@InProceedings{deJager:1991:SCZ,
author = "Bram de Jager",
title = "Symbolic calculation of zero dynamics for nonlinear
control systems",
crossref = "Watt:1991:IPI",
pages = "321--322",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p321-de_jager/",
abstract = "The calculation of the zero dynamics of a nonlinear
system is of advantage in the design of controllers for
this system. Because the calculation is difficult to do
by hand, symbolic algebra programs are used. To access
the usefulness of these programs and to solve some
design problems, a MAPLE procedure, ZERODYN, is written
to calculate the zero dynamics symbolically. The
procedure can, however, not solve all problems, mainly
because general symbolic algebra programs have
insufficient capabilities to solve sets of nonlinear
equations and partial differential equations. A
realistic analysis problem shows this.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. Eng., Eindhoven Univ. of Technol.,
Netherlands",
classification = "C1340K (Nonlinear systems); C7310 (Mathematics)",
keywords = "algorithms; experimentation; MAPLE procedure;
Nonlinear control systems; Nonlinear system; Partial
differential equations; Symbolic algebra; Zero
dynamics; ZERODYN",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Nonlinear control systems; Symbol manipulation",
}
@InProceedings{Diaz:1991:DSD,
author = "A. Diaz and E. Kaltofen and K. Schmitz and T. Valente
and M. Hitz and A. Lobo and P. Smyth",
title = "{DSC}: a system for distributed symbolic computation",
crossref = "Watt:1991:IPI",
pages = "323--332",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p323-diaz/",
abstract = "DSC is a general purpose tool that allows the
distribution of a computation over a network of Unix
workstations. Its control mechanisms automatically
start up daemon processes on the participating
workstations in order to communicate data by the
standard IP/TCP/UDP protocols. The user's program
distributes either remote procedure calls or source
code of programs and their corresponding input data
files by calling a DSC library function. The authors
have tested DSC with a primarily test for large
integers and with a factorization algorithm for
polynomials over large finite fields and observed
significant speed-ups over executing the best-known
methods on a single workstation computation. These
experiments have been carried out not only on our local
area network but also on off-site workstations at the
University of Delaware.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Distributed symbolic computation; DSC;
experimentation; Factorization algorithm; Large
integers; Polynomials; Primarily test; Unix
workstations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf D.2.2} Software, SOFTWARE
ENGINEERING, Design Tools and Techniques, User
interfaces.",
thesaurus = "Distributed processing; Software packages; Symbol
manipulation",
}
@InProceedings{Faradzev:1991:CCC,
author = "I. A. Faradzev and M. H. Klin",
title = "For computations with coherent configurations",
crossref = "Watt:1991:IPI",
pages = "219--223",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p219-faradzev/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory. {\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Permutations and
combinations.",
}
@InProceedings{Faradzev:1991:CPC,
author = "I. A. Faradzev and M. H. Klin",
title = "Computer package for computations with coherent
configurations",
crossref = "Watt:1991:IPI",
pages = "219--223",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A collection of computer programs based on the Galois
correspondence between coherent configurations and
permutation groups is described. A number of examples
of application of this package for construction of
combinatorial objects with interesting properties and
for solving some group theoretical problems (extension
of a permutation group and intersection of subgroups)
are presented.",
acknowledgement = ack-nhfb,
affiliation = "inst. for Syst. Studies, Acad. of Sci., Moscow, USSR",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "Coherent configurations; Combinatorial objects;
Computer programs; Galois correspondence; Group
theoretical problems; Permutation groups",
thesaurus = "Group theory; Mathematics computing; Software
packages; Symbol manipulation",
}
@InProceedings{Fateman:1991:CRL,
author = "Richard J. Fateman",
title = "Canonical representations in {Lisp} and applications
to computer algebra systems",
crossref = "Watt:1991:IPI",
pages = "360--369",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p360-fateman/",
abstract = "Lisp, as well as many other programming languages,
provides for the creation of compound data-structures
or objects. What if one follows a discipline in which
any time one constructs an object which happens to be
isomorphic to one previously stored, the constructor
function simply returns the same location in memory as
the first? The author discusses some of the advantages
and show how an implementation fits neatly into Common
Lisp. Some of the results are especially relevant for
the design and implementation of efficient `general
representation' computer algebra systems. The author
gives some experimental results showing speedups of a
factor of ten or more in basic operations such as
simplification of sums.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electron. Eng. and Comput. Sci., California
Univ., Berkeley, CA, USA",
classification = "C6120 (File organisation); C6140D (High level
languages); C7310 (Mathematics)",
keywords = "algorithms; Canonical representation; Computer algebra
systems; experimentation; languages; Lisp",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Common Lisp. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Data structures; LISP; Symbol manipulation",
}
@InProceedings{Gaal:1991:RIF,
author = "I. Ga{\'a}l and A. Peth{\"o} and M. Pohst",
title = "On the resolution of index form equations",
crossref = "Watt:1991:IPI",
pages = "185--186",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p185-gaal/",
abstract = "For practical applications it is very important to
know a power integral basis of the algebraic number
field $K$. The solutions of the index form equation,
$I(x_2,\ldots{},x_n)=\pm 1$ in $x_2,\ldots{},x_n$ in
$Z$ enable one to determine all power integral bases of
$K$. If there are no power integral bases, then the
best is to determine all integral elements of $K$,
having the least possible index, i.e. to determine the
least positive $m$ in $Z$ for which
$I(x_2,\ldots{},x_n)=\pm m$ in $x_2,\ldots{},x_n$ in
$Z$ is soluble and to compute all solutions of this
equation to find all integral elements with least
index. The authors discuss their attempts at
constructing algorithms to solve the equations and
results obtained.",
acknowledgement = ack-nhfb,
affiliation = "Kossuth Lajos Univ., Debrecen, Hungary",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; Index form equations; Power integral
basis",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
thesaurus = "Algebra; Number theory",
}
@InProceedings{Ganzha:1991:SAD,
author = "V. G. Ganzha and B. Yu. Scobelev and E. V.
Vorozhtsov",
title = "Stability analysis of difference schemes by the
catastrophe theory methods and by means of computer
algebra",
crossref = "Watt:1991:IPI",
pages = "427--428",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p427-ganzha/",
abstract = "A new method for determining the stability domains of
difference schemes(d.s.) is based on the Fourier method
and the methods of catastrophe theory. In the paper the
authors propose a symbolic-numerical approach to a
realization of the method of the work.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Catastrophe theory; Computer algebra;
Difference schemes; Stability analysis; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Catastrophe theory; Convergence of numerical methods;
Difference equations; Symbol manipulation",
}
@InProceedings{Gao:1991:CPE,
author = "Xiao-Shan Gao and Shang-Ching Chou",
title = "Computations with parametric equations",
crossref = "Watt:1991:IPI",
pages = "122--127",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p122-gao/",
abstract = "The authors present a complete method of
implicitization for general rational parametric
equations. They also present a method to decide whether
the parameters of a set of parametric equations (PEs)
are independent, and if not, to reparameterize the PEs
so that the new PEs have independent parameters. They
give a method to compute the inversion maps of the PEs
with independent parameters, and as a consequence, they
can decide whether the PEs are proper. A new method to
find a proper reparameterization for a set of improper
PEs of algebraic curves is presented.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Algebraic curves; algorithms; Implicitization;
Independent parameters; Inversion maps; Rational
parametric equations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Gatermann:1991:MSS,
author = "Karin Gatermann",
title = "Mixed symbolic-numeric solution of symmetrical
nonlinear systems",
crossref = "Watt:1991:IPI",
pages = "431--432",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p431-gatermann/",
abstract = "The mixed symbolic-numeric algorithm SYMCON for the
fully automatic treatment of equivariant systems is
presented. The global aspects of the theory of
Vanderbauwhede (1982) for these systems are viewed with
regard to the full bifurcation scenario containing
solution paths with different isotropy groups and
symmetry preserving and symmetry breaking bifurcation
points. The advanced exploitation of symmetry in the
numerical computations causes a comprehensive symmetry
analysis and complicated organization of numerical work
which is done by the symbolic part of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Konrad-Zuse-Zentrum Berlin, Germany",
classification = "C1340K (Nonlinear systems); C4150 (Nonlinear and
functional equations)",
keywords = "algorithms; Bifurcation points; Equivariant systems;
Symbolic-numeric algorithm; SYMCON; Symmetrical
nonlinear systems; Symmetry analysis; theory",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Nonlinear systems; Symbol manipulation",
}
@InProceedings{Gebauer:1991:CCA,
author = "R. Gebauer and M. Kalkbrener and B. Wall and F.
Winkler",
title = "{CASA}: a computer algebra package for constructive
algebraic geometry",
crossref = "Watt:1991:IPI",
pages = "403--410",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p403-gebauer/",
abstract = "The program package CASA is designed to enhance the
power of a traditional computer algebra system by
adding programs for constructive algebraic geometry.
The objects that CASA works with are algebraic sets in
affine or projective spaces over a field. The geometric
objects may be given in various different
representations. CASA is able to analyse properties of
algebraic sets, such as to compute their dimensions,
compute their irreducible components, determine
singular points, determine intersection properties and
the like. The user can also create 2- and 3-dimensional
pictures of curves and surfaces.",
acknowledgement = ack-nhfb,
affiliation = "Johannes Kepler Univ., Linz, Austria",
classification = "C4190 (Other numerical methods)",
keywords = "Algebraic geometry; Algebraic sets; algorithms; CASA;
Computer algebra; Computer algebra package;
Constructive algebraic geometry; Intersection
properties; Irreducible components; Singular points",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational geometry; Symbol manipulation",
}
@InProceedings{Gerdt:1991:LSC,
author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
title = "{Lie--B{\"a}cklund} symmetries of coupled nonlinear
{Schr{\"o}dinger} equations",
crossref = "Watt:1991:IPI",
pages = "313--314",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p313-gerdt/",
abstract = "Applies computer-aided symmetry approach to an
investigation of an eight-parametric system of two
coupled nonlinear Schr{\"o}dinger equations. Symmetry
approach allows one not only to verify the necessary
integrability conditions which follow from the
existence of a higher infinitesimal or
Lie--B{\"a}cklund symmetry but often to find an
explicit form of the latter. The corresponding
necessary conditions in the form of existence of the
series of the local conservation laws lead to the
system of nonlinear algebraic equations in numeric
parameters. As a result of the first two necessary
integrability conditions the REDUCE program provided
with some new additional facilities, generates the
three set of algebraic equations.",
acknowledgement = ack-nhfb,
affiliation = "JINR, Moscow, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Lie--B{\"a}cklund symmetry; Nonlinear
Schr{\"o}dinger equations",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE.",
thesaurus = "Schr{\"o}dinger equation; Symbol manipulation",
}
@InProceedings{Giovini:1991:OSC,
author = "Alessandro Giovini and Teo Mora and Gianfranco Niesi
and Lorenzo Robbiano and Carlo Traverso",
title = "`One sugar cube, please' or selection strategies in
the {Buchberger} algorithm",
crossref = "Watt:1991:IPI",
pages = "49--54",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p49-giovini/",
abstract = "The paper describes some experimental findings on
selection strategies for Gr{\"o}bner basis computation
with the Buchberger algorithm. In particular, the
results suggest that the sugar flavor of the normal
selection is the best choice for a selection strategy.
It has to be combined with the straightforward
simplification strategy and with a special form of the
Gebauer--Moller criteria to obtain the best results.
The idea of the sugar flavor is the following: the
Buchberger algorithm for homogeneous ideals, with
degree-compatible term ordering and normal selection
strategy, usually works fine. Homogenizing the basis of
the ideal is good for the strategy, but bad for the
basis to be computed. The sugar flavor computes, for
every polynomial in the course of the algorithm, `the
degree that it would have if computed with the
homogeneous algorithm', and uses this phantom degree
(the sugar) only for the selection strategy.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genova Univ., Italy",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; experimentation; Selection strategies;
Buchberger algorithm; Gr{\"o}bner basis computation;
Sugar flavor; Normal selection; Straightforward
simplification strategy; Gebauer--Moller criteria;
Homogeneous ideals; Degree-compatible term ordering;
Polynomial; Homogeneous algorithm; Phantom degree",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Gonzalez-Vega:1991:STM,
author = "Laureano Gonz{\'a}lez-Vega",
title = "A subresultant theory for multivariate polynomials",
crossref = "Watt:1991:IPI",
pages = "79--85",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p79-gonzalez-vega/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Gonzalez-Vega:1991:WRA,
author = "Laureano Gonz{\'a}lez-Vega",
title = "Working with real algebraic plane curves in {REDUCE}
the {GCUR} package",
crossref = "Watt:1991:IPI",
pages = "397--402",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p397-gonzalez-vega/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Graph algorithms.",
}
@InProceedings{GonzalezVega:1991:STM,
author = "L. {Gonzalez Vega}",
title = "A subresultant theory for multivariate polynomials",
crossref = "Watt:1991:IPI",
pages = "79--85",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In computer algebra, subresultant theory provides a
powerful method to construct algorithms solving
problems for polynomials in one variable in an optimal
way. The paper extends the subresultant theory to the
multivariate case. In order to achieve this, first of
all, it introduces the definition of a subresultant
sequence associated to two polynomials in one variable
with coefficients in an integral domain, describing the
properties of this sequence that one would like to
extend to the multivariate case. In the second section
it generalizes the definition of a subresultant
polynomial to the multivariate case, showing that many
of the properties obtained in the one variable case
work also in the multivariate case. In this way it
shows how these subresultants can be used to get a
greatest common divisor of $n$ polynomials in
$D(x_1,\ldots{},x_{n-1})$ where $D$ is an integral
domain. The paper then applies this subresultant theory
to get a determinantal formula for the solution set of
almost all $0$-dimensional ideals defined by $n$
polynomials in $D(x_1, \ldots{}, x_n)$, with $D$ an
integral domain. Finally, some open problems related
with this construction are shown.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Matematicas, Cantabria Univ., Santander,
Spain",
classification = "C4130 (Interpolation and function approximation)",
keywords = "0-Dimensional ideals; Computer algebra; Determinantal
formula; Greatest common divisor; Integral domain;
Multivariate polynomials; Solution set; Subresultant
polynomial; Subresultant sequence; Subresultant
theory",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{GonzalezVega:1991:WRA,
author = "L. {Gonzalez Vega}",
title = "Working with real algebraic plane curves in {REDUCE}:
the {GCUR} package",
crossref = "Watt:1991:IPI",
pages = "397--402",
year = "1991",
bibdate = "Sat Apr 25 12:53:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents an implementation in Reduce of a package to
get topological and geometric information about real
algebraic plane curves defined as the real zeros of
polynomials in $Z(x, y)$. More precisely, if $P$ in
$Z(x,y)$ the output using the package GCUR will be a
plane graph homeomorphic to the set:
$C(P)=((\alpha,\beta) {\rm in }
R^2/P(\alpha,\beta)=0)$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. Mat., Cantabria Univ., Santander, Spain",
classification = "C4190 (Other numerical methods)",
keywords = "Algebraic plane curves; GCUR; Geometric information;
Plane graph; REDUCE; Topological information",
thesaurus = "Computational geometry; Poles and zeros; Polynomials;
Symbol manipulation; Topology",
}
@InProceedings{Grigoriev:1991:ASR,
author = "Dima Yu. u. Grigoriev and Marek Karpinski",
title = "Algorithms for sparse rational interpolation",
crossref = "Watt:1991:IPI",
pages = "7--13",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p7-grigoriev/",
abstract = "Presents two algorithms for interpolating sparse
rational functions. The first is the interpolation
algorithm in a sense of sparse partial fraction
representation of rational functions. The second is the
algorithm for computing the entier and the remainder of
a rational function. The first algorithm works without
a priori known bound on the degree of a rational
function, the second one is in the parallel class NC
provided that the degree is known.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Bonn Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Entier; Interpolation algorithm; NC;
Parallel class; Remainder; Sparse partial fraction
representation; Sparse rational functions",
subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Computational complexity; Interpolation; Parallel
algorithms",
}
@InProceedings{Grudtsin:1991:ISI,
author = "S. N. Grudtsin and V. N. Larin",
title = "Integrated system {INTERCOMP} and computer language
for physicists",
crossref = "Watt:1991:IPI",
pages = "377--381",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p377-grudtsin/",
abstract = "Contains a description of a general approach to
physics related integrated software elaborations. A
development history and modern stage of the INTERCOMP
system, containing a large set of language and program
means for a description and computer analysis of
physical models are also described. The system has a
high level interpreted language and includes a powerful
symbolic algebraic computation subsystem, a numeric
algorithms library, a relational DBMS, a graphic
package, editor and text processor.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for High Energy Phys., Protvino, USSR",
classification = "C6140D (High level languages); C7320 (Physics and
Chemistry)",
keywords = "Algebraic; Computer analysis; Computer language;
Graphic package; Integrated software elaborations;
INTERCOMP; languages; Numeric algorithms; Physical
models; Relational DBMS; Symbolic computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "High level languages; Physics computing; Symbol
manipulation",
}
@InProceedings{Havas:1991:CES,
author = "George Havas",
title = "Coset enumeration strategies",
crossref = "Watt:1991:IPI",
pages = "191--199",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p191-havas/",
abstract = "A primary reference on computer implementation of
coset enumeration procedures is a 1973 paper of Cannon,
Dimino, Havas and Watson. Programs and techniques
described there are updated in this paper. Improved
coset definition strategies, space saving techniques
and advice for obtaining improved performance are
included. New coset definition strategies for
Felsch-type methods give substantial reductions in
total cosets defined for some pathological
enumerations. Significant time savings are achieved for
coset enumeration procedures in general. Statistics on
performance are presented, both in terms of time and in
terms of maximum and total cosets defined for selected
enumerations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Queensland Univ., St. Lucia,
Qld., Australia",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "Coset definition strategies; Coset enumeration
procedures; Felsch-type methods; Pathological
enumerations; performance; Subgroups",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, CAYLEY.",
thesaurus = "Mathematics computing; Set theory",
}
@InProceedings{Hietarinta:1991:SIP,
author = "Jarmo Hietarinta",
title = "Searching for integrable {PDE}'s by testing {Hirota}'s
three-soliton condition",
crossref = "Watt:1991:IPI",
pages = "295--300",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p295-hietarinta/",
abstract = "The search for integrable PDE's has been an active
research subject with computer algebra as a necessary
tool. The author describes a search method based on the
requirement that standard type three- and four-soliton
solution exist in the bilinear formalism of Hirota. The
existence of $N$-soliton solutions can be formulated as
a requirement that a certain high degree polynomial in
$N*M$ variables vanishes on an affine manifold defined
by $N$ polynomials of $M$ variables each. An exhaustive
search has been carried out for certain classes of
typical equations and several new equations have been
found.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Phys., Turku Univ., Finland",
classification = "A0230 (Function theory, analysis); A0340K (Waves and
wave propagation: general mathematical aspects)",
keywords = "algorithms; Bilinear formalism; Computer algebra;
Integrable PDE's; Search method; theory; Three-soliton
condition",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Partial differential equations; Search problems;
Solitons; Symbol manipulation",
}
@InProceedings{Ilyin:1991:PIF,
author = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and
A. Yu. Taranov",
title = "{PC} implementation of fast {Dirac} matrix trace
calculations",
crossref = "Watt:1991:IPI",
pages = "456--457",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p456-ilyin/",
abstract = "Presents an implementation of a fast algorithm for
Dirac matrix trace calculations. This implementation is
made for IBM compatible PC and works under REDUCE
3.3.1. Name of package is CVIT. The algorithm is based
on intense use of Fierz identities in N-dimensional
space ($N$ is arbitrary natural number or symbol) and
may be considered as an extension of well known Kahane
algorithm on higher space dimensions.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR",
classification = "C7320 (Physics and Chemistry)",
keywords = "algorithms; CVIT; Dirac matrix trace calculations;
Fierz identities; IBM compatible PC; Kahane algorithm;
N-dimensional space; REDUCE 3.3.1",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics.",
thesaurus = "IBM computers; Matrix algebra; Physics computing;
Symbol manipulation",
}
@InProceedings{Ilyin:1991:SST,
author = "V. A. Ilyin and A. P. Kryukov",
title = "Symbolic simplification of tensor expressions using
symmetries, dummy indices and identities",
crossref = "Watt:1991:IPI",
pages = "224--228",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p224-ilyin/",
abstract = "The algorithm based on simple geometrical ideas is
suggested for simplification of tensor expressions
which takes into account symmetries, dummy indices, and
linear identities with many terms. The results of the
realization in REDUCE system are adduced. The Riemann
tensor is used as an example.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "algorithms; Dummy indices; Geometrical ideas; Linear
identities; REDUCE; Simplification; Symbolic
simplification; Symmetries; Tensor expressions",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Kleczka:1991:SCA,
author = "W. Kleczka and E. Kreuzer",
title = "Systematic computer-aided analysis of dynamic
systems",
crossref = "Watt:1991:IPI",
pages = "429--430",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p429-kleczka/",
abstract = "An automated numerical-symbolical analysis concept for
dynamic systems in engineering mechanics is outlined.
Besides the computerized generation of symbolic
equations of motion, the subsequent analysis is also
performed by means of computer algebra in combination
with well-established numerical methods.",
acknowledgement = ack-nhfb,
affiliation = "Meerestech. II, Tech. Univ., Hamburg-Harburg,
Germany",
classification = "C1210 (General system theory); C7440 (Civil and
mechanical engineering)",
keywords = "algorithms; Computer-aided analysis; Dynamic systems;
Engineering mechanics; Numerical-symbolical analysis;
Symbolic equations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Engineering. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods).",
thesaurus = "Computer aided analysis; Convergence of numerical
methods; Mechanical engineering computing; Symbol
manipulation",
}
@InProceedings{Kornyak:1991:PSA,
author = "V. V. Kornyak and W. I. Fushchich",
title = "A program for symmetry analysis of differential
equations",
crossref = "Watt:1991:IPI",
pages = "315--316",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p315-kornyak/",
abstract = "Proposes in this work a program for determining
Lie--B{\"a}cklund (LB) symmetries of (partial or
ordinary) differential equations and for classification
of equations containing arbitrary functions and
parameters with respect to symmetries of this kind. The
program was implemented in Turbo C language and
designed in such a way to be more effective for systems
of equations with multidimensional spaces of
independent and dependent variables. The internal data
structures for representation of expressions are
right-threaded binary trees. The program reduces input
system of equations to the passive form, computes the
differential consequences of equations up to the needed
order, constructs the invariance conditions for a given
order LB symmetries, eliminates the dependencies
between the invariance conditions using differential
manifold, separates the determining equations and tries
to integrate them.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Res., Acad. of Sci., Kiev, Ukrainian
SSR, USSR",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Differential equations; languages;
Lie--B{\"a}cklund symmetries; Symmetry analysis",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Turbo C.",
thesaurus = "Differential equations",
}
@InProceedings{Kuchlin:1991:MCI,
author = "Wolfgang K{\"u}chlin",
title = "On the multi-threaded computation of integral
polynomial greatest common divisors",
crossref = "Watt:1991:IPI",
pages = "333--342",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p333-kuchlin/",
abstract = "Reports experiences and practical results from
parallelizing the Brown--Collins polynomial g.c.d.
algorithm, starting from Collins' SAC-2 implementation
IPGCDC. The parallelization environment is PARSAC-2, a
multi-threaded version of SAC-2 programmed in C with
the parallelization constructs of the C Threads
library. IPGCDC computes the g.c.d. and its co-factors
of two polynomials in $Z(x_1,\ldots{},x_r)$, by first
reducing the problem to multiple calculations of
modular polynomial g.c.d.'s in $Z_p(x_1,\ldots{},x_r)$,
and then recovering the result by Chinese remaindering.
After studying timings of the SAC-2 algorithm, the
author first parallelizes the Chinese remainder
algorithm, and then parallelizes the main loop of
IPGCDC by executing the modular g.c.d. computations
concurrently. Finally, he determines speed-up's and
speed-up efficiencies of our parallel algorithms over a
wide range of polynomials. The experiments were
conducted on a 12 processor Encore Multimax under
Mach.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Brown--Collins polynomial g.c.d.
algorithm; Chinese remaindering; Encore Multimax;
Multi-threaded computation; PARSAC-2; Polynomial
greatest common divisors",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf I.1.3} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Mathematics computing; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Langemyr:1991:ASA,
author = "Lars Langemyr",
title = "An analysis of the subresultant algorithm over an
algebraic number field",
crossref = "Watt:1991:IPI",
pages = "167--172",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p167-langemyr/",
abstract = "The author shows that one can compute the subresultant
polynomial remainder sequence over an algebraic number
field in $O((n^5m^3+n^4m^5) \log^2(nDE^m))$ binary
operations, where the generator of the field is given
by a monic irreducible polynomial of degree $m$ with
integer coefficients bounded by $E$ in absolute value,
and where the two input polynomials are of degree at
most $n$ and with integer coefficients bounded by $D$
in absolute value.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Algebraic number field; algorithms; Greatest common
division; Integer coefficients; Monic irreducible
polynomial; Subresultant polynomial remainder
sequence",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Number-theoretic computations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Algebra; Computational complexity; Mathematics
computing; Number theory; Polynomials",
}
@InProceedings{Letichevsky:1991:APO,
author = "A. A. Letichevsky and J. V. Kapitonova and S. V.
Konozenko",
title = "Algebraic programs optimization",
crossref = "Watt:1991:IPI",
pages = "370--376",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p370-letichevsky/",
abstract = "Algebraic program is a system of relations (equalities
of data algebra) with a given strategy for applying
these relations as rewriting rules. An algebraic
program may be optimized by transforming a system of
relations or by transforming a strategy. Only second
case of optimization is considered in the paper. The
problem of algebraic program optimization is
investigated in the context of programming in the APS-1
system.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
Ukrainian SSR, USSR",
classification = "C6110 (Systems analysis and programming); C7310
(Mathematics)",
keywords = "Algebraic program optimization; algorithms; APS-1;
Data algebra; languages; Programming; Rewriting rules;
System of relations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.6} Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures.",
thesaurus = "Optimisation; Programming; Symbol manipulation",
}
@InProceedings{Liska:1991:ADS,
author = "Richard Liska and Michail Yu. u. Shashkov",
title = "Algorithms for difference schemes construction on
non-orthogonal logically rectangular meshes",
crossref = "Watt:1991:IPI",
pages = "419--426",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p419-liska/",
abstract = "Deals with the formalization of the basic operator
method for construction of difference schemes for the
numerical solving of partial differential equations.
The strength of the basic operator method lies in the
fact that it produces fully conservative difference
schemes. The difference mesh can be non-orthogonal but
has to be logically orthogonal. Algorithms for working
with grid functions and grid operators in symbolic form
which are necessary in the basic operator method are
described. The algorithms have been implemented in the
computer algebra system REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Czech Tech. Univ.,
Prague, Czechoslovakia",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Basic operator method; Computer algebra;
Difference mesh; Difference schemes; Grid functions;
Grid operators; Logically orthogonal; Numerical
solving; Partial differential equations; Rectangular
meshes; REDUCE",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Numerical methods; Partial differential equations;
Symbol manipulation",
}
@InProceedings{Manocha:1991:ETM,
author = "Dinesh Manocha and John Canny",
title = "Efficient techniques for multipolynomial resultant
algorithms",
crossref = "Watt:1991:IPI",
pages = "86--95",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p86-manocha/",
abstract = "The paper presents efficient techniques for applying
multipolynomial resultant algorithms and shows their
effectiveness for manipulating systems of polynomial
equations. In particular, it presents efficient
algorithms for computing the resultant of a system of
polynomial equations (whose coefficients may be
symbolic variables). These algorithms can be used for
interpolating polynomials from their values and
expanding symbolic determinants. Moreover, it uses
multipolynomial resultants for computing the real or
complex solutions of nonlinear polynomial equations. It
also discusses the implementation of these algorithms
in the context of certain applications.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Complex solutions; Efficient algorithms;
Multipolynomial resultant algorithms; Nonlinear
polynomial equations; Polynomial interpolation; Real
solutions; Symbolic determinants; Symbolic variables",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Algorithm theory; Interpolation; Polynomials",
}
@InProceedings{Marinari:1991:GBI,
author = "M. G. Marinari and H. M. M{\"o}ller and T. Mora",
title = "{Gr{\"o}bner} bases of ideals given by dual bases",
crossref = "Watt:1991:IPI",
pages = "55--63",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p55-marinari/",
abstract = "In 1982, Buchberger and Moller proposed an algorithm
which, given a finite number of rational points in the
affine $n$-dimensional space, computes a Gr{\"o}bner
basis for the ideal I of the polynomials vanishing at
the points. In 1988, Faugere, Gianni, Lazard and Mora
supplied an algorithm, which, given the reduced
Gr{\"o}bner basis w.r.t. some term-ordering $<_1$ of a
0-dim. ideal I, returns its reduced Gr{\"o}bner basis
w.r.t. some other term-ordering $<_2$. The paper
systematizes and generalizes the common properties of
the Buchberger--M{\"o}ller and the FGLM algorithms to
the frame of ideals defined by functionals. It gives
two algorithms to compute the Gr{\"o}bner basis of an
ideal defined by functionals, together with a set of
biorthogonal polynomials: the first one is a direct
generalization of the B-M and the FGLM algorithms; the
second one iteratively for each $i$ solves the question
for the ideals defined by $L_1,\ldots{}, L_i$. It then
measures the complexity of the algorithms in terms of
the number of additions+multiplications in $K$ which
they require and proves that both have a complexity of
$1/2 s^3+s^2 b+f s (s+b)<=O (n s^3+f n s^2)$.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genova Univ., Italy",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Gr{\"o}bner bases; Ideals; Dual bases;
Rational points; Affine $n$-dimensional space;
Term-ordering; Functionals; Biorthogonal polynomials;
Complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Marzinkewitsch:1991:OCA,
author = "Reiner Marzinkewitsch",
title = "Operating computer algebra systems by handprinted
input",
crossref = "Watt:1991:IPI",
pages = "411--413",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p411-marzinkewitsch/",
abstract = "Nearly twenty years have passed since the first
computer algebra systems (CAS) came up in the beginning
of the seventies. Since then CAS have gained a lot of
computational power. In contrast to this fact CAS have
not experienced the deserved widespread use by
potential users. The main reason for this discrepancy
is the unnatural operation of CAS by artificial
linearized notations, which tend to give little
comprehensive survey of the problem under work.
Calculation with pencil and paper not only offers many
efficient techniques but also appeals to the user's
ease. Especially occasional users need a familiar i.e.
paperlike interface to CAS. In this paper an integrated
system is presented, which offers the demanded
facilities: Calculating by hand in a traditional, `two
dimensional' fashion with the computational support of
a CAS.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich 14, Saarlandes Univ., Saarbrucken,
Germany",
classification = "C5260B (Computer vision and picture processing);
C5530 (Pattern recognition and computer vision
equipment); C5540 (Terminals and graphic displays);
C7310 (Mathematics)",
keywords = "algorithms; CAS; Computer algebra systems; design;
Handprinted input",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
H.5.2} Information Systems, INFORMATION INTERFACES AND
PRESENTATION, User Interfaces, Interaction styles.",
thesaurus = "Character recognition; Neural nets; Symbol
manipulation; Workstations",
}
@InProceedings{Molenkamp:1991:IAA,
author = "J. H. J. Molenkamp and V. V. Goldman and J. A. {van
Hulzen}",
title = "An improved approach to automatic error cumulation
control",
crossref = "Watt:1991:IPI",
pages = "414--418",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p414-molenkamp/",
abstract = "For evaluation of arithmetical expressions using
multiple precision floating-point arithmetic, a method
is given to automatically perform error cumulation
control prior to the actual computations. Individual
errors and their effects are identified, and it is
shown how to compute these effects efficiently via
automatic differentiation. In the presented approach
these effects are used to determine which precisions
have to be chosen during the real computations, in
order to limit error cumulation to admissible, user
chosen error bounds.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Twente Univ., Enschede,
Netherlands",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
keywords = "algorithms; Arithmetical expressions; Computations;
Error bounds; Error cumulation control; Multiple
precision floating-point arithmetic",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Digital arithmetic; Error analysis",
}
@InProceedings{Oevel:1991:YES,
author = "Walter Oevel and Klaus Strack",
title = "The {Yang--Baxter} equation and a systematic search
for {Poisson} brackets on associative algebras",
crossref = "Watt:1991:IPI",
pages = "229--236",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p229-oevel/",
abstract = "Starting with an associative algebra equipped with a
linear map solving the Yang--Baxter equation three
Poisson brackets may be constructed admitting a common
hierarchy of functions in involution. Realizations of
the algebra lead to various integrable hierarchies
known to admit an infinite number of invariant Poisson
brackets. In all cases three of these brackets are
known to originate from the three abstract brackets
defined on the algebra. A systematic search for
abstract versions of the higher Poisson brackets is
performed using computer algebra. It is shown that
apart from the three known brackets no further relevant
abstract brackets of a certain `local' form may be
constructed from solutions of the Yang--Baxter
equations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Univ. of Technol., Loubhborough,
UK",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Abstract brackets; algorithms; Associative algebras;
Computer algebra; Integrable hierarchies; Poisson
brackets; Yang--Baxter equation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Algebra; Mathematics computing",
}
@InProceedings{Pecelli:1991:FMD,
author = "Giampiero Pecelli",
title = "Formal methods in delay-differential equations",
crossref = "Watt:1991:IPI",
pages = "317--318",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p317-pecelli/",
abstract = "Studies formal methods in the solution of
delay-differential equations (DDEs). The motivation for
such study comes from the introduction of Hopf
bifurcation techniques and the method of averaging to
the study of stable oscillations in such systems. The
author concentrates on the formal aspects associated
with the construction of solutions required for an
application of the methods. These classes of solutions
are quite simple, being solutions to linear systems.
The paper concentrates on completing the formalization
and showing that an automated system is possible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Lowell Univ., MA, USA",
classification = "C4170 (Differential equations)",
keywords = "algorithms; DDEs; Delay-differential equations; Formal
methods; Hopf bifurcation; Stable oscillations",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Differential equations",
}
@InProceedings{Petho:1991:AGB,
author = "Attila Peth{\"o}",
title = "Application of {Gr{\"o}bner} bases to the resolution
of systems of norm equations",
crossref = "Watt:1991:IPI",
pages = "144--150",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p144-petho/",
abstract = "Let $K$ be a cubic extension of the rational number
field $Q$. Denote by $Z_K$ the ring of integers of $K$
and by $N_KQ/(\gamma )$ the norm of $\gamma$ in $K$.
Let $P(x)=x^2+cx+d$ in $Z(x)$ and $a,b,n_1,n_2,n_3$, in
$Z$. The paper gives necessary and sufficient
conditions for the existence of cubic number fields $K$
and elements $\eta$ in $Z_K$ such that
$N_KQ/(\eta)=n_1,N_KQ/(\eta-a)=n_2,N_KQ/(\eta-b)=n_3$;
or $N_KQ/(\eta)=n_1,N_KQ/(P(\eta))=n_2$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Kossuth Lajos Univ., Debrecen,
Hungary",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; theory; Gr{\"o}bner bases; Norm equations;
Cubic extension; Rational number field; Integers;
Necessary and sufficient conditions; Cubic number
fields",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Number theory; Polynomials",
}
@InProceedings{Reid:1991:RSD,
author = "G. J. Reid and A. Boulton",
title = "Reduction of systems of differential equations to
standard form and their integration using directed
graphs",
crossref = "Watt:1991:IPI",
pages = "308--312",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p308-reid/",
abstract = "Discusses an algorithm developed in earlier work which
has been implemented in MACSYMA that reduces systems of
partial differential equations to a simplified standard
form by eliminating redundances and including all
integrability conditions. Once a system has been put in
standard form the authors show how directed graphs
representing the dependencies amongst the system's
variables can be used to simplify the problem of
explicitly or numerically integrating the system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., British Columbia Univ., Vancouver, BC,
Canada",
classification = "C1160 (Combinatorial mathematics); C4160 (Numerical
integration and differentiation); C4170 (Differential
equations)",
keywords = "algorithms; Directed graphs; Integration; MACSYMA;
Partial differential equations; Standard form",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, MACSYMA.",
thesaurus = "Directed graphs; Integration; Partial differential
equations",
}
@InProceedings{Renner:1991:NEE,
author = "Friedrich Renner",
title = "Nonlinear evolution equations and the {Painleve}
analysis: a constructive approach with {REDUCE}",
crossref = "Watt:1991:IPI",
pages = "289--294",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p289-renner/",
abstract = "A number of necessary conditions for a class of
nonlinear partial differential equations to pass the
Painleve test with the Kruskal ansatz is given. Using
these one can (theoretically) construct all evolution
equations of certain form and this property with a
computer algebra package based on REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "Kassel Univ., Germany",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Computer algebra package; Evolution
equations; Kruskal ansatz; Nonlinear partial
differential equations; Painleve test; REDUCE; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Nonlinear differential equations; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Richardson:1991:TCN,
author = "Daniel Richardson",
title = "Towards computing nonalgebraic cylindrical
decompositions",
crossref = "Watt:1991:IPI",
pages = "247--255",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p247-richardson/",
abstract = "Non algebraic cylindrical decompositions are
discussed. False derivatives and local Sturm sequences
are defined as tools for computing them. The crucial
fact in the algebraic case is that one can characterize
the number of distinct real roots of a polynomial
$p(y)$ by a condition on the coefficients. An attempt
is made to obtain an analogous characterization for
nonalgebraic functions such as polynomials in monomials
which are defined by algebraic differential equations.
An example would be an exponential polynomial
$p(y,e^y)$. The difficulties of applying this
characterization are described, using the example of
exponential polynomials in two variables,
$p(x,e^y,y,e^y)$. The characterization obtained does
not lead to quantifier elimination.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Bath Univ., UK",
classification = "C1110 (Algebra); C1120 (Analysis); C7310
(Mathematics)",
keywords = "Algebraic differential equations; algorithms;
Cylindrical decompositions; Differential geometry;
Distinct real roots; Exponential polynomials; Local
Sturm sequences; Monomials; Nonalgebraic functions;
theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Nonalgebraic algorithms.",
thesaurus = "Algebra; Differential equations; Polynomials",
}
@InProceedings{Roch-Siebert:1991:PFE,
author = "Fran{\c{c}}oise Roch-Siebert and Gilles Villard",
title = "{PAC}: first experiments on a 128 transputers
m{\'e}ganode",
crossref = "Watt:1991:IPI",
pages = "343--351",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p343-roch-siebert/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Parallel algorithms. {\bf G.1.3} Mathematics
of Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods).
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf C.1.2}
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Multiple-instruction-stream, multiple-data-stream
processors (MIMD).",
}
@InProceedings{RochSiebert:1991:PFE,
author = "F. Roch-Siebert and G. Villard",
title = "{PAC}: first experiments on a 128 transputers
meganode",
crossref = "Watt:1991:IPI",
pages = "343--351",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "From its beginning three years ago, the PAC project:
parallel algebraic computing, has been exploiting a 16
processors hypercube to validate some algebraic
computation algorithms, and to justify the use of
parallelism. Going further, the authors begin to
generalize the previous results and study new problems.
Experiments are now held on a more massively parallel
computer: a 128 Transputers network. The authors
present the first results have obtained: as an example,
they have been interested in applying the Chinese
remainder theorem in linear algebra. For a fixed number
of processors, they show how the behaviour of an
algorithm is influenced by the chosen network topology.
They point out the communication costs and the
constraints due to the storage requirements.",
acknowledgement = ack-nhfb,
affiliation = "Equipe Calcul Parallele et Calcul Formel, CNRS,
Grenoble, France",
classification = "C4140 (Linear algebra); C7310 (Mathematics)",
keywords = "Algebraic computation; Chinese remainder theorem;
Linear algebra; Network topology; PAC project; Parallel
algebraic computing; Parallelism",
thesaurus = "Linear algebra; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Roelofs:1991:IMO,
author = "Marcel Roelofs and Peter K. H. Gragert",
title = "Implementation of multilinear operators in {REDUCE}
and applications in mathematics",
crossref = "Watt:1991:IPI",
pages = "390--396",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p390-roelofs/",
abstract = "Introduces and implement a concept for dealing with
mathematical bases of linear spaces and mappings
(multi)linear with respect to such bases, in REDUCE
(cf. (1)). Using this concept the authors give some
examples how to implement some well known (multi)linear
mappings in mathematics with very little effort.
Moreover they implement a procedure operatorcoeff
similar to the standard REDUCE procedure coeff, but now
for linear spaces instead of polynomial rings.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Twente Univ., Enschede,
Netherlands",
classification = "C4140 (Linear algebra); C7310 (Mathematics)",
keywords = "algorithms; Linear spaces; Mappings; Multilinear
operators; REDUCE",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
thesaurus = "Linear algebra; Symbol manipulation",
}
@InProceedings{Roque:1991:QRD,
author = "W. L. Roque and R. P. {dos Santos}",
title = "Qualitative reasoning, dimensional analysis and
computer algebra",
crossref = "Watt:1991:IPI",
pages = "460--461",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p460-roque/",
abstract = "In this short application report the authors discuss
qualitative reasoning about physical processes under
the framework of dimensional analysis. The symbolic
system QDR-Qualitative Dimensional Reasoner-has been
developed to automate the whole qualitative reasoning
analysis.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence)",
keywords = "algorithms; Computer algebra; Dimensional analysis;
languages; Physical processes; Qualitative reasoning;
Reasoning; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics. {\bf I.1.4} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Special-purpose
algebraic systems.",
thesaurus = "Inference mechanisms; Symbol manipulation",
}
@InProceedings{Rudenko:1991:ACA,
author = "V. M. Rudenko and V. V. Leonov and A. F. Bragazin and
I. P. Shmyglevsky",
title = "Application of computer algebra to the investigation
of the orbital satellite motion",
crossref = "Watt:1991:IPI",
pages = "450--451",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p450-rudenko/",
abstract = "Presents the features of a program package
`Polymech-symbol' helping to solve some laborious
mechanical problems. The package was written by means
of the REDUCE system and contains several algorithms in
a form of REDUCE procedures. The authors consider the
problems of navigation and center of mass motion on
board a satellite.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Problems of Mech., Acad. of Sci., Moscow,
USSR",
classification = "C7460 (Aerospace engineering)",
keywords = "algorithms; Center of mass motion; Computer algebra;
Navigation; Orbital satellite motion; Polymech-symbol;
REDUCE system",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Aerospace.",
thesaurus = "Aerospace computing; Artificial satellites; Symbol
manipulation",
}
@InProceedings{Rybowicz:1991:ACI,
author = "Marc Rybowicz",
title = "An algorithm for computing integral bases of an
algebraic function field",
crossref = "Watt:1991:IPI",
pages = "157--166",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p157-rybowicz/",
abstract = "The author presents a new algorithm for function
fields which borrows techniques from previous methods
and works in any characteristic. Theorem 5 allows one
to reduce the problem to the factorization of rational
primes via some standard linear algebra techniques. He,
in turn, reduces this factorization problem to study
how two branches of the underlying curve intersect.
This latter task is achieved with the help of the
`Hamburger--Noether Development', a special type of
local parametrization. He expects the algorithm to be
more efficient than Zassenhaus' global approach and to
highlight the classical local approach. Moreover, the
techniques presented allow one to build a function with
specified zeros in any characteristic and could be
applied to other problems. Although the algorithm is
complete, some steps clearly need to be improved and
studied more carefully before attempting any
implementation. In particular, he assumes that the
constant field is algebraically closed, but a
`rational' extension of the algorithm would be
welcome.",
acknowledgement = ack-nhfb,
affiliation = "Symbolic Comput. Group, Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "Algebraic function field; algorithms; Factorization;
Hamburger--Noether Development; Integral bases; Linear
algebra; Local parametrization; Rational primes",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Group theory; Mathematics computing; Number theory;
Symbol manipulation",
}
@InProceedings{Schlegel:1991:DRS,
author = "H. Schlegel",
title = "Determination of the root system of semisimple {Lie}
algebras from the {Dynkin} diagram",
crossref = "Watt:1991:IPI",
pages = "239--240",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p239-schlegel/",
abstract = "One way to represent the properties of the Lie algebra
for calculations is by means of the commutation
relations, i.e. the structure constants. The paper
shows a way of the calculation of the Cartan--Weyl
basis for all simple Lie algebras starting from the
Dynkin diagram. The package DYNKIN written in REDUCE
implements the described relations and can as an
application be used to perform the calculations for a
specified Lie algebra.",
acknowledgement = ack-nhfb,
affiliation = "Zentralinstitut fur Elektronenphys., Berlin, Germany",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "algorithms; Cartan--Weyl basis; Commutation relations;
Dynkin diagram; Root system; Semisimple Lie algebras;
Simple Lie algebras; Structure constants",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Diagrams; Mathematics computing",
}
@InProceedings{Schmitt:1991:EAA,
author = "Joacheim Schmitt",
title = "An embedding algorithm for algebraic congruence
function fields",
crossref = "Watt:1991:IPI",
pages = "187--188",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p187-schmitt/",
abstract = "Provides an analogue of the Round 4 algorithm of
Ford/Zassenhaus (1978) for algebraic congruence
function fields. The reduction steps can also be used
in other embedding algorithms. The algorithm is
implemented within the computer algebra system SIMATH.
The corresponding programs are written in C. The
results can be used in integration and cryptography.",
acknowledgement = ack-nhfb,
affiliation = "Saarlandes Univ., Saarbrucken, Germany",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "Algebraic congruence function fields; algorithms;
Computer algebra system; Cryptography; Embedding
algorithms; Integration; Round 4 algorithm; SIMATH",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Number theory",
}
@InProceedings{Schonhage:1991:FRC,
author = "Arnold Sch{\"o}nhage",
title = "Fast reduction and composition of binary quadratic
forms",
crossref = "Watt:1991:IPI",
pages = "128--133",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p128-schonhage/",
abstract = "Similar to the fast computation of integer gcd's,
reduction of binary quadratic forms $ax^2+bxy+cy^2$
with integral coefficients $a, b, c$ bounded by $2^n$
is possible in time $O (\mu (n) \log{}n)$, where
$\mu(n)$ is a time bound for $n$-bit integer
multiplication. This result is obtained by a
corresponding algorithm for the monotone reduction of
positive forms. The same time bound holds for the
composition of forms. Moreover, finding a reduced form
is shown to be at least as difficult as extended gcd
computation, up to terms of order $\mu (n)$.",
acknowledgement = ack-nhfb,
affiliation = "Bonn Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory)",
keywords = "algorithms; Binary quadratic forms; Integer
multiplication; Integral coefficients; Monotone
reduction; Positive forms; Time bound",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Schulze-Pillot:1991:ACG,
author = "Rainer Schulze-Pillot",
title = "An algorithm for computing genera of ternary and
quaternary quadratic forms",
crossref = "Watt:1991:IPI",
pages = "134--143",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p134-schulze-pillot/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
}
@InProceedings{SchulzePillot:1991:ACG,
author = "R. Schulze-Pillot",
title = "An algorithm for computing genera of ternary and
quaternary quadratic forms",
crossref = "Watt:1991:IPI",
pages = "134--143",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The paper reports on an algorithm for computing genera
of ternary and quaternary positive definite quadratic
forms over Z. It is well known that due to the simple
shape of the reduction conditions in these dimensions
it is in principle no problem to compute
representatives of all classes of such quadratic forms
whose discriminant is below a given bound. It is,
however, sometimes desirable to be able to quickly
determine representatives of all classes in some fixed
genus of quadratic forms of possibly high discriminant
without having to generate along the way all forms of
smaller discriminant. An obvious attempt in such a case
is to use Kneser's method of neighbouring or adjacent
lattices. The paper draws attention to the fact that it
is indeed not difficult to use this method in
dimensions 3 and 4 as the basis of an algorithm that
serves the purpose. With almost no extra work one
obtains at the same time the adjacency graph of the
classes determined; this has interesting arithmetic and
graph theoretic applications. It is intended to use the
algorithm for the experimental investigation of the
Fourier and Fourier--Jacobi coefficients of certain
linear combinations of Siegel $\theta$ series of
quaternary quadratic forms.",
acknowledgement = ack-nhfb,
affiliation = "Fakultat fur Math., Bielefeld Univ., Germany",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Adjacency graph; Adjacent lattices; Discriminant;
Fourier--Jacobi coefficients; Genera; Linear
combinations; Neighbouring lattices; Quaternary
positive definite quadratic forms; Reduction
conditions; Siegel $\theta$ series; Ternary positive
definite quadratic forms",
thesaurus = "Number theory",
}
@InProceedings{Schwarz:1991:ETP,
author = "Fritz Schwarz",
title = "Existence theorems for polynomial first integrals",
crossref = "Watt:1991:IPI",
pages = "256--264",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p256-schwarz/",
abstract = "In various areas of applied mathematics there occur
autonomous systems of ordinary differential equations
of the form $x_i= \omega _i(x,c), i=1,\ldots{}n$ where
the right hand sides are polynomial in all arguments
$x=(x_1,\ldots{}x_n)$ and $c=(c_1,c_2,\ldots{})$; the
latter variables are parameters which are a priori
unspecified. There arises the following question: Do
first integrals of a certain type, e.g. polynomial
first integrals? The computer algebra package DYNSYS
allows one to find all polynomial first integrals up to
a given highest degree $D$ but does not provide any
information beyond $D$. To obtain a complete answer
these packages should be complemented by rigorous
results concerning the possible existence of first
integrals of any degree. Theorems of this kind are
obtained. The basic principle for obtaining them is to
identify subsystems of the determining system which
have a certain structure independent of $D$. This
method is applied to several two- and three-dimensional
systems. It is shown for example that the famous Lorenz
system in general does not allow any polynomial first
integrals. Furthermore some ideas are presented on how
these methods may be converted into algorithms such
that a machine may perform the necessary analysis.",
acknowledgement = ack-nhfb,
affiliation = "GMD, Inst. F1, St. Augustin, Germany",
classification = "C1120 (Analysis); C4170 (Differential equations);
C4180 (Integral equations)",
keywords = "algorithms; Applied mathematics; Autonomous systems;
Computer algebra package; DYNSYS; Lorenz system;
Ordinary differential equations; Polynomial first
integrals; theory; Three-dimensional systems",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Special-purpose algebraic
systems.",
thesaurus = "Differential equations; Integral equations;
Polynomials",
}
@InProceedings{Shoup:1991:FDA,
author = "Victor Shoup",
title = "A fast deterministic algorithm for factoring
polynomials over finite fields of small
characteristic",
crossref = "Watt:1991:IPI",
pages = "14--21",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p14-shoup/",
abstract = "Presents a new algorithm for factoring polynomials
over finite fields. The algorithm is deterministic, and
its running time is `almost' quadratic when the
characteristic is a small fixed prime. As such, the
algorithm is asymptotically faster than previously
known deterministic algorithms for factoring
polynomials over finite fields of small
characteristic.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Toronto Univ., Toronto, Ont.,
Canada",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Deterministic algorithm; Finite fields;
Polynomial factorisation; Small characteristic; Small
fixed prime; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Sit:1991:TPL,
author = "William Y. Sit",
title = "A theory for parametric linear systems",
crossref = "Watt:1991:IPI",
pages = "112--121",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p112-sit/",
abstract = "Presents a theoretical foundation for studying
parametric systems of linear equations and proves an
efficient algorithm for identifying all parametric
values (including degenerate cases) for which the
system is consistent. The algorithm gives a small set
of regimes where for each regime, the solutions of the
specialized systems may be given uniformly. For
homogeneous systems, or for systems where the right
hand side is arbitrary, this small set is irredundant.
A complexity analysis of the Gaussian elimination
method is given and compared with the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
classification = "C4140 (Linear algebra); C4240 (Programming and
algorithm theory)",
keywords = "algorithms; Complexity analysis; Degenerate cases;
Gaussian elimination; Homogeneous systems; Linear
equations; Parametric systems; Parametric values;
Regimes; Right hand side; Specialized systems; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
systems (direct and iterative methods).",
thesaurus = "Computational complexity; Linear algebra",
}
@InProceedings{Stein:1991:ADR,
author = "Andreas Stein and Horst G{\"u}nter Zimmer",
title = "An algorithm for determining the regulator and the
fundamental unit of a hyperelliptic congruence function
field",
crossref = "Watt:1991:IPI",
pages = "183--184",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p183-stein/",
abstract = "A continued fraction algorithm (baby steps) is
described by B. Weis, H. G. Zimmer (Mitt. Math. Ges:
Hamburg, 1991) for determining the regulator and the
fundamental unit of the congruence function field $K/k$
with respect to the indeterminate $X$. The algorithm is
based on work of Artin (Math Z vol. 19, p. 153--246,
1924) and was implemented within the computer algebra
system SIMATH. The authors show how the algorithm can
be substantially improved by applying to the function
field case D. Shanks' (1972) idea of the infrastructure
of a real quadratic number field. The improved version
of this algorithm has been implemented within the
computer algebra system SIMATH, too.",
acknowledgement = ack-nhfb,
affiliation = "Saarlandes Univ., Saarbrucken, Germany",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "algorithms; Baby steps; Computer algebra system;
Congruence function field; Continued fraction
algorithm; Function field; Fundamental unit;
Hyperelliptic congruence function field; Indeterminate;
Real quadratic number field; Regulator; SIMATH",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Number theory; Symbol manipulation",
}
@InProceedings{Surguladze:1991:APC,
author = "Levan R. Surguladze and Mark A. Samuel",
title = "Algebraic perturbative calculations in high energy
physics. {Methods}, algorithms, computer programs and
physical applications",
crossref = "Watt:1991:IPI",
pages = "439--447",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p439-surguladze/",
abstract = "The methods and algorithms for high order algebraic
perturbative calculations in theoretical high energy
physics are briefly reviewed. The SCHOONSCHIP program
MINCER and the REDUCE program LOOPS for analytical
computation of arbitrary massless, one-, two- and
three-loop Feynman diagrams of the propagator type are
described. The version of the program LOOPS for
personal computers and the extended version of the
program MINCER for four-loop renormalization group
calculations are presented. The new program for
algebraic perturbative calculations is also discussed.
This program is written on the new algebraic
programming system FORM. Some recent results of
application to the high energy physics are given.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Res., Acad. of Sci., Moscow, USSR",
classification = "A0270 (Computational techniques); A1110G
(Renormalization); C7320 (Physics and Chemistry)",
keywords = "Algebraic perturbative calculations; algorithms;
Feynman diagrams; High energy physics; LOOPS; MINCER;
REDUCE; SCHOONSCHIP program",
subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
thesaurus = "Feynman diagrams; Physics computing; Renormalisation;
Symbol manipulation",
}
@InProceedings{Trenkov:1991:ARS,
author = "I. Trenkov and M. Spiridonova and M. Daskalova",
title = "An application of the {REDUCE} system for solving a
mathematical geodesy problem",
crossref = "Watt:1991:IPI",
pages = "448--449",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p448-trenkov/",
abstract = "A REDUCE program package for solving some mathematical
geodesy problems now under development includes
capabilities for solving the problem: the geographical
coordinates (the geographical density $B_p$ and the
geographical longitude $L_p$) of a point $P$ on the
earthly ellipsoid are to be calculated when $n$
different points $C_i(i=1, 2, \ldots{}, n)$ with their
geographical coordinates $B_i$ and $L_i$ are given and
the azimuths $A_{ip}$ in all points $C_i$ to the point
$P$ are measured.",
acknowledgement = ack-nhfb,
affiliation = "Central Lab. for Geodesy, Bulgarian Acad. of Sci.,
Sofia, Bulgaria",
classification = "A9110B (Mathematical geodesy: general theory); C7310
(Mathematics); C7340 (Geophysics)",
keywords = "algorithms; Geographical coordinates; Mathematical
geodesy; Program package; REDUCE system",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Earth and atmospheric sciences.",
thesaurus = "Computational geometry; Geodesy; Geophysics computing;
Symbol manipulation",
}
@InProceedings{Trevisan:1991:PFU,
author = "Vilmar Trevisan and Paul Wang",
title = "Practical factorization of univariate polynomials over
finite fields",
crossref = "Watt:1991:IPI",
pages = "22--31",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p22-trevisan/",
abstract = "The research presented is part of an effort to
establish state-of-the-art factoring routines for
polynomials. The foundation of such algorithms lies in
the efficient factorization over a finite field
$\mbox{GF}(p^k)$. The Cantor--Zassenhaus algorithm
together with innovative ideas suggested by others is
compared with the Berlekamp algorithm. The studies led
to the design of a hybrid algorithm that combines the
strengths of the different approaches. The algorithms
are also implemented and machine timings are obtained
to measure the performance of these algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Berlekamp algorithm; Cantor--Zassenhaus
algorithm; Factoring routines; Factorization; Finite
fields; Hybrid algorithm; performance; Univariate
polynomials",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations in finite fields.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Vinette:1991:FSC,
author = "F. Vinette",
title = "Features of symbolic computation exploited in the
calculation of lower energy bounds of cyclic polyene
models",
crossref = "Watt:1991:IPI",
pages = "458--459",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p458-vinette/",
abstract = "Symbolic computation has been applied in many
scientific disciplines and has proved to be a very
valuable research tool. In earlier studies, features of
symbolic computation including algebraic manipulations
and high decimal precision, were shown to be very
useful to solve nonrelativistic quantum mechanical
problems. The author illustrates the valuable
assistance of symbolic computation in solving quantum
chemical problems. The symbolic computational language
MAPLE is used throughout this study. The computational
aspects of the application of Lowdin's Optimized Inner
Projection (OIP) to determine lower bounds to the
ground state energy of the Pariser--Parr--Pople (PPP)
model of cyclic polyenes, is briefly presented. A
diagrammatic approach for evaluating the required
matrix elements is needed: this method is often used in
quantum chemistry. The evaluation of Brandow diagrams,
which is very tedious and almost impossible to do by
hand, is easily obtained using MAPLE.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Stat., York Univ., North York,
Ont., Canada",
classification = "A3115 (General mathematical and computational
developments); A3120 (Specific calculations and
results); C7320 (Physics and Chemistry)",
keywords = "algorithms; Brandow diagrams; Cyclic polyene models;
Ground state energy; languages; Lower energy bounds;
MAPLE; Optimized Inner Projection;
Pariser--Parr--Pople; Quantum chemical problems;
Symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Chemistry. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN.",
thesaurus = "Chemistry computing; Molecular energy level
calculations; Organic compounds; Quantum chemistry;
Symbol manipulation",
}
@InProceedings{Wang:1991:TMI,
author = "Dongming Wang",
title = "A toolkit for manipulating indefinite summations with
application to neural networks",
crossref = "Watt:1991:IPI",
pages = "462--463",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p462-wang/",
abstract = "Presents the design of some rules and the
implementation of an application-oriented toolkit in
Macsyma by amending some of its incorrect computations
for the manipulation of indefinite summations. The
application of this toolkit to the analysis and
derivation of neural networks is briefly discussed.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C6115 (Programming support); C6170 (Expert
systems)",
keywords = "algorithms; Application-oriented toolkit; design;
Indefinite summations; Macsyma; Neural networks",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.4}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Applications. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA. {\bf I.2.6} Computing
Methodologies, ARTIFICIAL INTELLIGENCE, Learning,
Connectionism and neural nets.",
thesaurus = "Neural nets; Software tools; Symbol manipulation",
}
@InProceedings{Weibel:1991:AP,
author = "Trudy Weibel and Gaston H. Gonnet",
title = "An algebra of properties",
crossref = "Watt:1991:IPI",
pages = "352--359",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p352-weibel/",
abstract = "The purpose of the paper is to build a framework and
give algorithms to solve queries of the form obj in
Prop where the object obj is expressible in terms of
other given objects. The authors develop an algebra of
properties, PROP, in which we carry out computations.
They present a set of rules (axioms Ax1-Ax7) for the
behaviour of the basic functions on properties. In
addition, they represent the algorithmic components
such as if and while by the algebra operations meet and
join. They conclude by proposing an implementation of
the algebra PROP.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Theor. Comput. Sci., Zurich, Switzerland",
classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
keywords = "Algebra; Algebra of properties; Algorithmic
components; algorithms; PROP",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous.",
thesaurus = "Symbol manipulation",
}
@InProceedings{Yakubovich:1991:EIS,
author = "S. B. Yakubovich and Yu. F. Luchko",
title = "The evaluation of integrals and series with respect to
indices (parameters) of hypergeometric functions",
crossref = "Watt:1991:IPI",
pages = "271--280",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p271-yakubovich/",
abstract = "A general method for the evaluation of some integrals
of hypergeometric functions, and programming package,
which works on the basis of this method, were described
in Adamchik, Luchko, Marichev (1990). But many
integrals which have appeared in practice don't belong
to the class of convolution type integrals and,
consequently, one can't use the previous method for the
evaluation of such integrals. In particular, one needs
original methods for the evaluation of integrals and
series with respect to indices of special functions.",
acknowledgement = ack-nhfb,
affiliation = "Byelorussian State Univ., Minsk, Byelorussian SSR,
USSR",
classification = "C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Evaluation of integrals; Hypergeometric
functions; Indices; Integrals; Special functions;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations.",
thesaurus = "Integration; Series [mathematics]",
}
@InProceedings{Ziel:1991:RFD,
author = "Richard Ziel",
title = "Rational function decomposition",
crossref = "Watt:1991:IPI",
pages = "1--6",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p1-zippel/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Zippel:1991:RFD,
author = "R. Zippel",
title = "Rational function decomposition",
crossref = "Watt:1991:IPI",
pages = "1--6",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a polynomial time algorithm for determining
whether a given univariate rational function over an
arbitrary field is the composition of two rational
functions over that field, and finds them if so.",
acknowledgement = ack-nhfb,
affiliation = "Cornell Univ., Ithaca, NY, USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Arbitrary field; Polynomial time algorithm; Univariate
rational function",
thesaurus = "Polynomials",
}
@InProceedings{Zolotykh:1991:PCS,
author = "A. A. Zolotykh",
title = "A package for computations in simple {Lie} algebra
representations",
crossref = "Watt:1991:IPI",
pages = "237--238",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p237-zolotykh/",
abstract = "The author present a software package for calculations
of some numerical characteristics of simple Lie
algebras of rank not more than 12 and their irreducible
finite-dimensional representations over algebraically
closed fields of characteristic zero (for example, over
the field of complex numbers). Times of some
computations on an IBM PC/AT (processor 286) are given:
the times of character computations and times of tensor
square computations for the fundamental (basic)
representation of exceptional Lie algebras and of
12-rank Lie algebras. The table contains also the
dimensions of corresponding fundamental
representations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Algebraically closed fields; algorithms; IBM PC/AT;
Irreducible finite-dimensional representations;
Numerical characteristics; Simple Lie algebra
representations; Tensor square computations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Special-purpose
algebraic systems.",
thesaurus = "Algebra; Mathematics computing; Microcomputer
applications",
xxtitle = "A package for computation in simple {Lie} algebra
representations",
}
@InProceedings{Bischof:1992:AAD,
author = "Christian Bischof and Alan Carle and George Corliss
and Andreas Griewank",
title = "{ADIFOR}: {Automatic} differentiation in a source
translator environment",
crossref = "Wang:1992:PII",
pages = "294--302",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p294-bischof/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; experimentation; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.6}
Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Gradient methods. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems.",
}
@InProceedings{Bronstein:1992:LOD,
author = "Manuel Bronstein",
title = "Linear ordinary differential equations: breaking
through the order 2 barrier",
crossref = "Wang:1992:PII",
pages = "42--48",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p42-bronstein/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Burnel:1992:CCY,
author = "A. Burnel and H. Caprasse",
title = "The computation of $1$-loop contributions in {Y.M.}
theories with class {III} nonrelativistic gauges and
{REDUCE}",
crossref = "Wang:1992:PII",
pages = "103--107",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p103-burnel/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; Yang--Mills",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
}
@InProceedings{Butler:1992:ECA,
author = "Greg Butler",
title = "Experimental comparison of algorithms for {Sylow}
subgroups",
crossref = "Wang:1992:PII",
pages = "251--262",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p251-butler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous.",
}
@InProceedings{Cetinkaya:1992:SAL,
author = "Cetin Cetinkaya",
title = "On stability analysis of linear stochastic and
time-varying deterministic systems",
crossref = "Wang:1992:PII",
pages = "278--283",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p278-cetinkaya/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Eigenvalues and eigenvectors (direct
and iterative methods). {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods).
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Codutti:1992:NNL,
author = "M. Codutti",
title = "{NODES}: non linear ordinary differential equations
solver",
crossref = "Wang:1992:PII",
pages = "69--79",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p69-codutti/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
}
@InProceedings{Collins:1992:EAI,
author = "George E. Collins and Werner Krandick",
title = "An efficient algorithm for infallible polynomial
complex root isolation",
crossref = "Wang:1992:PII",
pages = "189--194",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p189-collins/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Cook:1992:CGA,
author = "Grant O. {Cook, Jr.}",
title = "Code generation in {ALPAL} using symbolic techniques",
crossref = "Wang:1992:PII",
pages = "27--35",
year = "1992",
DOI = "https://doi.org/10.1145/143242.143260",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p27-cook/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
FORTRAN. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, C. {\bf G.1.6} Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization. {\bf
D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
Code generation.",
}
@InProceedings{Cooperman:1992:FCB,
author = "Gene Cooperman and Larry Finkelstein",
title = "A fast cyclic base change for permutation groups",
crossref = "Wang:1992:PII",
pages = "224--232",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p224-cooperman/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Trees. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS, Probabilistic algorithms
(including Monte Carlo).",
}
@InProceedings{Crouch:1992:ECI,
author = "P. E. Crouch and R. L. Grossman",
title = "The explicit computation of integration algorithms and
first integrals for ordinary differential equations
with polynomial coefficients using trees",
crossref = "Wang:1992:PII",
pages = "89--94",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p89-crouch/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Trees. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms.",
}
@InProceedings{Dalmas:1992:PFL,
author = "St{\'e}phane Dalmas",
title = "A polymorphic functional language applied to symbolic
computation",
crossref = "Wang:1992:PII",
pages = "369--375",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p369-dalmas/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf F.3.3} Theory
of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Studies of Program Constructs, Type structure. {\bf
F.3.3} Theory of Computation, LOGICS AND MEANINGS OF
PROGRAMS, Studies of Program Constructs, Functional
constructs. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, SCRATCHPAD.",
}
@InProceedings{Davenport:1992:PTR,
author = "J. H. Davenport",
title = "Primality testing revisited",
crossref = "Wang:1992:PII",
pages = "123--129",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p123-davenport/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations.",
}
@InProceedings{Dewar:1992:UCA,
author = "Michael C. Dewar",
title = "Using computer algebra to select numerical
algorithms",
crossref = "Wang:1992:PII",
pages = "1--8",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p1-dewar/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
}
@InProceedings{Fateman:1992:HPG,
author = "Richard Fateman",
title = "Honest plotting, global extrema, and interval
arithmetic",
crossref = "Wang:1992:PII",
pages = "216--223",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p216-fateman/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.",
}
@InProceedings{Ganzha:1992:NSA,
author = "V. G. Ganzha and E. V. Vorozhtsov and J. A. {van
Hulzen}",
title = "A new symbolic-numeric approach to stability analysis
of difference schemes",
crossref = "Wang:1992:PII",
pages = "9--15",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p9-ganzha/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.4}
Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation, Finite
difference methods. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
}
@InProceedings{Gao:1992:SPA,
author = "Xiao-Shan Gao and Shang-Ching Chou",
title = "Solving parametric algebraic systems",
crossref = "Wang:1992:PII",
pages = "335--341",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p335-gao/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Geddes:1992:HSI,
author = "K. O. Geddes and G. J. Fee",
title = "Hybrid symbolic-numeric integration in {MAPLE}",
crossref = "Wang:1992:PII",
pages = "36--41",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p36-geddes/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@InProceedings{Gil:1992:CJC,
author = "Isabelle Gil",
title = "Computation of the {Jordan} canonical form of a square
matrix (using the {Axiom} programming language)",
crossref = "Wang:1992:PII",
pages = "138--145",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p138-gil/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Eigenvalues and eigenvectors (direct
and iterative methods). {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Grigoriev:1992:ESP,
author = "Dima Y. u. Grigoriev and Marek Karpinski and Andrew M.
Odlyzko",
title = "Existence of short proofs for nondivisibility of
sparse polynomials under the extended {Riemann}
hypothesis",
crossref = "Wang:1992:PII",
pages = "117--122",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p117-grigoriev/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial).",
}
@InProceedings{Gutierrez:1992:PIT,
author = "Jaime Gutierrez and Tomas Recio",
title = "A practical implementation of two rational function
decomposition algorithms",
crossref = "Wang:1992:PII",
pages = "152--157",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p152-gutierrez/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
}
@InProceedings{Hietarinta:1992:SCQ,
author = "Jarmo Hietarinta",
title = "Solving the constant quantum {Yang--Baxter} equation
in $2$ dimensions with massive use of factorizing
{Gr{\"o}bner} basis computations",
crossref = "Wang:1992:PII",
pages = "350--357",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p350-hietarinta/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
}
@InProceedings{Hong:1992:SSF,
author = "Hoon Hong",
title = "Simple solution formula construction in cylindrical
algebraic decomposition based quantifier elimination",
crossref = "Wang:1992:PII",
pages = "177--188",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p177-hong/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications.",
}
@InProceedings{Johnson:1992:RAN,
author = "J. R. Johnson",
title = "Real algebraic number computation using interval
arithmetic",
crossref = "Wang:1992:PII",
pages = "195--205",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p195-johnson/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Kajler:1992:CPE,
author = "Norbert Kajler",
title = "{CAS\slash PI}: a portable and extensible interface
for computer algebra systems",
crossref = "Wang:1992:PII",
pages = "376--386",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p376-kajler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
H.5.2} Information Systems, INFORMATION INTERFACES AND
PRESENTATION, User Interfaces. {\bf D.2.2} Software,
SOFTWARE ENGINEERING, Design Tools and Techniques, User
interfaces. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Kaltofen:1992:CDM,
author = "Erich Kaltofen",
title = "On computing determinants of matrices without
divisions",
crossref = "Wang:1992:PII",
pages = "342--349",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p342-kaltofen/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Kirrinnis:1992:FCN,
author = "Peter Kirrinnis",
title = "Fast computation of numerical partial fraction
decompositions and contour integrals of rational
functions",
crossref = "Wang:1992:PII",
pages = "16--26",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p16-kirrinnis/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@InProceedings{Kuhn:1992:CPS,
author = "Norbert Kuhn and Klaus Madlener and Friedrich Otto",
title = "Computing presentations for subgroups of context-free
groups",
crossref = "Wang:1992:PII",
pages = "240--250",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p240-kuhn/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems, Decision
problems. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes.",
}
@InProceedings{Lamagna:1992:DUI,
author = "Edmund A. Lamagna and Michael B. Hayden and Catherine
W. Johnson",
title = "The design of a user interface to a computer algebra
system for introductory calculus",
crossref = "Wang:1992:PII",
pages = "358--368",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p358-lamagna/",
acknowledgement = ack-nhfb,
keywords = "algorithms; human factors",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf H.5.2} Information
Systems, INFORMATION INTERFACES AND PRESENTATION, User
Interfaces, Interaction styles. {\bf H.5.2} Information
Systems, INFORMATION INTERFACES AND PRESENTATION, User
Interfaces, Input devices and strategies.",
}
@InProceedings{Lempken:1992:SPS,
author = "W. Lempken and R. Staszewski",
title = "The structure of the {PIMs} of {SL(3,4)} in
characteristic 2",
crossref = "Wang:1992:PII",
pages = "233--239",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p233-lempken/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Representations
(general and polynomial).",
}
@InProceedings{Manocha:1992:MRL,
author = "Dinesh Manocha and John F. Canny",
title = "Multipolynomial resultants and linear algebra",
crossref = "Wang:1992:PII",
pages = "158--167",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p158-manocha/",
acknowledgement = ack-nhfb,
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Sparse, structured, and very
large systems (direct and iterative methods). {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@InProceedings{Marinuzzi:1992:LNS,
author = "Francesco Marinuzzi and Stefano Soliani",
title = "{LISA}: {A} new symbolic package for the definition,
analysis and resolution of {Markovian} processes:
symbolic and inductive techniques",
crossref = "Wang:1992:PII",
pages = "303--311",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p303-marinuzzi/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic.",
}
@InProceedings{Moller:1992:GBC,
author = "H. Michael M{\"o}ller and Teo Mora and Carlo
Traverso",
title = "Gr{\"o}bner bases computation using syzygies",
crossref = "Wang:1992:PII",
pages = "320--328",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p320-moller/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Morain:1992:ENE,
author = "F. Morain",
title = "Easy numbers for the elliptic curve primality proving
algorithm",
crossref = "Wang:1992:PII",
pages = "263--268",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p263-morain/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.2.m} Mathematics of
Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Mutrie:1992:AFE,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "An approach for floating-point error analysis using
computer algebra",
crossref = "Wang:1992:PII",
pages = "284--293",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf G.2.2} Mathematics
of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
algorithms.",
}
@InProceedings{Noro:1992:RCA,
author = "Masayuki Noro and Taku Takeshima",
title = "{Risa\slash Asir} --- a computer algebra system",
crossref = "Wang:1992:PII",
pages = "387--396",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p387-noro/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf D.2.5} Software,
SOFTWARE ENGINEERING, Testing and Debugging, Debugging
aids.",
}
@InProceedings{Painter:1992:MES,
author = "Jeffrey F. Painter",
title = "The matrix editor for symbolic {Jacobians} in
{ALPAL}",
crossref = "Wang:1992:PII",
pages = "312--319",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p312-painter/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Reid:1992:ADC,
author = "G. J. Reid and I. G. Lisle and A. Boulton and A. D.
Wittkopf",
title = "Algorithmic determination of commutation relations for
{Lie} symmetry algebras of {PDEs}",
crossref = "Wang:1992:PII",
pages = "63--68",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p63-reid/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Richardson:1992:ECP,
author = "Daniel Richardson",
title = "The elementary constant problem",
crossref = "Wang:1992:PII",
pages = "108--116",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p108-richardson/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Rioboo:1992:RAC,
author = "Renaud Rioboo",
title = "Real algebraic closure of an ordered field:
implementation in {Axiom}",
crossref = "Wang:1992:PII",
pages = "206--215",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p206-rioboo/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial).",
}
@InProceedings{Russo:1992:CSA,
author = "Mark F. Russo",
title = "A combined symbolic\slash numeric approach for the
integration of stiff nonlinear systems of {ODE}'s",
crossref = "Wang:1992:PII",
pages = "80--88",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p80-russo/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear
approximation.",
}
@InProceedings{Salvy:1992:AEF,
author = "Bruno Salvy and John Shackell",
title = "Asymptotic expansions of functional inverses",
crossref = "Wang:1992:PII",
pages = "130--137",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p130-salvy/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Analysis of algorithms.",
}
@InProceedings{Schwarz:1992:RCA,
author = "Fritz Schwarz",
title = "Reduction and completion algorithms for partial
differential equations",
crossref = "Wang:1992:PII",
pages = "49--56",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p49-schwarz/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Singer:1992:LST,
author = "Michael F. Singer and Felix Ulmer",
title = "{Liouvillian} solutions of third order linear
differential equations: new bounds and necessary
conditions",
crossref = "Wang:1992:PII",
pages = "57--62",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p57-singer/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Viklund:1992:OLS,
author = "Lars Viklund and Peter Fritzson",
title = "An object-oriented language for symbolic computation
--- applied to machine element analysis",
crossref = "Wang:1992:PII",
pages = "397--405",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p397-viklund/",
acknowledgement = ack-nhfb,
keywords = "design; languages",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Object-oriented languages. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C++. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Villard:1992:PLB,
author = "Gilles Villard",
title = "Parallel lattice basis reduction",
crossref = "Wang:1992:PII",
pages = "269--277",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p269-villard/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf G.2.m} Mathematics
of Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Wang:1992:PUA,
author = "Paul S. Wang",
title = "Parallel univariate $p$-adic lifting on shared-memory
multiprocessors",
crossref = "Wang:1992:PII",
pages = "168--176",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p168-wang/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@InProceedings{Weispfenning:1992:FGB,
author = "V. Weispfenning",
title = "Finite {Gr{\"o}bner} bases in {non-Noetherian} skew
polynomial rings",
crossref = "Wang:1992:PII",
pages = "329--334",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p329-weispfenning/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Weisss:1992:HDP,
author = "J{\"u}rgen Weis{\ss}",
title = "Homogeneous decomposition of polynomials",
crossref = "Wang:1992:PII",
pages = "146--151",
year = "1992",
bibdate = "Wed Feb 06 10:44:34 2002",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p146-weiszlig/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Ye:1992:SLI,
author = "Honglin Ye and Robert M. Corless",
title = "Solving linear integral equations in {Maple}",
crossref = "Wang:1992:PII",
pages = "95--102",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p95-ye/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations.",
}
@InProceedings{Abramov:1993:DS,
author = "S. A. Abramov",
title = "On {d'Alembert} substitution",
crossref = "Bronstein:1993:IPI",
pages = "20--26",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p20-abramov/",
abstract = "Let some homogeneous linear ordinary differential
equation with coefficients in a differential field $F$
be given. If we know a nonzero solution $\psi$, then
the order of the equation can be reduced by d'Alembert
substitution $y= \psi integral \nu dx$, where $\nu$ is
a new unknown function. In the situation when
$\psi\in{}F$, after d'Alembert substitution an equation
with coefficients in $F$ arises again. Let the obtained
equation have a nonzero solution $\psi \in F$, then it
is possible to reduce the order of the equation again
and so on, until an equation without nonzero solutions
in $F$ is obtained. If we can find solutions not only
in $F$ but in some larger set $L$ as well ($L$ can be a
field or a linear space), then we can build up a
certain subspace $M$ (d'Alembertian subspace) of the
space of all solutions of the original equation. Thus
if we have algorithms $A_F$ and $A_L$ to search for the
solutions in $F$ and $L$, then by incorporating
d'Alembert substitution we can design a more general
algorithm (in case $L=F$ we will obtain a more general
algorithm than $A_F$). We would like, certainly, to
know the kind of solutions that can be found by the new
algorithm. The construction of the subspace $M$ is
described.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C1180 (Optimisation techniques); C4170 (Differential
equations); C6130 (Data handling techniques); C7310
(Mathematics computing)",
keywords = "Alembert substitution; algorithms; Computer algebra
algorithms; Differential field; General algorithm;
Homogeneous linear ordinary differential equation;
Linear space; Nonzero solution; Search problems;
Subspace; theory; verification",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Linear differential equations; Search problems; Symbol
manipulation",
}
@InProceedings{Abramov:1993:DSP,
author = "S. A. Abramov",
title = "On {d'Alembert} substitution",
crossref = "Bronstein:1993:IPI",
pages = "20--26",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
computation",
}
@InProceedings{Abramov:1993:GCD,
author = "S. A. Abramov and K. Y. u. Kvashenko",
title = "On the greatest common divisor of polynomials which
depend on a parameter",
crossref = "Bronstein:1993:IPI",
pages = "152--156",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p152-abramov/",
abstract = "The following computer algebra problem is considered:
how to compute the gcd of the polynomials $u(x,a)$ and
$v(x,a)$ for various values of the parameter $a$?. This
problem appears, for example, in solving systems of
algebraic equations by elimination methods, in
computing the logarithmic part of the integral of a
rational function, in solving difference and
differential equations, in summing rational functions,
etc. A fast algorithm to solve this problem is
described, and some applications of this algorithm are
discussed.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "B0210 (Algebra); B0290F (Interpolation and function
approximation); C1110 (Algebra); C4130 (Interpolation
and function approximation); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algebraic equations;
algorithms; Computer algebra problem; Differential
equations; Elimination methods; Fast algorithm, ISSAC;
Greatest common divisor; languages; Polynomials;
Rational function; Rational functions; SIGSAM; symbolic
computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Babai:1993:DCA,
author = "L{\'a}szl{\'o} Babai and Katalin Friedl and Markus
Stricker",
title = "Decomposition of $0*$-closed algebras in polynomial
time",
crossref = "Bronstein:1993:IPI",
pages = "86--94",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p86-babai/",
abstract = "Let A be a matrix algebra over $C$, closed under
Hermitian adjoints, and given by a basis. The authors
consider the classical problem of splitting the space
into the sum of A-irreducible subspaces. This includes
the problem of finding irreducible constituents of a
given unitary representation of a finite group. The
authors describe an algorithm which accomplishes the
splitting in a polynomial number of arithmetic
operations. Their model of computation assumes exact
arithmetic with complex numbers. Floating point
arithmetic is a reasonable approximation to this model;
they prove that their procedures are stable under minor
perturbation. The basic idea of their algorithms is
averaging via generalized Casimir operators. The result
generalizes to Frobenius algebras (algebras with a
non-degenerate associative bilinear form). The
corresponding problem in the model of exact symbolic
arithmetic does not seem tractable since it appears to
require handling field extensions of exponentially
large degree.",
acknowledgement = ack-nhfb,
affiliation = "Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
keywords = "A-irreducible subspaces; ACM; algebraic computation;
Algorithm; algorithms; Arithmetic operations; Asterisk
closed algebra; Complex numbers; Computation theory;
Decomposition; Floating point arithmetic; Frobenius
algebra; Generalized Casimir operator; Hermitian
adjoints; Irreducible constituents; ISSAC; Matrix
algebra; Model; Nondegenerate associative bilinear
form; Polynomial number; Polynomial time; SIGSAM; Space
splitting; Subspace; Symbolic arithmetic; symbolic
computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Algorithm theory; Matrix algebra; Matrix
decomposition; Polynomial matrices",
xxtitle = "Decomposition of $*$-closed algebras in polynomial
time",
}
@InProceedings{Babai:1993:DFM,
author = "L{\'a}szl{\'o} Babai and Robert Beals and Daniel
Rockmore",
title = "Deciding finiteness of matrix groups in deterministic
polynomial time",
crossref = "Bronstein:1993:IPI",
pages = "117--126",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p117-babai/",
abstract = "Let $G$ be a group of matrices with entries over an
algebraic number field $F$ (given symbolically). The
group $G$ is given by a list of generators. The authors
give several algorithms, both deterministic and
randomized, which can decide in polynomial time whether
or not $G$ is finite. It is easy to reduce the problem
to the case $F=Q$. As a next step, they present a
polynomial time algorithm which transforms $G$ into a
group of integral matrices whenever possible. Having
done so, the main results of the paper are several
polynomial time algorithms to handle the case of
integral matrices. They give both randomized and
deterministic algorithms to decide finiteness for
finitely generated integral matrix groups. Although
they are able to prove much better upper bounds for the
complexity of the deterministic algorithms, in
practice, the randomized algorithms support a much more
efficient implementation. Thus, both kinds of
algorithms are presented but only the implementation of
the randomized algorithm is explored.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "ACM; algebraic computation; Algorithm theory;
algorithms; Complexity; Deciding finiteness;
Deterministic algorithm; Deterministic polynomial time;
Finitely generated integral matrix groups; Group
theory; Integral matrices; Las Vegas algorithm, ISSAC;
Matrix algebra; Matrix groups; Monte Carlo algorithms;
Polynomial time algorithm; Randomized algorithm;
SIGSAM; Size; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS, Random number generation.",
thesaurus = "Decidability; Deterministic algorithms; Group theory;
Matrix algebra; Polynomial matrices; Randomised
algorithms",
}
@InProceedings{Beals:1993:EAC,
author = "Robert Beals",
title = "An elementary algorithm for computing the composition
factors of a permutation group",
crossref = "Bronstein:1993:IPI",
pages = "127--134",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p127-beals/",
abstract = "A permutation group $G$ may be concisely described by
a set $S$ of generators ($mod S mod$ need not be larger
than $\log\bmod{}G mod$ ). From such a short
description, however, it is not immediately clear how
to efficiently obtain various kinds of information
about the group. Furst, Hopcroft, and Luks (1980)
showed that an algorithm of Sims (1971) for computing
the order of $G$ and performing membership tests runs
in polynomial time. Sims's algorithm relies on
combinatorial methods, and there is no deep group
theory involved in the analysis. Polynomial time
algorithms for determining various aspects of the
structure of $G$ are also known. However, it seems that
algorithms which give us more information about $G$
require increasing amounts of group theory for their
analyses. An example is Luks's algorithm (1987) to find
composition factors (the `building blocks' of $G$),
which requires the classification of finite simple
groups (CFSG) for its proof of correctness. Kantor's
algorithm (1985) for finding Sylow subgroups likewise
requires CFSG. As the proof of CFSG is 15,000
manuscript pages long, it is reasonable to ask whether
so much group theory is necessary to study the
computational complexity of permutation group problems.
We give a deterministic polynomial time algorithm to
compute the composition factors of a permutation group,
given by a set of generators. This is the first
polynomial time algorithm for the composition factor
problem with an analysis that does not depend on CFSG.
In addition, we give a Monte Carlo version of our
algorithm which runs in nearly linear ($0(n \log^c n)$)
time for the class of `small-base' permutation groups
introduced by (Babai et al., 1991).",
acknowledgement = ack-nhfb,
classification = "C1110 (Algebra); C1140G (Monte Carlo methods);
C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; algorithms; CFSG;
Combinatorial methods; Composition factors;
Computational complexity; Deterministic polynomial time
algorithm; Elementary algorithm; Finite simple groups;
Group theory; Membership tests; Monte Carlo version,
ISSAC; Permutation group; Permutation group problems;
Polynomial time; Polynomial time algorithms; SIGSAM;
symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes.",
thesaurus = "Computational complexity; Group theory; Monte Carlo
methods",
}
@InProceedings{Bini:1993:PCT,
author = "Dario Bini and Victor Pan",
title = "Parallel computations with {Toeplitz-like} and
{Hankel-like} matrices",
crossref = "Bronstein:1993:IPI",
pages = "193--200",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p193-bini/",
abstract = "The known fast algorithms for computations with
general Toeplitz, Hankel, Toeplitz-like, and
Hankel-like matrices are inherently sequential. We
develop some new techniques in order to devise fast
parallel algorithms for computations with such
matrices, including the evaluation of their
characteristic polynomials, with further extensions to
computing the solution to a linear system of equations
with such a matrix and to several polynomial
computations (such as computing gcd, lcm, Pad{\'e}
approximation and extended Euclidean scheme for two
polynomials), as well as to computing the minimum span
of a linear recurrence sequence. The algorithms can be
applied over any field of constants, consist of simple
computational blocks (mostly reduced to fast Fourier
transforms, FFT's), and have potential practical value.
We also extend them to the case of matrices
representable as the sums of Toeplitz-like and
Hankel-like matrices.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Pisa Univ., Italy",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B0290Z (Other numerical
methods); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4190 (Other
numerical methods); C4240P (Parallel programming and
algorithm theory)",
keywords = "ACM; algebraic computation; algorithms; Characteristic
polynomials; Computational blocks; Extended Euclidean
scheme; Fast Fourier transforms, ISSAC; Hankel-like
matrices; Pad{\'e} approximation; Parallel algorithms;
Parallel computations; Polynomials; SIGSAM; symbolic
computation; theory; Toeplitz-like matrices",
subject = "{\bf I.0} Computing Methodologies, GENERAL. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computation of transforms.",
thesaurus = "Fast Fourier transforms; Hankel matrices; Parallel
algorithms; Polynomials; Toeplitz matrices",
}
@InProceedings{Bronstein:1993:FPF,
author = "Manuel Bronstein and Bruno Salvy",
title = "Full Partial Fraction Decomposition of Rational
Functions",
crossref = "Bronstein:1993:IPI",
pages = "157--160",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p157-bronstein/",
abstract = "We describe a rational algorithm that computes the
full partial fraction expansion of a rational function
over the algebraic closure of its field of definition.
The algorithm uses only gcd operations over the initial
field but the resulting decomposition is expressed with
linear denominators. We give examples from its Axiom
and Maple implementations.",
acknowledgement = ack-nhfb,
affiliation = "Wissenschaftliches Rechnen, Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "B0290D (Functional analysis); B0290H (Linear
algebra); B0290M (Numerical integration and
differentiation); C4120 (Functional analysis); C4140
(Linear algebra); C4160 (Numerical integration and
differentiation); C7310 (Mathematics computing)",
keywords = "ACM; Algebraic closure; algebraic computation; Axiom;
Decomposition; Full partial fraction decomposition; Gcd
operations; Maple; Polynomial; Rational functions;
SIGSAM; symbolic computation; Symbolic integration,
ISSAC; theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Function evaluation; Integration; Matrix
decomposition; Polynomial matrices; Symbol
manipulation",
}
@InProceedings{Caboara:1993:DAG,
author = "Massimo Caboara",
title = "A Dynamic Algorithm for {Gr{\"o}bner} basis
computation",
crossref = "Bronstein:1993:IPI",
pages = "275--283",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p275-caboara/",
abstract = "We recall preliminaries on Gr{\"o}bner bases,
Gr{\"o}bner Fans and Hilbert functions. We give an
outline of the dynamic algorithm. We report statistics
on some experiments and a few conclusions are given.
Experiments performed (and reported in this paper) show
an actual improvement of the combinatorial complexity.
However this doesn't reflect on timings, since the
`arithmetical' complexity both of the basis (number of
monomials appearing in it) and of the algorithm (number
of monomial operations) is not reduced. In the
important case of binomial ideals (where the
arithmetical complexity of the basis is constant), the
dynamic algorithm gives superior timings than the
classical one.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genoa Univ., Italy",
classification = "C4240C (Computational complexity); C6130 (Data
handling techniques); C7310 (Mathematics computing)",
keywords = "algorithms; theory; ISSAC; symbolic computation;
algebraic computation; ACM; SIGSAM; Dynamic algorithm;
Gr{\"o}bner basis computation; Gr{\"o}bner Fans;
Hilbert functions; Combinatorial complexity; Monomial
operations; Binomial ideals; Arithmetical complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Symbol manipulation",
}
@InProceedings{Cantone:1993:DPS,
author = "Domenico Cantone and Vincenzo Cutello",
title = "Decision procedures for stratified set-theoretic
syllogistics",
crossref = "Bronstein:1993:IPI",
pages = "105--110",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p105-cantone/",
abstract = "It is shown that a class of unquantified multi-sorted
set-theoretic formulae involving the notions of
powerset, general union, and singleton has a solvable
satisfiability problem. The authors show by means of a
model normalization procedure that any given
satisfiable formula in their theory has a finite model
whose size is bounded by a function of the number of
variables occurring in it.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Catania Univ., Italy",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C4210L (Formal languages and computational
linguistics)",
keywords = "ACM; algebraic computation; Computation theory;
Decidability; Decision procedure; Finite model; Formal
logic, ISSAC; General union; languages; Model
normalization procedure; Multisorted language;
Powerset; Set theory; SIGSAM; Singleton; Solvability;
Solvable satisfiability problem; Stratified
set-theoretic syllogistics; Syllogistic; symbolic
computation; theory; Unquantified multi-sorted
set-theoretic formulae",
subject = "{\bf F.4.3} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Formal Languages, Decision
problems. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Computability theory. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Computability; Computation theory; Decidability;
Decision theory; Set theory",
}
@InProceedings{Chou:1993:AGT,
author = "Shang-Ching Chou and Xiao-Shan Gao and Jing-Zhong
Zhang",
title = "Automated geometry theorem proving by vector
calculation",
crossref = "Bronstein:1993:IPI",
pages = "284--291",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p284-chou/",
abstract = "Based on a vector approach, we present a theorem
proving method for a class of constructive geometric
statements which covers a large portion of the equality
type geometry theorems about lines and circles. The
method is to eliminate the constructed points from the
conclusions of geometry statements based on a few basic
equalities on the inner and vector products of vectors
in the Euclidean plane. The method has been implemented
and the program has proved 410 nontrivial theorems
entirely automatically. The proofs produced by our
program are significantly shorter than the proofs
provided by programs based on the coordinate approach.
In spite of fact that the complexity of our algorithm
is exponential in the number of points in the geometry
statements, our program is practically very fast: 75
(95) percent of the 410 theorems can be proved within
one (five) second (seconds).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Wichita State Univ., KS, USA",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C4240C (Computational complexity); C4260
(Computational geometry)",
keywords = "algorithms; Automated geometry theorem proving;
Circles; Complexity; Equality type geometry theorems;
Euclidean plane; experimentation; Lines; theory; Vector
calculation; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving. {\bf I.1.4}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Applications.",
thesaurus = "Computational complexity; Computational geometry;
Theorem proving",
}
@InProceedings{Collins:1993:HMH,
author = "George E. Collins and Werner Krandick",
title = "A Hybrid Method for High Precision Calculation of
Polynomial Real Roots",
crossref = "Bronstein:1993:IPI",
pages = "47--52",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p47-collins/",
abstract = "A straightforward implementation of Newton's method
for polynomial real root calculation using exact
arithmetic is inefficient. In each step the length of
the iterate multiplies by the degree of the polynomial
while its accuracy merely doubles. We present an exact
algorithm which keeps the length of each iterate
proportional to its accuracy. The resulting speed up is
dramatic. The average computing time can be further
reduced by trying floating point computations. Several
floating point Newton steps are executed; interval
arithmetic is used to check whether the result is
sufficiently close to the root; if this condition
cannot be verified the exact algorithm is invoked.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Average
computing time; Exact algorithm; Floating point
computations; Floating point Newton steps; High
precision calculation; Hybrid method; Interval
arithmetic, ISSAC; Newton method; Polynomial real
roots; SIGSAM; symbolic computation; verification",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Floating point arithmetic; Mathematics computing;
Newton method; Polynomials",
}
@InProceedings{Edneral:1993:CGN,
author = "Victor F. Edneral",
title = "Computer Generation of Normalizing Transformation for
Systems of Nonlinear {ODE}",
crossref = "Bronstein:1993:IPI",
pages = "14--19",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p14-edneral/",
abstract = "The article describes the Standard LISP program for
building a normal form and a corresponding normalizing
transformation of a system of ordinary differential
equations (ODE) in A. D. Bruno's notation (1972) up to
the specified order. This program also includes a
complete set of procedures of arithmetic for the
truncated power series and input/output services. This
gives us an opportunity to continue a treatment of
obtained results autonomically or in a REDUCE
environment. The program can work in a rational
arithmetic or in an approximate rational arithmetic, or
in a floating point arithmetic. The program usage is
illustrated by treating systems of weakly nonlinear
ODEs in the language of the truncated series. The
approximate solution is produced from the normal form
calculated up to enough high order and from the
corresponding normalizing transformation. This method
demonstrates rather good agreement with numerical
solutions of some well known equations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow Univ., Russia",
classification = "C4170 (Differential equations); C6110 (Systems
analysis and programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; algorithms; Approximate
rational arithmetic; Computer generation; Floating
point arithmetic; Input/output services; languages;
Nonlinear ODE systems; Normal form; Normalizing
transformation; Ordinary differential equations; REDUCE
environment; SIGSAM; Standard LISP program; symbolic
computation; Truncated power series; Truncated series,
ISSAC; verification; Weakly nonlinear ODEs",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods). {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Difference equations; LISP; Programming; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Emiris:1993:PMS,
author = "Ioannis Emiris and John Canny",
title = "A Practical Method for the Sparse Resultant",
crossref = "Bronstein:1993:IPI",
pages = "183--192",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p183-emiris/",
abstract = "We propose an efficient method for computing the
resultant of a sparse polynomial system of $n+1$
equations in $n$ unknowns. Our approach constructs a
matrix whose determinant is a non-zero multiple of the
resultant and from which the latter is easily
extracted. For certain classes of systems, it attains
optimality by expressing the resultant as a single
determinant. An implementation of the algorithm is
described and empirical results presented and compared
with previous works. In addition, the important
subproblem of computing mixed volumes is examined and
an efficient algorithm is implemented.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "ACM; algebraic computation; algorithms;
experimentation; Mixed volumes, ISSAC; SIGSAM; Sparse
polynomial system; Sparse resultant; symbolic
computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.2.9} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Robotics. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Polynomials",
}
@InProceedings{Ganzha:1993:PSM,
author = "V. G. Ganzha and E. V. Vorozhtsov",
title = "A Probabilistic Symbolic-Numerical Method for the
Stability Analyses of Difference Schemes for {PDEs}",
crossref = "Bronstein:1993:IPI",
pages = "9--13",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p9-ganzha/",
abstract = "We present a new symbolic numerical method for an
automatic stability analysis of difference schemes
approximating scalar linear of nonlinear partial
differential equations (PDEs) of hyperbolic or
parabolic type. In this method the grid values of the
numerical solution for any fixed moment of time are
considered as random correlated variables obeying the
normal distribution law. Therefore, one can apply the
notion of the C. E. Shannon's (1948) entropy to
characterize the stability of a difference scheme. The
reduction of this entropy, or uncertainty, is taken as
a stability criterion. It is shown at a number of
examples that this criterion yields the same stability
regions in the cases of linear difference initial value
problems, as the Fourier method. In the case of two
spatial variables the present probabilistic method is
computationally faster than the Fourier method by two
orders of magnitude.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, Russia",
classification = "C1140Z (Other topics in statistics); C4170
(Differential equations); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; algorithms; Automatic
stability analysis; Difference schemes; Fixed moment;
Fourier method; Grid values; Linear difference initial
value problems; Nonlinear partial differential
equations; Normal distribution law; Parabolic type;
PDEs; Probabilistic symbolic-numerical method; Random
correlated variables; SIGSAM; Spatial variables, ISSAC;
Stability analyses; Stability criterion; symbolic
computation; Symbolic numerical method; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Finite difference methods.",
thesaurus = "Difference equations; Nonlinear differential
equations; Normal distribution; Numerical stability;
Partial differential equations; Symbol manipulation",
}
@InProceedings{Godlevsky:1993:PPA,
author = "A. B. Godlevsky and A. E. Doroshenko",
title = "Parallelizing Programs with {APS}",
crossref = "Bronstein:1993:IPI",
pages = "55--62",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p55-godlevsky/",
abstract = "An approach to parallelizing sequential programs as
rewriting rules application by means of the algebraic
programming system APS is considered. It gives the
advantages of rapid prototyping and evolutionary
development of efficient parallelizers.",
acknowledgement = ack-nhfb,
affiliation = "V. M. Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
Ukraine",
classification = "C4210L (Formal languages and computational
linguistics); C5440 (Multiprocessing systems); C6110P
(Parallel programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic programming
system; algorithms; APS; Distributed memory parallel
computers; Efficient parallelizers; Evolutionary
development; ISSAC; languages; Massively parallel
computer systems; Rapid prototyping; Rewriting rules;
SIGSAM, Sequential program parallelization; symbolic
computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent
Programming, Parallel programming.",
thesaurus = "Distributed memory systems; Parallel programming;
Rewriting systems; Software prototyping; Symbol
manipulation",
}
@InProceedings{Gruntz:1993:NAC,
author = "Dominik Gruntz",
title = "A New Algorithm for Computing Asymptotic Series",
crossref = "Bronstein:1993:IPI",
pages = "239--244",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p239-gruntz/",
abstract = "We describe a new algorithm for computing asymptotic
expansions for a large class of expressions, whereby
the asymptotic series are of a form more complicated
than mere Puiseux series. Today's computer algebra
systems still lack good algorithms for handling such
asymptotic expansions, although in theory some
algorithms have been presented. The algorithm we
present in this article is directly induced by the
limit computation algorithm presented in Gonnet and
Gruntz (1992) which is based on series computations in
terms of the most rapidly varying subexpression of a
given expression. Examples of the algorithm implemented
in Maple are shown.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Sci. Comput., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "C1100 (Mathematical techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Asymptotic
expansions; Computer algebra; ISSAC; Maple; SIGSAM,
Asymptotic series; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems.",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Gutnik:1993:ACA,
author = "S. A. Gutnik",
title = "Application of Computer Algebra to Investigation of
the Relative Equilibria of a Satellite",
crossref = "Bronstein:1993:IPI",
pages = "63--64",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p63-gutnik/",
abstract = "A new approach for the symbolic analysis of the
satellites dynamical equations is presented. The
investigation is made by means of Gr{\"o}bner Basis
method. The presence of various perturbations is
supposed, such as gravitational and constant torques.
It is shown that a satellite moving in a circular orbit
with a prescribed constant torque and prescribed
central moments of inertia has at most 24 equilibrium
positions in an orbiting frame in the general case.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Comput. Aided Design, Acad. of Sci., Moscow,
Russia",
classification = "C7310 (Mathematics computing)",
keywords = "algorithms; Computer algebra; Relative equilibria;
Symbolic analysis; Satellites dynamical equations;
Gr{\"o}bner Basis; Perturbations; Gravitational
torques; Constant torques; Circular orbit, ISSAC;
symbolic computation; algebraic computation; ACM;
SIGSAM",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Aerospace. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
thesaurus = "Angular velocity; Symbol manipulation",
}
@InProceedings{Halstead:1993:APS,
author = "R. H. Halstead and T. Chikayama and R. Gabriel and D.
Waltz",
title = "Applications for Parallel Symbolic Computation",
crossref = "Halstead:1993:PSC",
pages = "417--417",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hong:1993:QEF,
author = "Hoon Hong",
title = "Quantifier elimination for formulas constrained by
quadratic equations",
crossref = "Bronstein:1993:IPI",
pages = "264--274",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p264-hong/",
abstract = "An algorithm is given for constructing a quantifier
free formula (a boolean expression of polynomial
equations and inequalities) equivalent to a given
formula of the form: (There exists $x$ in
$R$)($a_2x^2+a_1x+a_0=O V-product F$), where $F$ is a
quantifier free formula in $x_1,\ldots{},x_r,x,$ and
$a_2, a_1, a_0$ are polynomials in $x_1,\ldots{},x_r$
with real coefficients such that the system
($a_2=0,a_1=0, a_0=0$) has no solution in $R^r$.
Formulas of this form frequently occur in the context
of constraint logic programming over the real numbers.
The output formulas are made of resultants and two
variants, which we call trace and slope resultants.
Both of these variant resultants can be expressed as
determinants of certain matrices.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence); C4130
(Interpolation and function approximation); C4210
(Formal logic); C6110L (Logic programming)",
keywords = "algorithms; Boolean expression; Constraint logic
programming; Determinants; Inequalities; Polynomial
equations; Polynomials; Quadratic equations; Quantifier
elimination; Quantifier free formula; theory;
verification",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Analysis of algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Boolean algebra; Logic programming; Polynomials",
}
@InProceedings{Ito:1993:MPA,
author = "T. Ito and R. Nikhil and J. Padget and N. Suzuki",
title = "Massively Parallel Architectures and Symbolic
Computation",
crossref = "Halstead:1993:PSC",
pages = "408--416",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jebelean:1993:GBG,
author = "T. Jebelean",
title = "A Generalization of the Binary {GCD} Algorithm",
crossref = "Bronstein:1993:IPI",
pages = "111--116",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p111-jebelean/",
abstract = "A generalization of the binary algorithm for operation
at `word level' by using a new concept of `modular
conjugates' computes the GCD of multiprecision integers
two times faster than the Lehmer--Euclid method. Most
importantly, however, the new algorithm is suitable for
systolic parallelization, in `least-significant digits
first' pipelined manner and for aggregation with other
systolic algorithms for the arithmetic of
multiprecision rational numbers.",
acknowledgement = ack-nhfb,
affiliation = "RISC, Linz, Austria",
classification = "C4240P (Parallel programming and algorithm theory)",
keywords = "ACM; algebraic computation; algorithms; Arithmetic;
Binary algorithm; Binary GCD algorithm; Computation
speed; Computational efficiency; experimentation;
Least-significant digits first; Modular conjugates;
Multiprecision integer; Multiprecision rational
numbers; Parallel processing; Pipelined; SIGSAM;
symbolic computation; Systolic algorithm; Systolic
array, ISSAC; Systolic parallelization; Word level",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf F.1.2}
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Modes of Computation, Parallelism and concurrency. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algorithm theory; Parallel algorithms; Symbol
manipulation; Systolic arrays",
}
@InProceedings{Jeffrey:1993:IOE,
author = "D. J. Jeffrey",
title = "Integration to obtain expressions valid on domains of
maximum extent",
crossref = "Bronstein:1993:IPI",
pages = "34--41",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p34-jeffrey/",
abstract = "In certain circumstances, the integration routines
used by computer algebra systems return expressions
whose domains of validity are unnecessarily restricted
by the presence of discontinuities. It is argued that
this is undesirable and that integration routines
should meet an additional requirement: they should
return expressions that are valid on domains of maximum
extent. The contention is supported by general
mathematical arguments, by an examination of existing
practises and by a demonstration that two standard
algorithms can be modified to meet the requirement.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Univ. of Western Ontario,
London, Ont., Canada",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Computer
algebra systems; Discontinuities; General mathematical
arguments; Integration routines; languages; Maximum
extent; SIGSAM; Standard algorithms, ISSAC; symbolic
computation; Validity domains",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Integration; Symbol manipulation",
}
@InProceedings{Jinzhao:1993:RPG,
author = "Wu-Jinzhao and Li-Lian",
title = "The regular problem and {Green} equivalences for
special monoids",
crossref = "Bronstein:1993:IPI",
pages = "78--85",
year = "1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For the monoid presented by a finite special
Church--Rosser Thue system, whether it is a regular
semigroup is decidable in polynomial time. The number
of each kind of Green equivalence classes is either one
or infinite and it is computable in polynomial time.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1160 (Combinatorial mathematics); C4210L (Formal
languages and computational linguistics)",
keywords = "ACM; algebraic computation; Computability; Computation
theory; Decidability; Decidable; Finite special
Church--Rosser Thue system; Green equivalences; ISSAC;
Polynomial time; Regular problem; Regular semigroup;
SIGSAM; Special monoid; String rewriting Green
equivalence class; symbolic computation",
thesaurus = "Computability; Decidability; Equivalence classes;
Group theory; Rewriting systems",
}
@InProceedings{Kalkbrener:1993:UBN,
author = "Michael Kalkbrener",
title = "An upper bound on the number of monomials in the
{Sylvester} resultant",
crossref = "Bronstein:1993:IPI",
pages = "161--163",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p161-kalkbrener/",
abstract = "The Sylvester resultant is not only a classical
concept in commutative algebra but also a useful tool
for actually computing solutions of systems of
algebraic equations. We derive an upper bound on the
number of monomials in the Sylvester resultant using a
result from the theory of partially ordered sets.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Eidgenossische Tech. Hochschule,
Zurich, Switzerland",
classification = "B0210 (Algebra); B0250 (Combinatorial mathematics);
B0290F (Interpolation and function approximation);
C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic equations;
algorithms; Commutative algebra $b$; Monomials;
Partially ordered sets, ISSAC; SIGSAM; Sylvester
resultant; symbolic computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Polynomials; Set theory; Symbol manipulation",
}
@InProceedings{Keady:1993:AIS,
author = "G. Keady and M. G. Richardson",
title = "An application of {IRENA} to systems of nonlinear
equations arising in equilibrium flows in networks",
crossref = "Bronstein:1993:IPI",
pages = "311--320",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p311-keady/",
abstract = "IRENA --- an Interface from REDUCE to NAG --- runs
under the REDUCE Computer Algebra (CA) system and
provides an interactive front end to the NAG Fortran
Library. Here IRENA is tested on a problem closer to an
engineering problem than previously published
examples. We also illustrate the use of the codeonly
switch, which is relevant to larger scale problems. We
describe progress on an issue raised in the `Future
Developments' section in our SIGSAM Bulletin article by
K. A. Broughan et al. (1991): the progress improves the
practical effectiveness of IRENA.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Western Australia Univ., Nedlands, WA,
Australia",
classification = "C4150 (Nonlinear and functional equations); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Codeonly
switch; Equilibrium flows; Interactive front end;
Interface from REDUCE to NAG; ISSAC; languages; NAG
Fortran Library; REDUCE Computer Algebra; SIGSAM,
IRENA; symbolic computation; Systems of nonlinear
equations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Network problems.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Mathematics computing; Nonlinear equations; Symbol
manipulation",
}
@InProceedings{Klimov:1993:SEN,
author = "D. M. Klimov and V. M. Rudenko and V. V. Leonov",
title = "Symbolic Evaluation in the Nonlinear Mechanical
Systems",
crossref = "Bronstein:1993:IPI",
pages = "53--54",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p53-klimov/",
abstract = "The paper presents the features of a program package,
Polymech-symbol, helping to solve some laborious
mechanical problems. The package was written by means
of the REDUCE system and contains several algorithms in
a form of REDUCE procedures. The computer algebra
methods may be successfully used for solving the
problems of navigation and defining the trajectory of
satellite mass centre motion. The preliminary
analytical research provides the effective algorithm
for on-board solving the problem of prediction. To
assure necessary accuracy, we need to construct several
higher approximations. Such sophisticated problems can
be solved only with the help of symbolic computations
that deal with the processing of cumbersome analytical
expressions. For effective analytical investigation of
such kinds of problems, the choice of parameters which
describe the perturbed orbital motion is critical. In
addition to the natural requirements of the calculation
process efficiency and the absence of singularities in
equations of motion, it is useful to have a unified
mathematical description for the angular motion and for
the motion of the mass centre.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Problems of Mech., Acad. of Sci., Moscow,
Russia",
classification = "C7310 (Mathematics computing); C7320 (Physics and
chemistry computing)",
keywords = "ACM; algebraic computation; algorithms; Analytical
expressions; Angular motion; Calculation process
efficiency; Computer algebra methods; Higher
approximations; languages; Mass centre motion, ISSAC;
Mechanical problems; Nonlinear mechanical systems;
Perturbed orbital motion; Polymech-symbol; Prediction;
Program package; REDUCE procedures; REDUCE system;
Satellite mass centre motion; SIGSAM; symbolic
computation; Symbolic computations; Symbolic
evaluation; Trajectory; Unified mathematical
description",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Mechanics; Physics computing; Symbol manipulation",
}
@InProceedings{Lin:1993:SRT,
author = "Dongdai Lin and Zhuojun Liu",
title = "Some results on theorem proving in geometry over
finite fields",
crossref = "Bronstein:1993:IPI",
pages = "292--300",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p292-lin/",
abstract = "In this paper, we discuss Wu's well ordering principle
and theorem proving over finite fields, try to prove
some theorems in the geometry over finite fields.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1230 (Artificial intelligence); C4210 (Formal
logic); C4240 (Programming and algorithm theory); C4260
(Computational geometry)",
keywords = "ACM; algebraic computation; algorithms; Finite fields;
ISSAC; SIGSAM; symbolic computation; Theorem proving;
theory; verification; Well ordering principle",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations in finite fields. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Mechanical theorem proving. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Madlener:1993:CGB,
author = "Klaus Madlener and Birgit Reinert",
title = "Computing {Gr{\"o}bner} Bases in Monoid and Group
Rings",
crossref = "Bronstein:1993:IPI",
pages = "254--263",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p254-madlener/",
abstract = "Following Buchberger's approach to computing a
Gr{\"o}bner basis of a polynomial ideal in polynomial
rings, a completion procedure for finitely generated
right ideals in $Z(H)$ is given, where $H$ is an
ordered monoid presented by a finite, convergent
semi-Thue system $(\Sigma,T)$. Taking a finite set $F$
contained in $Z(H)$ we get a (possibly infinite) basis
of the right ideal generated by $F$, such that using
this basis we have unique normal forms for all $p$ in
$Z(H)$ (especially the normal form is zero in case $p$
is an element of the right ideal generated by $F$). As
the ordering and multiplication on H need not be
compatible, reduction has to be defined carefully in
order to make it Noetherian. Further we no longer have
$p.x$ to $-{}_p0$ for $p$ in $Z(H)$, $x$ in $H$.
Similar to Buchberger's $s$-polynomials, confluence
criteria are developed and a completion procedure is
given. In case $T= \phi$ or $(\Sigma,T)$ is a
convergent, 2-monadic presentation of a group with
inverses of length 1, termination can be shown. An
application to the subgroup problem is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
keywords = "algorithms; theory; verification; ISSAC; symbolic
computation; algebraic computation; ACM; SIGSAM, Group
rings; Gr{\"o}bner bases; Polynomial rings; Semi-Thue
system; Monoid rings",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Group theory; Polynomials; Symbol manipulation",
}
@InProceedings{Monagan:1993:GAD,
author = "Michael B. Monagan and Walter M. Neuenschwander",
title = "{GRADIENT}: algorithmic differentiation in {Maple}",
crossref = "Bronstein:1993:IPI",
pages = "68--76",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p68-monagan/",
abstract = "Many scientific applications require computation of
the derivatives of a function $f:R^n$ to $R^m$ as well
as the function values of $f$ itself. All computer
algebra systems can differentiate functions represented
by formulae. But not all functions can be described by
formulae. And formulae are not always the most
effective means for representing functions and
derivatives. In this paper we describe the algorithms
used by the Maple (2) routine GRADIENT that accepts as
input a Maple procedure for the computation of $f$ and
outputs a new Maple procedure that computes the
gradient of $f$. The design of the GRADIENT routine is
such that it is also trivial to generate Maple
procedures for the computation of Jacobians and
Hessians.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algorithmic
differentiation; algorithms; Computer algebra systems;
Function values; GRADIENT; Hessians, ISSAC; Jacobians;
languages; Maple; Scientific applications; SIGSAM;
symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures.",
thesaurus = "Differentiation; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Mourrain:1993:GPP,
author = "B. Mourrain",
title = "The 40 ``generic'' positions of a parallel robot",
crossref = "Bronstein:1993:IPI",
pages = "173--182",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p173-mourrain/",
abstract = "We consider the direct kinematic problem of a parallel
robot (called the Stewart platform or left hand). We
want to show how the use of formal tools help us to
guess the solution of this problem and then to
establish it. We do not try to give real-time and
numerical solutions to the problem of inverse images
but focus on tools of effective algebra, which can help
us to know a little more about the geometric aspects of
the question. We describe experiments done in order to
obtain the number of generic positions of this robot,
once the length of the arms are known. We also sketch
the proof that the degree of the corresponding map is
40. We use explicit elimination techniques in order to
remove the solution at infinity and we use Bezout's
theorem on surfaces with circularity as a conclusion.",
acknowledgement = ack-nhfb,
affiliation = "SAFIR, Valbonne, France",
classification = "C1110 (Algebra); C1310 (Control system analysis and
synthesis methods); C3390M (Manipulators); C4260
(Computational geometry); C7420D (Control system design
and analysis)",
keywords = "ACM; algebraic computation; Arms; Bezout's theorem;
Circularity, ISSAC; Direct kinematic problem; Effective
algebra; experimentation; Explicit elimination
techniques; Formal tools; Generic positions; Geometric
aspects; Left hand; Parallel robot; Proof; SIGSAM;
Stewart platform; Surfaces; symbolic computation;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.2.9}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Robotics. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures.",
thesaurus = "Algebra; Computational geometry; Control system
analysis computing; Manipulator kinematics; Theorem
proving",
}
@InProceedings{Petkovsek:1993:FAH,
author = "M. Petkovsek and B. Salvy",
title = "Finding All Hypergeometric Solutions of Linear
Differential Equations",
crossref = "Bronstein:1993:IPI",
pages = "27--33",
year = "1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Hypergeometric sequences are such that the quotient of
two successive terms is a fixed rational function of
the index. We give a generalization of M. Petkovsek's
algorithm (1992) to find all hypergeometric sequence
solutions of linear recurrences, and we describe a
program to find all hypergeometric functions that solve
a linear differential equation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Ljubljana Univ., Slovenia",
classification = "C4170 (Differential equations); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; Computer algebra, ISSAC;
Fixed rational function; Hypergeometric sequences;
Hypergeometric solutions; Linear differential
equations; Linear recurrences; Quotient; SIGSAM;
Successive terms; symbolic computation",
thesaurus = "Linear differential equations; Sequences; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Petkovsek:1993:FAHb,
author = "Marko Petkov{\v{s}}ek and Bruno Salvy",
title = "Finding all hypergeometric solutions of linear
differential equations",
crossref = "Bronstein:1993:IPI",
pages = "27--33",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p27-petkovscaronek/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Richardson:1993:ZST,
author = "Daniel Richardson",
title = "A Zero Structure Theorem for Exponential Polynomials",
crossref = "Bronstein:1993:IPI",
pages = "144--151",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p144-richardson/",
abstract = "An exponential system is a system of equations
$(S=O,E=O)$, where $S$ is a finite set of polynomials
in $Q(x_1,\ldots{},x_n,y_1,\ldots{},y_n)$, and $E$ is a
subset of $(y_1-e^{x1},\ldots{},y_n-e^{xn})$. Wu's
method (1984) is used effectively to decompose such
systems into finitely many subsystems which have
triangular algebraic part, and whose solution sets in
$C^{2n}$ are equidimensional and also, in a sense
explained, non singular. The problem of solving
exponential systems in bounded regions of $R^n$ is also
discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Bath Univ., UK",
classification = "B0210 (Algebra); B0290F (Interpolation and function
approximation); B0290H (Linear algebra); C1110
(Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra)",
keywords = "ACM; algebraic computation; algorithms; Bounded
regions; Exponential polynomials; Exponential system;
ISSAC; SIGSAM, Zero structure theorem; Solution sets;
symbolic computation; theory; Triangular algebraic
part",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Matrix decomposition; Polynomial matrices",
}
@InProceedings{Roy:1993:AGA,
author = "Marie-Fran{\c{c}}oise Roy and T. {Van Effelterre}",
title = "Aspect graphs of algebraic surfaces",
crossref = "Bronstein:1993:IPI",
pages = "135--143",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p135-roy/",
abstract = "An aspect graph is a representation of 3D objects that
is used in the field of computer vision for recognition
in 2D images. The viewspace around the object is
tesselated in a finite number of cells by the semi
algebraic visual events locus. The topology of the
image contour remains stable in each cell and may only
change on the visual events locus. An aspect graph
represents a 3D object whose surface boundary is
algebraic or semi algebraic by the finite number of
different topological aspects of its image contour and
by the visual events that make a stable aspect switch
to another one. We show that the number of different
topological aspects of an algebraic surface of degree
$d$ is upper bounded by a $O(d^{12})$ for orthographic
projection and $O(d^{18})$ for perspective projection.
This result is a generalisation of the upper bound of
$O(d^6)$ obtained by M.-F. Roy and T. Van Effelterre
(1992) for surfaces of revolution under perspective
projection and improves the most recent upper bounds of
$O(d^{20})$ for orthographic projection and $O(d^{30})$
for perspective projection. We also show how to compute
the equations of the visual events locus with
Gr{\"o}bner bases systems and Hermite's method.",
acknowledgement = ack-nhfb,
affiliation = "IRMAR, Rennes I Univ., France",
classification = "C1160 (Combinatorial mathematics); C4260
(Computational geometry); C5260B (Computer vision and
image processing techniques)",
keywords = "algorithms; design; Aspect graph; Algebraic surfaces;
3D objects; Computer vision; 2D image recognition;
Viewspace; Semi algebraic visual events locus; Image
contour; Visual events locus; Surface boundary;
Orthographic projection; Perspective projection;
Gr{\"o}bner bases systems; Hermite method, ISSAC;
symbolic computation; algebraic computation; ACM;
SIGSAM",
subject = "{\bf I.0} Computing Methodologies, GENERAL. {\bf
I.5.4} Computing Methodologies, PATTERN RECOGNITION,
Applications, Computer vision. {\bf J.6} Computer
Applications, COMPUTER-AIDED ENGINEERING,
Computer-aided design (CAD).",
thesaurus = "Computational geometry; Computer vision; Graph theory;
Object recognition",
}
@InProceedings{Santas:1993:TSC,
author = "Phillip S. Santas",
title = "A type system for computer algebra (abstract)",
crossref = "Bronstein:1993:IPI",
pages = "77--77",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p77-santas/",
abstract = "Summary form only given. Examines type systems for
support of subtypes and categories in computer algebra
systems. By modelling representation of instances in
terms of existential types instead of recursive types,
the author obtains not only a simplified model, but
also builds a basis for defining subtyping among
algebraic domains. The introduction of metaclasses
facilitates the task by allowing the inference of type
classes. By means of type classes and existential
subtypes, relations are constructed without involving
coercions.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Sci. Comput., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "ACM; algebraic computation; Algebraic domain;
Categories; Computer algebra; design; Existential
subtype; Existential type; ISSAC; Metaclass; Model;
Representation of instances; SIGSAM, Type system;
Subtype; Subtyping; symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.3.3} Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Type structure.",
thesaurus = "Process algebra; Symbol manipulation; Type theory",
}
@InProceedings{Sendra:1993:EAH,
author = "Juan R. Sendra and Juan Llovet",
title = "Efficient algorithms for {Hankel} matrices over
${Z}(x_1,\ldots{},x_r)$",
crossref = "Bronstein:1993:IPI",
pages = "201--208",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p201-sendra/",
abstract = "In this paper, we investigate the problem of the rank
and the determinant of Hankel matrices over
$Z(x_1,\ldots{},x_r)$. A modular algorithm for
determining the rank of a Hankel matrix with entries
that are multivariate polynomials over the integers is
presented. The algorithm is based on modular
techniques, which consist in computing the rank of
Hankel matrices over finite fields by a special
algorithm that needs $O(n^2)$ arithmetic operations,
where $n$ is the order of the matrix. The general
solution is achieved by determining the maximum of the
ranks computed over the finite fields. Similarly, we
give a theorem that shows how to compute Hankel
determinants in $O(n^2)$ arithmetic operations. The
worst case complexity of the algorithm is
$O((n^{r+3}G^r+n^{r+2}G^{r+1}) \log{}n \log^2 L)$,
where $G$ and $L$ are some appropriate bounds for the
degree and the norm of the entries respectively.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Alcala Univ., Madrid, Spain",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity)",
keywords = "ACM; algebraic computation; algorithms; Determinant;
Hankel matrices; Modular algorithm; Multivariate
polynomials, ISSAC; Rank; SIGSAM; symbolic computation;
theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations in finite fields. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Hankel
matrices; Polynomials",
}
@InProceedings{Shackell:1993:NEH,
author = "John Shackell",
title = "Nested Expansions and {Hardy} Fields",
crossref = "Bronstein:1993:IPI",
pages = "234--238",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p234-shackell/",
abstract = "Let $X$ denote the ring of germs, at $+ \infty$, of
$C^\infty$ real-valued functions each defined on some
subinterval of $R$ of the form $(a, infinity )$. Using
a common abuse of terminology we shall often treat
elements of $X$ as functions rather than the germs of
functions. A Hardy field is a subfield of $X$ closed
under differentiation. The definition is simple and
natural, but the connection with asymptotics is perhaps
not apparent at first sight. Let $F$ be any Hardy
field. A non-zero element, $f$, of $F$ has to have an
inverse in $F$ and so cannot have arbitrarily large
zeros. Therefore $f$ is either ultimately positive or
ultimately negative. If $g$ is another element of $F$
we can define $f > g$ to mean that $f-g$ is ultimately
positive. This makes $F$ into a totally ordered field
with the order reflecting the asymptotic behaviour of
elements. Since $F$ is closed under differentiation,
its elements must either be ultimately increasing,
ultimately decreasing or ultimately constant. Hardy,
showed that the exp-log functions form a field with
these properties. One of the obvious difficulties with
nested expansions is the fact that they are complicated
to manipulate. However that need not be a barrier for
computer algebra systems. A complexity which is doubly
exponential in the number of terms could be more
serious though. Perhaps only experience will determine
whether this is a real obstacle in practice.",
acknowledgement = ack-nhfb,
classification = "C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Asymptotics;
Complexity; Computer algebra systems; Hardy field;
ISSAC; Nested expansions; SIGSAM, Hardy fields;
symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Shevchenko:1993:SRP,
author = "Ivan I. Shevchenko and Andrej G. Sokolsky",
title = "Studies of Regular Precessions of a Symmetric
Satellite by Means of Computer Algebra",
crossref = "Bronstein:1993:IPI",
pages = "65--67",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p65-shevchenko/",
abstract = "The perturbed motion in the neighbourhood of regular
precessions of a dynamically symmetric satellite on a
circular orbit is studied. The `Norma' specialized
program package (A. G. Sokolsky, I. I. Shevenko, 1990;
1991), intended for normalization of autonomous
Hamiltonian systems by means of computer algebra, is
used to obtain normal forms of the Hamiltonian. A full
catalogue of non resonant and resonant normal forms up
to the 6th order of normalization is constructed for
the case of hyperboloidal precession. The case of
cylindrical precession, more complicated in analytical
sense, is considered as well. Analytical expressions
for coefficients of terms of the normal forms are
derived as dependences on the frequencies and the
initial physical parameters of the system. Though the
intermediary expressions occupy megabytes of computer
memory, the final normal forms are compact.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. Astron., Acad. of Sci., St.
Petersburg, Russia",
classification = "C4140 (Linear algebra); C6130 (Data handling
techniques); C7310 (Mathematics computing); C7350
(Astronomy and astrophysics computing)",
keywords = "ACM; algebraic computation; algorithms; Analytical
expressions; Autonomous Hamiltonian systems; Circular
orbit; Computer algebra; Cylindrical precession;
design; Dynamically symmetric satellite; Hyperboloidal
precession; Initial physical parameters; Intermediary
expressions, ISSAC; Norma specialized program package;
Perturbed motion; Regular precessions; Resonant normal
forms; SIGSAM; symbolic computation; Symmetric
satellite",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf J.2} Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Aerospace.",
thesaurus = "Astronomy computing; Matrix algebra; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Siegl:1993:PAS,
author = "K. Siegl",
title = "Parallelizing algorithms for symbolic computation
using $\parallel${Maple}$\parallel$",
crossref = "ACM:1993:PFA",
pages = "179--186",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
standardno = "1",
}
@InProceedings{Stifter:1993:GTP,
author = "Sabine Stifter",
title = "Geometry Theorem Proving in Vector Spaces by Means of
{Gr{\"o}bner} Bases",
crossref = "Bronstein:1993:IPI",
pages = "301--310",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p301-stifter/",
abstract = "Within the last few years several approaches to
automated geometry theorem proving have been developed
and proposed that are based (1) on the formulation of a
geometric statement as the implication of a polynomial
equation (the `conclusion') from a set of polynomial
equations (the `hypotheses'), and (2) the proof of the
implication by algebraic methods, namely Gr{\"o}bner
bases and Ritt's bases. All these approaches require
the introduction of coordinates for the points
involved. Many geometric theorems, however, can be
formulated as relations between points directly,
without needing coordinates. In this paper we develop a
new method, based on Gr{\"o}bner bases in vector
spaces, that can prove geometric theorems that are
formulated as relations between points directly. Our
approach has the advantages that theorems can be
formulated more naturally and fewer variables are
needed for their formulations. This results in shorter
and faster proofs.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence); C4210 (Formal
logic); C4260 (Computational geometry)",
keywords = "theory; Geometry theorem proving; Vector spaces;
Gr{\"o}bner bases; Geometric statement; Coordinates;
Geometric theorems, ISSAC; symbolic computation;
algebraic computation; ACM; SIGSAM",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Vallier:1993:ACN,
author = "L. Vallier",
title = "An Algorithm for the Computation of Normal Forms and
Invariant Manifolds",
crossref = "Bronstein:1993:IPI",
pages = "225--233",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p225-vallier/",
abstract = "This paper deals with an algorithm to compute normal
forms and invariant manifolds of ordinary differential
equations. This algorithm based on transformation
theory, gives us a useful tool in the study of such
equations, in the neighborhood of singular points. This
tool involves a lot of computations on homogeneous
polynomials. Then in addition, a tree data structure is
described to represent homogeneous polynomials in an
efficient way, and we give the cost of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "LMC, IMAG, Grenoble, France",
classification = "B0290F (Interpolation and function approximation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4170 (Differential
equations); C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; Algorithm, ISSAC;
algorithms; Homogeneous polynomials; Invariant
manifolds; Normal forms; Ordinary differential
equations; SIGSAM; Singular points; symbolic
computation; theory; Transformation theory; Tree data
structure",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf E.1} Data, DATA
STRUCTURES, Trees. {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Computational complexity; Differential equations;
Polynomials; Tree data structures",
}
@InProceedings{vanderPut:1993:RRK,
author = "Marius {van der Put} and Peter A. Hendriks",
title = "A rationality result for {Kovacic}'s algorithm",
crossref = "Bronstein:1993:IPI",
pages = "4--8",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p4-van_der_put/",
abstract = "We want to prove the following rationality result (J.
J. Kovacic, 1986). Suppose that the Riccati equation
$u^1+u^2=r$ has a solution, which is algebraic over
$Q^{cl}(x)$. Then there exists an algebraic solution
$u$ of minimal degree $n$ of the Riccati equation such
that the coefficients of the minimum polynomial of $u$
over $Q^{cl}(x)$ lie in a field $K(x)$ with $(K:Q)<=2$.
Moreover, only in the cases: $n=1$ and $G$ is the
multiplicative group $G_m$ or a finite cyclic group of
order $>2$ or $n=4$ and $G$ the tetrahedral group, a
field extension $K$ of degree 2 of $Q$ can be needed.",
acknowledgement = ack-nhfb,
classification = "C1160 (Combinatorial mathematics); C4140 (Linear
algebra); C4170 (Differential equations)",
keywords = "ACM; algebraic computation; Algebraic solution;
algorithms; Field extension; Finite cyclic group;
ISSAC; Kovacic algorithm; Minimum polynomial;
Multiplicative group; Riccati equation; SIGSAM,
Rationality result; symbolic computation; Tetrahedral
group; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic.",
thesaurus = "Group theory; Linear differential equations; Riccati
equations",
}
@InProceedings{Villard:1993:CSN,
author = "Gilles Villard",
title = "Computation of the {Smith} normal form of polynomial
matrices",
crossref = "Bronstein:1993:IPI",
pages = "209--217",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p209-villard/",
abstract = "We describe a new algorithm for the computation of the
Smith normal form of polynomial matrices. This
algorithm computes the normal form and pre- and
post-multipliers in deterministic polynomial time.
Noticing that the computation reduces to a linear
algebra problem over the field of the coefficients, we
obtain a good worst-case complexity bound.",
acknowledgement = ack-nhfb,
affiliation = "Lab. LMC, IMAG, Grenoble, France",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity)",
keywords = "ACM; algebraic computation; algorithms; Deterministic
polynomial time; Linear algebra, ISSAC; Polynomial
matrices; SIGSAM; Smith normal form; symbolic
computation; theory; Worst-case complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Linear algebra; Polynomial
matrices",
}
@InProceedings{Volcheck:1993:NSS,
author = "E. J. Volcheck",
title = "{Noether}'s {S-transformation} simplifies curve
singularities rationally: a local analysis",
crossref = "Bronstein:1993:IPI",
pages = "164--172",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The singularities of algebraic plane curves over $Q$
may be resolved into ordinary multiple points by the
classical method of standard quadratic transformations.
The author analyzes a birational plane transformation
described by Max Noether (1884) which improves upon the
classical method in two ways: first, it requires no
ground field extension; second, the degree of the curve
it produces is an exponential factor lower than that
produced by the standard method.",
acknowledgement = ack-nhfb,
classification = "B0210 (Algebra); B0230 (Integral transforms); C1110
(Algebra); C1130 (Integral transforms); C7310
(Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic plane curves;
Birational plane transformation; Curve singularities;
ISSAC; Local analysis; Quadratic transformations;
SIGSAM, Noether S-transformation; Singularities;
symbolic computation",
thesaurus = "Polynomials; Symbol manipulation; Transforms",
}
@InProceedings{Volcheck:1993:NTS,
author = "Emil J. Volcheck",
title = "{Noether}'s ${S}$-transformation simplifies curve
singularities rationally: a local analysis",
crossref = "Bronstein:1993:IPI",
pages = "164--172",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p164-volcheck/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple.",
}
@InProceedings{Weispfenning:1993:DT,
author = "Volker Weispfenning",
title = "Differential term-orders",
crossref = "Bronstein:1993:IPI",
pages = "245--253",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p245-weispfenning/",
abstract = "In the theory of Gr{\"o}bner bases for multivariate
polynomials the concept of a term-order plays a central
role. Such term-orders can be characterized by linear
forms, whose coefficients are univariate real
polynomials. For multivariate partial differential
polynomials a corresponding concept is of great
importance for potential extensions of the
Riquier--Janet technique. So far, only the weaker
concepts of rankings and comparative rank have been
defined by Kolchin. This note presents an axiomatic
definition of differential term-orders on arbitrary
partial differential terms and proves that all these
orders are well-orders. Moreover, we give a
characterization of differential term-orders in terms
of systems of linear forms whose coefficients are
univariate real polynomials. This characterization
provides an explicit construction of an abundance of
differential term-orders. As an application, we obtain
a simple characterization of differential term-orders
on finite sets of differential terms and an algorithm
for computing all differential term-orders on such
sets. Finally, we characterize the term-orders, for
which differentiation preserves the ordering between
the highest terms of non-zero differential
polynomials.",
acknowledgement = ack-nhfb,
affiliation = "Passau Univ., Germany",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics computing)",
keywords = "algorithms; theory; verification; Gr{\"o}bner bases;
Multivariate polynomials; Multivariate partial
differential polynomials; Differential term-orders;
Term-order",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Weispfenning:1993:DTP,
author = "V. Weispfenning",
title = "Differential Term-Orders",
crossref = "Bronstein:1993:IPI",
pages = "245--253",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
computation",
}
@InProceedings{Willis:1993:CSP,
author = "T. J. Willis and E. A. Bogucz",
title = "Coupling Symbolic Processing with Parallel Numeric
Computation",
crossref = "Sincovec:1993:PSS",
pages = "788--792",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wu:1993:ACU,
author = "Hongzhong Wu",
title = "On the assignment complexity of uniform trees",
crossref = "Bronstein:1993:IPI",
pages = "95--104",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p95-wu/",
abstract = "This paper discusses the assignment complexity of the
uniform tree, which is made up of identical cells
realizing a function $f$. The assignment complexity of
a tree is defined as the cardinal number of the minimum
complete assignment set of the tree. When a complete
assignment set is applied to the primary input lines of
the tree, every internal $f$ cell in the tree can be
excited by all possible input combinations. The
assignment problem is a basic problem in the VLSI
system design, test and optimization. The relation
between the property of $f$ and the assignment
complexity of the uniform tree is analyzed. It is shown
that, the assignment complexity of a balanced uniform
tree with $n$ primary input lines is either $O(1)$ or
$Omega ((\lg{}n)^{\alpha}) (\alpha in (0,1))$. In the
first case, the cardinal number of the minimum complete
assignment set for a tree is constant and independent
of the size and structure of the tree. In the second
case, the assignment complexity depends on the number
of the primary input lines of the tree. If a balanced
uniform tree is based on a commutative function, then
it is either $Theta (1)$ or $Theta (\lg{}n)$
assignable.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Saarlandes Univ., Saarbrucken,
Germany",
classification = "B0250 (Combinatorial mathematics); B1110 (Network
topology); B1130 (General circuit analysis and
synthesis methods); C1160 (Combinatorial mathematics);
C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; algorithms; Assignable;
Assignment complexity; Cardinal number; Commutative
function; Computational complexity; Computer circuit
design; design; Identical cells; ISSAC; Minimum
complete assignment set; Optimization; SIGSAM; symbolic
computation; Test; theory; Tree; Uniform trees; VLSI
system design",
subject = "{\bf B.7.1} Hardware, INTEGRATED CIRCUITS, Types and
Design Styles, VLSI (very large scale integration).
{\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Trees. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Network synthesis; Network
topology; Trees [mathematics]; VLSI",
}
@InProceedings{Wu:1993:RPG,
author = "Jinzhao Wu and Lian Li",
title = "The regular problem and green equivalences for special
monoids",
crossref = "Bronstein:1993:IPI",
pages = "78--85",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p78-wu/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.1.3}
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
}
@InProceedings{Yokoyama:1993:HCE,
author = "Kazuhiro Yokoyama and Taku Takeshima",
title = "On {Hensel} Construction of Eigenvalues and
Eigenvectors of Matrices with Polynomial Entries",
crossref = "Bronstein:1993:IPI",
pages = "218--224",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p218-yokoyama/",
abstract = "Hensel's lemma is now widely used in algebraic
computation as a tool of lifting procedure in modular
methods, and this lifting procedure based on Hensel's
lemma is called a Hensel construction. Significant
examples are found in polynomial computation problems;
factorization, GCD computation and division.
Furthermore, several Hensel constructions are applied
to solve systems of polynomial equations or to compute
inverses of matrices with polynomial entries
(Krishnamurthy, 1985). For a natural application, we
propose a method for finding eigenvalues and
eigenvectors of matrices simultaneously. The authors
study the problem and show several Hensel constructions
for the problem. For simplicity, they only deal with
matrices with univariate polynomial entries over a
field and they consider linear lifting.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Labs. Ltd., Shizuoka, Japan",
classification = "C4140 (Linear algebra); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algebraic computation;
algorithms; Eigenvalues; Eigenvectors; Hensel
construction; Linear lifting; Matrices; Polynomial
computation, ISSAC; Polynomial entries; SIGSAM;
symbolic computation; theory; Univariate polynomial
entries; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods). {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Eigenvalues and eigenfunctions; Polynomial matrices;
Symbol manipulation",
}
@InProceedings{Zharkov:1993:ASF,
author = "Alexey Y. Zharkov",
title = "On algebraic solutions of first order {Riccatti}
equation",
crossref = "Bronstein:1993:IPI",
pages = "1--3",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p1-zharkov/",
abstract = "In this paper we prove the following theorem. If the
Riccatti equation $w^1+w^2=R(x)$, $R$ in $Q(x)$, has
algebraic solutions then one can find a minimal
polynomial defining such solutions whose coefficients
are in a quadratic extension of the field $Q$.",
acknowledgement = ack-nhfb,
affiliation = "Saratov Univ., Russia",
classification = "C4140 (Linear algebra); C4170 (Differential
equations)",
keywords = "ACM; algebraic computation; Algebraic solutions;
algorithms; Coefficients; Differential equations,
ISSAC; First order Riccatti equation; Minimal
polynomial; Quadratic extension; SIGSAM; symbolic
computation; Theorem proving; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic. {\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations.",
thesaurus = "Differential equations; Polynomials; Riccati
equations; Theorem proving",
}
@InProceedings{Zima:1993:NCO,
author = "E. V. Zima",
title = "Numeric Code Optimization in Computer Algebra Systems
and Recurrent Relations Technique",
crossref = "Bronstein:1993:IPI",
pages = "42--46",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p42-zima/",
abstract = "Computer algebra provides good tools for code
optimization. In particular it concerns
source-to-source optimization. But existing tools
(SCOPE, Gentran, etc.) provide code transmission from
computer algebra system to numeric system only. That's
why we have started developing in MSU a
source-to-source optimization library using Reduce as
an intellectual tool. This library contains algorithms
and special tools that provide reliable bilateral
connection between Reduce and systems for numeric
computations on MS DOS computers (Turbo-Pascal,
Turbo-C, MathCad, etc.).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Math. and Cybern., Moscow State
Univ., Russia",
classification = "C6110 (Systems analysis and programming); C6130
(Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Code
optimization; Code transmission; Computer algebra
systems; Gentran; Intellectual tool; languages; MS DOS
computers, ISSAC; Numeric code optimization;
performance; Recurrent relations technique; Reduce;
Reliable bilateral connection; SCOPE; SIGSAM;
Source-to-source optimization; Source-to-source
optimization library; symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Pascal.",
thesaurus = "Optimising compilers; Programming; Symbol
manipulation",
}
@InProceedings{Abramov:1994:DSL,
author = "Sergei A. Abramov and Marko Petkov{\v{s}}ek",
title = "{D'Alembertian} solutions of linear differential and
difference equations",
crossref = "ACM:1994:IPI",
pages = "169--174",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p169-abramov/",
abstract = "D'Alembertian solutions of differential (resp.
difference) equations are those expressible as nested
indefinite integrals (resp. sums) of hyperexponential
functions. They are a subclass of Liouvillian
solutions, and can be constructed by recursively
finding hyperexponential solutions and reducing the
order. Knowing d'Alembertian solutions of $Ly=0$, one
can write down the corresponding solutions of $Ly=f$
and of $L*y=0$.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C4170 (Differential equations)",
keywords = "algorithms; D'Alembertian solutions; Difference
equations; Hyperexponential functions; Hyperexponential
solutions; Linear differential equations; Liouvillian
solutions; Nested indefinite integrals; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Difference equations; Linear differential equations",
}
@InProceedings{Andreoli:1994:CKB,
author = "J.-M. Andreoli and U. M. Borghoff and R. Pareschi",
title = "Constraint-Based Knowledge Brokers",
crossref = "Hong:1994:FIS",
pages = "1--11",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Attardi:1994:SPB,
author = "G. Attardi and C. Traverso",
title = "A strategy-accurate parallel {Buchberger} algorithm",
crossref = "Hong:1994:FIS",
pages = "12--21",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bachmann:1994:CRM,
author = "Olaf Bachmann and Paul S. Wang and Eugene V. Zima",
title = "Chains of recurrences --- a method to expedite the
evaluation of closed-form functions",
crossref = "ACM:1994:IPI",
pages = "242--249",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p242-bachmann/",
abstract = "Chains of Recurrences (CRs) are introduced as an
effective method to evaluate functions at regular
intervals. Algebraic properties of CRs are examined and
an algorithm that constructs a CR for a given function
is explained. Finally, an implementation of the method
in MAXIMA/Common Lisp is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
keywords = "Algebraic properties; algorithms; Chains of
recurrences; Closed-form functions; languages;
MAXIMA/Common Lisp; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, Common Lisp. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Function evaluation; Symbol manipulation",
}
@InProceedings{Baddoura:1994:CIF,
author = "Jamil Baddoura",
title = "A conjecture on integration in finite terms with
elementary functions and polylogarithms",
crossref = "ACM:1994:IPI",
pages = "158--162",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p158-baddoura/",
abstract = "In this abstract, we report on a conjecture that gives
the form of an integral if it can be expressed using
elementary functions and polylogarithms. The conjecture
is proved by the author in the cases of the dilogarithm
and the trilogarithm (1993) and consists of a
generalization of Liouville's theorem on integration in
finite terms with elementary functions. Those last
structure theorems, for the dilogarithm and the
trilogarithm, are the first case of structure theorems
where logarithms can appear with non-constant
coefficients. In order to prove the conjecture for
higher polylogarithms we need to find the functional
identities, for the polylogarithms that we are using,
that characterize all the possible algebraic relations
among the considered polylogarithms of functions that
are built up from the rational functions by taking the
considered polylogarithms, exponentials, logarithms and
algebraics. The task of finding those functional
identities seems to be a difficult one and is an
unsolved problem for the most part to this date.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., MIT, Cambridge, MA, USA",
classification = "C4160 (Numerical integration and differentiation);
C7310 (Mathematics computing)",
keywords = "algorithms; Elementary functions; Integration;
Polylogarithms; Structure theorems; theory;
Trilogarithm; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Integration; Symbol manipulation",
}
@InProceedings{Becker:1994:SSL,
author = "Eberhard Becker and Teo Mora and Maria Grazia Marinari
and Carlo Traverso",
title = "The shape of the {Shape Lemma}",
crossref = "ACM:1994:IPI",
pages = "129--133",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p129-becker/",
abstract = "The Shape Lemma was originally introduced in 1989 and
so christened by Lakshman (1990). It is an easy
generalization of the Primitive Element Theorem and it
states that a $O$-dimensional radical ideal in a
polynomial ring$ k(X_1,\ldots{},X_n)$, after most
changes of coordinates, has a basis
$(g_1(X_1),X_2-g_2(X_2),\ldots{},X_n-g_n(X_1))$.
Notwithstanding its triviality, it has proved
ubiquitous in recent papers on polynomial system
solving. The obvious example $(X^2, XY, Y^2)$ is
sufficient to show that some assumption is needed on a
$O$-dimensional ideal in order that it holds; the
obvious example $(X^2, Y)$ is sufficient to show that
radicality is too strong an assumption. Since most of
the results making use of the Shape Lemma are valid
whenever the Shape Lemma holds and are of interest also
for non radical ideals, it is worthwhile to exactly
characterize those $O$-dimensional ideals to which the
Shape Lemma applies. It turns out that this exact
characterization is as trivial as the original Shape
Lemma itself. In fact both this characterization and
the generalization of it we give are easy
specializations of a classical result in algebraic
geometry on the minimum dimension of a generic
biregular projection of a variety as a function of its
dimension and of the dimension of its tangent bundle.
We give a direct, elementary, self-contained proof of
this specialization.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math., Dortmund Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4260
(Computational geometry); C7310 (Mathematics
computing)",
keywords = "Algebraic geometry; algorithms; Polynomial ring;
Primitive Element Theorem; Shape lemma; theory;
verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Berman:1994:OCR,
author = "Benjamin P. Berman and Richard J. Fateman",
title = "Optical character recognition for typeset
mathematics",
crossref = "ACM:1994:IPI",
pages = "348--353",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p348-berman/",
abstract = "There is a wealth of mathematical knowledge that could
be potentially very useful in many computational
applications, but is not available in electronic form.
This knowledge comes in the form of mechanically
typeset books and journals going back more than a
hundred years. Besides these older sources, there are a
great many current publications, filled with useful
mathematical information, which are difficult if not
impossible to obtain in electronic form. What we would
like to do is extract character information from these
documents, which could then be passed to higher-level
parsing routines for further extraction of mathematical
content (or any other useful $2$-dimensional semantic
content). Unfortunately, current commercial OCR
(optical character recognition) software packages are
quite unable to handle mathematical formulas, since
their algorithms at all levels use heuristics developed
for other document styles. We are concerned with the
development of OCR methods that are able to handle this
specialized task of mathematical expression
recognition.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1250B (Character recognition); C5260B (Computer
vision and image processing techniques); C7310
(Mathematics computing)",
keywords = "algorithms; Character information; Higher-level
parsing routines; Journals; Mechanically typeset books;
Optical character recognition; Software packages;
Typeset mathematics",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf B.4.2}
Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
Input/Output Devices. {\bf I.5.4} Computing
Methodologies, PATTERN RECOGNITION, Applications, Text
processing.",
thesaurus = "Grammars; Optical character recognition; Symbol
manipulation",
}
@InProceedings{Bertrand:1994:INA,
author = "Laurent Bertrand",
title = "On the implementation of a new algorithm for the
computation of hyperelliptic integrals",
crossref = "ACM:1994:IPI",
pages = "211--215",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p211-bertrand/",
abstract = "We present an implementation in Maple of a new
algorithm for the algebraic function integration
problem in the particular case of hyperelliptic
integrals. This algorithm is based on the general
algorithm of Trager (1984) and on the arithmetic in the
Jacobian of hyperelliptic curves of Cantor (1987).",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Arithmetique, Calcul Formel et Optimisation,
Limoges Univ., France",
classification = "B0290M (Numerical integration and differentiation);
B0290R (Integral equations); C4160 (Numerical
integration and differentiation); C4180 (Integral
equations); C7310 (Mathematics computing)",
keywords = "Algebraic function integration problem; algorithms;
Hyperelliptic curves; Hyperelliptic integrals; Maple;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Elliptic equations; Integral equations; Integration;
Symbol manipulation",
}
@InProceedings{Bonacina:1994:RPD,
author = "M. P. Bonacina",
title = "On the reconstruction of proofs in distributed theorem
proving with contraction: a modified {Clause-Diffusion}
method",
crossref = "Hong:1994:FIS",
pages = "22--33",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Borst:1994:GRP,
author = "W. N. Borst and V. V. Goldman and J. A. {Van Hulzen}",
title = "{GENTRAN} 90: a {REDUCE} package for the generation of
{Fortran} 90 code",
crossref = "ACM:1994:IPI",
pages = "45--51",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p45-borst/",
abstract = "GENTRAN is a code generator and translator running
under REDUCE and MACSYMA. It is a tool for generating
Fortran 77, RATFOR or C programs from program
specifications and symbolic expressions. Its facilities
include template processing, automatic segmentation of
large expressions and a file handling mechanism.
GENTRAN can be used in combination with SCOPE 1.5, a
source code optimization package for REDUCE. We present
an extension of the REDUCE version of GENTRAN, called
GENTRAN 90. It makes generation of Fortran 90 code
possible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Twente Univ., Enschede,
Netherlands",
classification = "C6115 (Programming support); C6140D (High level
languages); C6150C (Compilers, interpreters and other
processors); C7310 (Mathematics computing)",
keywords = "algorithms; C; Code generation; Code generator; Code
translator; design; File handling; Fortran 77; Fortran
90 code; GENTRAN 90; languages; MACSYMA; Program
specifications; RATFOR; REDUCE; REDUCE package; SCOPE
1.5; Source code optimization package; Symbolic
expression; Template processing",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Fortran 90. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Translator writing systems and
compiler generators.",
thesaurus = "FORTRAN; Optimisation; Program interpreters; Software
packages; Software tools; Symbol manipulation",
}
@InProceedings{Bosma:1994:PAS,
author = "Wieb Bosma and John Cannon and Graham Matthews",
title = "Programming with algebraic structures: design of the
{Magma} language",
crossref = "ACM:1994:IPI",
pages = "52--57",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p52-bosma/",
abstract = "MAGMA is a new software system for computational
algebra, number theory and geometry whose design is
centred on the concept of algebraic structure (magma).
The use of algebraic structure as a design paradigm
provides a natural strong typing mechanism. Further,
structures and their morphisms appear in the language
as first class objects. Standard mathematical notions
are used for the basic data types. The result is a
powerful, clean language which deals with objects in a
mathematically rigorous manner. The conceptual and
implementation ideas behind MAGMA will be examined in
this paper. This conceptual base differs significantly
from those underlying other computer algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Sydney Univ., NSW, Australia",
classification = "C1160 (Combinatorial mathematics); C6110 (Systems
analysis and programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "Algebraic structures; algorithms; Computational
algebra; Computer algebra systems; Data types; design;
Magma language; Mathematical notions; Number theory;
Software system; Strong typing mechanism",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf F.3.3}
Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Studies of Program Constructs, Type structure. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Number theory; Programming; Symbol manipulation",
}
@InProceedings{Bratvold:1994:PFP,
author = "T. A. Bratvold",
title = "Parallelising a Functional Program Using a
List-Homomorphism Skeleton",
crossref = "Hong:1994:FIS",
pages = "44--53",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Briek:1994:SCT,
author = "S. Briek and A. Rauzy",
title = "Synchronization of Constrained Transition Systems",
crossref = "Hong:1994:FIS",
pages = "54--62",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bronstein:1994:IAF,
author = "Manuel Bronstein",
title = "An improved algorithm for factoring linear ordinary
differential operators",
crossref = "ACM:1994:IPI",
pages = "336--340",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p336-bronstein/",
abstract = "We describe an efficient algorithm for computing the
associated equations appearing in the Beke--Schlesinger
factorisation method for linear ordinary differential
operators. This algorithm, which is based on elementary
operations with sets of integers, can be easily
implemented for operators of any order, produces
several possible associated equations, of which only
the simplest can be selected for solving, and often
avoids the degenerate case, where the order of the
associated equation is less than in the generic case.
We conclude with some fast heuristics that can produce
some factorisations while using only linear
computations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
classification = "B0290P (Differential equations); C4170 (Differential
equations); C4240 (Programming and algorithm theory)",
keywords = "algorithms; Beke--Schlesinger factorisation method;
Efficient algorithm; Elementary operations; Fast
heuristics; Improved algorithm; Integer sets; Linear
ordinary differential operator factoring; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Algorithm theory; Difference equations; Mathematical
operators",
}
@InProceedings{Buendgen:1994:MAT,
author = "R. Buendgen and M. Goebel and W. Kuechlin",
title = "Multi-Threaded {AC} Term Rewriting",
crossref = "Hong:1994:FIS",
pages = "84--93",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bueno:1994:CSM,
author = "F. Bueno and M. {Garcia de la Banda} and M.
Hermenegildo",
title = "A Comparative Study of Methods for Automatic
Compile-time Parallelization of Logic Programs",
crossref = "Hong:1994:FIS",
pages = "63--73",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bundgen:1994:FPC,
author = "Reinhard B{\"u}ndgen and Manfred G{\"o}bel and
Wolfgang K{\"u}chlin",
title = "A fine-grained parallel completion procedure",
crossref = "ACM:1994:IPI",
pages = "269--277",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p269-bundgen/",
abstract = "We present a parallel Knuth--Bendix completion
algorithm where the inner loop, deriving the
consequences of adding a new rule to the system, is
multithreaded. The selection of the best new rule in
the outer loop, and hence the completion strategy, is
exactly the same as for the sequential algorithm. Our
implementation, which is within the PARSAC-2 parallel
symbolic computation system, exhibits good parallel
speedups on a standard multiprocessor workstation.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
Germany",
classification = "C4210L (Formal languages and computational
linguistics); C4240P (Parallel programming and
algorithm theory); C6130 (Data handling techniques);
C6150N (Distributed systems software); C7310
(Mathematics computing)",
keywords = "algorithms; Fine grained parallel completion
procedure; Fine-grained parallel completion procedure;
Multithreaded inner loop; Parallel Knuth--Bendix
completion algorithm; Parallel speedups; PARSAC-2
parallel symbolic computation system; Standard
multiprocessor workstation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf F.4.2} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Grammars and Other Rewriting Systems,
Parallel rewriting systems. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency.",
thesaurus = "Parallel algorithms; Parallel machines; Rewriting
systems; Symbol manipulation",
}
@InProceedings{Burke-Perline:1994:PCU,
author = "T. Burke-Perline",
title = "The Parallel Computation of $f(x)0(00-010)0/02 \bmod
h(x)$ using {Sugarbush 1.1}",
crossref = "Hong:1994:FIS",
pages = "74--83",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Char:1994:AIT,
author = "Bruce W. Char and Mark F. Russo",
title = "Automatic identification of time scales in enzyme
kinetics models",
crossref = "ACM:1994:IPI",
pages = "74--83",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p74-char/",
abstract = "Many chemical reaction systems studied in the
pharmaceutical industry have phenomena that occur on
two or more vastly different time scales. When modeling
the chemical reaction system as ordinary differential
equations, if a small parameter $E$ can be identified
then one can isolate the behavior of the system on long
and short time scales using singular perturbation
theory. In practice, the small parameter is discovered
using knowledge about the chemical reaction system that
is not necessarily contained in the mathematics of the
model. If a small parameter cannot be easily
identified, then the approach is typically abandoned.
The authors present a procedure that derives algebraic
expressions for dual time scales in mathematical models
of chemical reaction systems. Unlike conventional
practice, this derivation proceeds using only
information contained in the model, without knowledge
of a small parameter derived through external
considerations. The authors' procedure, Scales, is
based on rules that arise from the `art and practice'
of applying the quasi-steady-state assumption to derive
the Michaelis--Menton equations. The authors depart
from standard practice of singular perturbation theory,
using instead the viewpoint of Segel and Slemrod
(1989). They have implemented Scales in Maple. Scales
is closer to an `expert system' than a `scale oracle'
or decision procedure. Its shortcomings necessitate
subsequent verification of its results, typically
through numerical or laboratory experimentation. If
validated, additional computer algebra techniques can
be used to simplify the mathematical model and isolate
the long time scale behavior.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
classification = "A8220W (Computational modelling of chemical
kinetics); A8230V (Homogeneous catalysis); A8240
(Chemical kinetics and reactions: special regimes);
A8715D (Physical chemistry of biomolecular solutions;
C1220 (Simulation, modelling and identification); C4170
(Differential equations); C6170 (Expert systems); C7320
(Physics and chemistry computing); C7450 (Chemical
engineering computing); condensed states)",
keywords = "Algebraic expression; algorithms; Automatic
identification; Biochemistry; Biology computing;
Catalysis; Chemical kinetics model; Chemical reaction;
Dual time scale; Enzyme; Maple; Mathematical model;
Metabolism; Michaelis--Menton equations; Ordinary
differential equations; Pharmaceutical; Reaction
kinetics; Scales; Singular perturbation theory; Time
scale; verification",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Chemistry. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Chemical engineering computing; Differential
equations; Identification; Knowledge based systems;
Pharmaceutical industry; Proteins; Reaction kinetics
theory; Scaling phenomena; Symbol manipulation",
}
@InProceedings{Char:1994:SEP,
author = "B. Char and J. Johnson and D. Saunders and A. P.
Wack",
title = "Some Experiments with Parallel Bignum Arithmetic",
crossref = "Hong:1994:FIS",
pages = "94--103",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cooperman:1994:CPR,
author = "Gene Cooperman and Larry Finkelstein and Bryant York
and Michael Tselman",
title = "Constructing permutation representations for large
matrix groups",
crossref = "ACM:1994:IPI",
pages = "134--138",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p134-cooperman/",
abstract = "New techniques, both theoretical and practical, are
presented for constructing a permutation representation
for a matrix group. We assume that the resulting
permutation degree, $n,$ can be 10,000,000 and larger.
The key idea is to build the new permutation
representation using the conjugation action on a
conjugacy class of subgroups of prime order. A unique
signature for each group element corresponding to the
conjugacy class is used in order to avoid matrix
multiplication. The requirement of at least $n$ matrix
multiplications would otherwise have made the
computation hopelessly impractical. Additional software
optimizations are described, which reduce the CPU time
by at least an additional factor of 10. Further, a
special data structure is designed that serves both as
a search tree and as a hash array, while requiring
space of only $1.6 n log_2 n$ bits. The technique has
been implemented and tested on the sporadic simple
group Ly, discovered by Lyons (1972), in both a
sequential (SPARCserver 670 MP) and parallel SIMD
(MasPar MP-1) version. Starting with a generating set
for $Ly$ as a subgroup of $GL(111, 5)$, a set of
generating permutations for $Ly$ acting on 9, 606, 125
points is constructed as well as a base for this
permutation representation. The sequential version
required four days of CPU time to construct a data
structure which can be used to compute the permutation
image of an arbitrary matrix. The parallel version did
so in 12 hours. Work is in progress on a faster
parallel implementation.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity); C7310 (Mathematics computing)",
keywords = "algorithms; Conjugacy class; Conjugation action; Data
structure; design; Hash array; Large matrix groups;
Parallel version; performance; Permutation
representation; Permutation representations; Search
tree",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.2.1}
Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Permutations and combinations. {\bf E.1}
Data, DATA STRUCTURES, Arrays. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Matrix multiplication;
Symbol manipulation",
}
@InProceedings{Corless:1994:SAC,
author = "Robert M. Corless",
title = "Sufficiency analysis for the calculus of variations",
crossref = "ACM:1994:IPI",
pages = "197--204",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p197-corless/",
abstract = "Many of the computations in the calculus of variations
are algebraic in nature: computing the Euler--Lagrange
equations and solving them, for example. However,
deciding whether or not the computed extremals provide
minima or maxima is an analytic problem, and one that
has not been previously attempted in a computer algebra
package. I describe here a Maple implementation of some
techniques for making these decisions, and detail some
successes and failures. Some of the failures point to
areas where computer algebra systems could be
improved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Univ. of Western Ontario,
London, Ont., Canada",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algorithms; Calculus of variations; Computer algebra
package; Computer algebra systems; Euler--Lagrange
equations; Maple implementation; Sufficiency analysis;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Special-purpose algebraic systems.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Cremanns:1994:CCP,
author = "Robert Cremanns and Friedrich Otto",
title = "Constructing canonical presentations for subgroups of
context-free groups in polynomial time-extended
abstract",
crossref = "ACM:1994:IPI",
pages = "147--153",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p147-cremanns/",
abstract = "Canonical presentations of groups are of interest,
since they provide structurally simple algorithms for
computing normal forms. A class of groups that has
received much attention is the class of context-free
groups. This class of groups can be characterized
algebraically as well as through some language
theoretical properties as well as through certain
combinatorial properties of presentations. Here we use
the fact that a finitely generated group is
context-free if and only if it admits a finite
canonical presentation of a certain form that we call a
virtually free presentation. Since finitely generated
subgroups of context-free groups are again
context-free, they admit presentations of the same
form. We present a polynomial-time algorithm that,
given a finite virtually free presentation of a
context-free group $G$ and a finite subset $U$ of $G$
as input, computes a virtually free presentation for
the subgroup $<U>$ of $G$ that is generated by $U$.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math./Inf., Kassel Univ., Germany",
classification = "C1110 (Algebra); C4210L (Formal languages and
computational linguistics); C4240C (Computational
complexity)",
keywords = "algorithms; Canonical presentations; Context-free
groups; Language theoretical properties; languages;
Polynomial time; Subgroups; theory; verification;
Virtually free presentation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf F.4.2} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
Other Rewriting Systems, Grammar types. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Context-free languages;
Group theory",
}
@InProceedings{Dalmas:1994:DCA,
author = "S. Dalmas and M. Gaetano and A. Sausse",
title = "Distributed Computer Algebra: the Central Control
Approach",
crossref = "Hong:1994:FIS",
pages = "104--113",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DeBosschere:1994:LCB,
author = "K. {De Bosschere} and J.-M. Jacquet",
title = "Local and Conditional Blackboard Operations in Log:
Semantics, Applicability, and Implementation",
crossref = "Hong:1994:FIS",
pages = "34--43",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DelPozo-Prieto:1994:ISP,
author = "A. {Del Pozo-Prieto} and J. J. Moreno-Navarro",
title = "Independent Subexpressions Parallelism with Delayed
Synchronization for Functional Logic Languages",
crossref = "Hong:1994:FIS",
pages = "316--325",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Denzinger:1994:RAP,
author = "J. Denzinger and S. Schulz",
title = "Recording, Analyzing and Presenting Distributed
Deduction Processes",
crossref = "Hong:1994:FIS",
pages = "114--123",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dingle:1994:BCC,
author = "Adam Dingle and Richard J. Fateman",
title = "Branch cuts in computer algebra",
crossref = "ACM:1994:IPI",
pages = "250--257",
year = "1994",
DOI = "https://doi.org/10.1145/190347.190424",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p250-dingle/",
abstract = "Most computer algebra systems provide little
assistance in working with expressions involving
functions with complex branch cuts. Worse, by their
ignorance of the existence of branch cuts, algebra
systems sometimes simplify complex expressions
incorrectly. We propose a computer representation for
branch cuts; we show how a complex expression's branch
cuts may be mechanically computed, and how an
expression with branch cuts may sometimes be
algebraically simplified within each of its branches.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1100 (Mathematical techniques); C6130 (Data
handling techniques); C7310 (Mathematics computing)",
keywords = "Algebraic simplification; algorithms; Complex branch
cuts; Complex expressions; Computer algebra systems;
Computer representation; languages",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf I.1.1} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica.",
thesaurus = "Functions; Symbol manipulation",
}
@InProceedings{Du:1994:ISA,
author = "Hong Du",
title = "On the isomorphisms of smooth algebraic curves",
crossref = "ACM:1994:IPI",
pages = "15--19",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p15-du/",
abstract = "I consider some problems of algebraic curves in a
constructive way, especially, I provide an algorithm
for determining whether two given smooth plane curves
are isomorphic and find all isomorphic maps. I present
a survey of some miscellaneous results related to the
classification of curves. In the appendix, I give some
other results which implies a more efficient algorithm
for deciding whether two plane curves are isomorphic
and find all isomorphic maps. The method can be
generalized to smooth projective complete intersection
varieties.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C4130 (Interpolation and function approximation);
C4260 (Computational geometry)",
keywords = "algorithms; Curve classification; Isomorphic maps;
Isomorphisms; Plane curves; Smooth algebraic curves;
Smooth plane curves; Smooth projective complete
intersection; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations.",
thesaurus = "Computational geometry; Curve fitting",
xxabstract = "In this paper, I have considered some problems of
algebraic curves in some constructive way, especially,
I give an algorithm for determining whether two given
smooth plane curves are isomorphic and finding all
isomorphic maps. I also have given a survey of some
miscellaneous results related to the classification of
curves. In the appendix, I give some other results
which implies a more efficient algorithm for deciding
whether two plane curves are isomorphic and finding all
isomorphic maps. It is clear our method in this paper
can be generalized to smooth projective complete
intersection varieties.",
}
@InProceedings{Dyer:1994:ASC,
author = "Charles C. Dyer",
title = "An application of symbolic computation in the physical
sciences",
crossref = "ACM:1994:IPI",
pages = "181--186",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p181-dyer/",
abstract = "An example of a problem in the physical sciences is
discussed where application of various symbolic
computation facilities available in many algebraic
computing systems leads to a significant expansion of
the range of problems that can be solved. Since most
interesting problems in the physical sciences
eventually require the numerical solution of systems of
equations, of various types, we introduce an example
and describe an approach to a solution, beginning at
the development of relevant differential equations,
using, for example REDUCE, and leading eventually to
the generation of highly efficient and stable numerical
code for the solution, using, in our case, the C
language. The use of SCOPE and GENTRAN, as well as
series packages in REDUCE are discussed. In many areas
of interest, a considerable amount of work has to be
performed to arrive at the symbolic equations to solve,
and this is particularly true in General Relativity and
related gravitation theories. Some packages, such as
REDTEN, for calculation in this field are discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Astron., Toronto Univ., Ont., Canada",
classification = "C4170 (Differential equations); C7310 (Mathematics
computing); C7320 (Physics and chemistry computing)",
keywords = "Algebraic computing systems; algorithms; C language;
Calculation; Differential equations; General
Relativity; GENTRAN; Gravitation theories; languages;
Numerical code; Numerical solution; Physical sciences;
REDTEN; REDUCE; reliability; SCOPE; Series packages;
Symbolic computation; Symbolic equations;
verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics. {\bf D.2.5} Software, SOFTWARE ENGINEERING,
Testing and Debugging, Debugging aids.",
thesaurus = "Differential equations; Gravitation; Mathematics
computing; Physics computing; Symbol manipulation",
}
@InProceedings{Emiris:1994:MBP,
author = "Ioannis Z. Emiris and Ashutosh Rege",
title = "Monomial bases and polynomial system solving (extended
abstract)",
crossref = "ACM:1994:IPI",
pages = "114--122",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p114-emiris/",
abstract = "This paper addresses the problem of efficient
construction of monomial bases for the coordinate rings
of zero-dimensional varieties. Existing approaches rely
on Gr{\"o}bner bases methods-in contrast, we make use
of recent developments in sparse elimination techniques
which allow us to strongly exploit the structural
sparseness of the problem at hand. This is done by
establishing certain properties of a matrix formula for
the sparse resultant of the given polynomial system. We
use this matrix construction to give a simpler proof of
the result of Pedersen and Sturmfels (1994) for
constructing monomial bases. The monomial bases so
obtained enable the efficient generation of
multiplication maps in coordinate rings and provide a
method for computing the common roots of a generic
system of polynomial equations with complexity singly
exponential in the number of variables and polynomial
in the number of roots. i.e. describe the
implementations based on our algorithms and provide
empirical results on the well-known problem of cyclic
$n$-roots; our implementation gives the first known
upper bounds in the case of $n=10$ and $n=11$. We also
present some preliminary results on root finding for
the Stewart platform and motion from point matches
problems in robotics and vision respectively.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C7310 (Mathematics computing)",
keywords = "algorithms; theory; verification; Polynomial system
solving; Monomial bases; Coordinate rings;
Zero-dimensional varieties; Gr{\"o}bner bases; Sparse
elimination techniques; Matrix formula; Multiplication
maps; Root finding",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Encarnacion:1994:MAC,
author = "Mark J. Encarnaci{\'o}n",
title = "On a modular algorithm for computing {GCDs} of
polynomials over algebraic number fields",
crossref = "ACM:1994:IPI",
pages = "58--65",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p58-encarnacion/",
abstract = "Modular methods for computing the gcd of two
univariate polynomials over an algebraic number field
require {\em a priori\/} knowledge about the
denominators of the rational numbers in the
representation of the gcd. We derive a multiplicative
bound for these denominators without assuming that the
number generating the field is an algebraic integer.
Consequently, the gcd algorithm of Langemyr and
McCallum [{\em J. Symbolic Computation\/}, 8:429-448,
1989] can now be applied directly to polynomials that
are not necessarily represented in terms of an
algebraic integer. Worst-case analyses and experiments
with an implementation show that by avoiding a
conversion of representation the reduction in the
computing time can be significant. We also suggest the
use of an algorithm for recovering a rational number
from its modular residue so that the denominator bound
need not be computed explicitly. Experiments and
analyses indicate that this is a good practical
alternative.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
keywords = "A priori knowledge; Algebraic number fields;
algorithms; Computing GCDs; Denominators;
experimentation; Modular algorithm; Multiplicative
bound; Polynomials; theory; verification; Worst-case
analysis",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Faugere:1994:PGB,
author = "J. C. Faugere",
title = "Parallelization of {Gr{\"o}bner} Basis",
crossref = "Hong:1994:FIS",
pages = "124--132",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ganzha:1994:SSI,
author = "V. G. Ganzha and E. V. Vorozhtsov and J. Boers and J.
A. {van Hulzen}",
title = "Symbolic-numeric stability investigations of
{Jameson}'s schemes for the thin-layer {Navier--Stokes}
equations",
crossref = "ACM:1994:IPI",
pages = "234--241",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p234-ganzha/",
abstract = "The Navier--Stokes equations governing the
three-dimensional flows of a viscous, compressible,
heat-conducting gas and augmented by turbulence
modeling present the most realistic model for gas flows
around the elements of aircraft configurations. We
study the stability of one of the Jameson's schemes of
1981, which approximates the set of five Navier--Stokes
equations completed by the turbulence model of Baldwin
and Lomax (1978). The analysis procedure implements the
check-up of the necessary von Neumann stability
criterion. It is shown with the aid of the proposed
symbolic-numeric strategy that the physical viscosity
terms in the Navier--Stokes equations have a dominant
effect on the sizes of the stability region in
comparison with the heat conduction terms. It turns out
that the consideration of turbulence with the aid of
eddy viscosity model of Baldwin and Lomax has an
insignificant effect on the size of the necessary
stability region.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, Russia",
classification = "A0260 (Numerical approximation and analysis); A4710
(General fluid dynamics theory, simulation and other
computational methods); A4725 (Turbulent flows,
convection, and heat transfer); C4170 (Differential
equations); C7320 (Physics and chemistry computing)",
keywords = "3D flows; Aircraft configurations; algorithms;
Compressible gas; Eddy viscosity model; Heat-conducting
gas; Jameson schemes; languages; Stability region;
Symbolic-numeric stability; Thin-layer Navier--Stokes
equations; Turbulence modeling; Viscosity terms;
Viscous gas; Von Neumann stability",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Aerospace. {\bf J.2} Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Physics. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Navier--Stokes equations; Numerical stability; Physics
computing; Symbol manipulation; Turbulence; Viscosity",
}
@InProceedings{Gautier:1994:PSP,
author = "T. Gautier and J.-L. Roch",
title = "{PAC++} System and Parallel Algebraic Numbers
Computation",
crossref = "Hong:1994:FIS",
pages = "145--153",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:1994:FAR,
author = "Mark Giesbrecht",
title = "Fast algorithms for rational forms of integer
matrices",
crossref = "ACM:1994:IPI",
pages = "305--311",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p305-giesbrecht/",
abstract = "A Monte Carlo type probabilistic algorithm is
presented for finding the Frobenius rational form $F$
in $Z^{n*n}$ of any $A$ in $Z^{n*n}$ which requires an
expected number of $O(n^4(\log{}n+//A//)^2)$ bit
operations using standard integer and matrix arithmetic
(where $//A//$ is the largest absolute value of any
entry of $A$). This improves dramatically on the
fastest previously known algorithm, which requires
$O(n^6\log{}//A//)$ bit operations using fast integer
arithmetic. We also give a Las Vegas type probabilistic
algorithm which finds the Frobenius form $F$ and a
transition matrix $U$ in $Q^{n*n}$ such that
$U^{-1}/AU=F$ and requires an expected number of
$O(n^5(\log{}n+log //A//)^{52})$ bit operations.
Finally, a Las Vegas algorithm for computing the
rational Jordan form of an integer matrix is shown,
which requires about the same number of bit operations
as our algorithm to find the Frobenius form, plus the
time required to factor the characteristic polynomial
of that matrix.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
Canada",
classification = "C1140G (Monte Carlo methods); C4140 (Linear
algebra); C4240C (Computational complexity); C7310
(Mathematics computing)",
keywords = "algorithms; Bit operations; Characteristic polynomial;
Expected number; Fast algorithms; Fast integer
arithmetic; Frobenius rational form; Integer matrices;
Largest absolute value; Las Vegas type probabilistic
algorithm; Matrix arithmetic; Monte Carlo type
probabilistic algorithm; Rational Jordan form; Standard
integer arithmetic; Transition matrix; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.3} Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo). {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Matrix algebra; Monte Carlo
methods; Symbol manipulation",
}
@InProceedings{Gladitz:1994:PIG,
author = "K. Gladitz and H. Kuchen",
title = "Parallel Implementation of the Gamma-Operation on
Bags",
crossref = "Hong:1994:FIS",
pages = "154--163",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gonzalez:1994:MPE,
author = "A. Gonzalez and J. Tubella",
title = "The Multipath Parallel Execution Model for {Prolog}",
crossref = "Hong:1994:FIS",
pages = "164--173",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Goriely:1994:HCM,
author = "Alain Goriely and Michael Tabor",
title = "How to compute the {Melnikov} vector?",
crossref = "ACM:1994:IPI",
pages = "205--210",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p205-goriely/",
abstract = "It is shown that transverse homoclinic intersections
such as the ones described by the Melnikov theory can
be computed by a local analysis of the complex-time
singularities of the solutions. This provides a new
algorithmic procedure to compute homoclinic
intersections in $n$-dimensions once the homoclinic
manifold is known. It also gives new insights on the
singularity structure of integrable and nonintegrable
systems.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Libre de Bruxelles, Belgium",
classification = "C1110 (Algebra); C4170 (Differential equations);
C4240 (Programming and algorithm theory)",
keywords = "Algorithm; algorithms; Complex-time singularities;
Differential equations; Homoclinic intersection;
Homoclinic manifold; Local analysis; Melnikov theory;
Melnikov vector; N-dimensions; Singularity structure;
Symbolic computation; theory; Transverse homoclinic
intersections",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Algorithm theory; Differential equations; Symbol
manipulation; Vectors",
}
@InProceedings{Graebe:1994:PGF,
author = "H.-G. Graebe and W. Lassner",
title = "A Parallel {Gr{\"o}bner} Factorizer",
crossref = "Hong:1994:FIS",
pages = "174--180",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gray:1994:MPE,
author = "Simon Gray and Norbert Kajler and Paul Wang",
title = "{MP}: a protocol for efficient exchange of
mathematical expressions",
crossref = "ACM:1994:IPI",
pages = "330--335",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p330-gray/",
abstract = "The Multi Protocol (MP) is designed for integrating
symbolic, numeric, graphics, document processing, and
other tools for scientific computation, into a single
distributed problem-solving environment. MP is layered,
reflecting the logically distinct aspects of tool
integration. Data representation issues are addressed
by specifying a set of basic data types and a mechanism
for constructing non-basic types. MP passes all data in
the form of annotated parse trees. The parse tree
provides a simple, flexible and tool-independent way to
represent and exchange data, and annotations provide a
powerful and generic expressive facility for
transmitting additional information. MP also provides
efficient encodings for numeric data and includes
different types of optimizations to reduce the cost of
exchanging data. The optimizations are important when
transmitting large expressions typically encountered in
symbolic and numeric computation. MP is extensible.
Users can define additional sets of operators and
annotations as well as tailor the generic optimization
mechanisms to efficiently encode their own data
structures. A clear distinction between MP-defined and
user-defined definitions is enforced.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C1180 (Optimisation techniques); C4210L (Formal
languages and computational linguistics); C5640
(Protocols); C6115 (Programming support); C6120 (File
organisation); C6130B (Graphics techniques); C6130D
(Document processing techniques); C6150N (Distributed
systems software); C6170K (Knowledge engineering
techniques); C7310 (Mathematics computing)",
keywords = "algorithms; Annotated parse trees; Annotations; Basic
data types; Data exchange cost reduction; Data
representation issues; design; Distributed
problem-solving environment; Document processing;
Efficient encodings; Efficient mathematical expression
exchange; Generic optimization mechanisms; Graphics;
languages; Large expression transmission; Layered; MP
protocol; Multi Protocol; Nonbasic types; Numeric
processing; Operators; performance; Scientific
computation; Symbolic processing; Tool integration",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf D.2.2} Software, SOFTWARE
ENGINEERING, Design Tools and Techniques.",
thesaurus = "Computer graphics; Distributed processing; Document
handling; Grammars; Mathematics computing; Natural
sciences computing; Optimisation; Problem solving;
Protocols; Software tools; Symbol manipulation; Tree
data structures",
}
@InProceedings{Guergueb:1994:EAT,
author = "Ahmed Guergueb and Jean Mainguen{\'e} and
Marie-Fran{\c{c}}oise Roy",
title = "Examples of automatic theorem proving in real
geometry",
crossref = "ACM:1994:IPI",
pages = "20--24",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p20-guergueb/",
abstract = "We show that computer algebra methods in mechanical
geometry theorem proving can also be applied to obtain
new theorems involving inequalities. An interesting
feature is that in real geometry, several cases can
occur, none of them being more generic than the other.
The examples we give come from the geometry of the
triangle, more precisely comparing radii of circles
defined in the triangle.",
acknowledgement = ack-nhfb,
affiliation = "Rennes I Univ., France",
classification = "C4260 (Computational geometry); C7310 (Mathematics
computing)",
keywords = "algorithms; Automatic theorem proving; Computer
algebra methods; Inequalities; Mechanical geometry
theorem proving; Radii of circles; theory; Triangle;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Computational geometry; Symbol manipulation; Theorem
proving",
xxtitle = "Examples of automatic theorem proving a real
geometry",
}
@InProceedings{Hammond:1994:PFP,
author = "K. Hammond",
title = "Parallel Functional Programming: An Introduction
(Invited Tutorial)",
crossref = "Hong:1994:FIS",
pages = "181--193",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Harris:1994:IRR,
author = "Jason F. Harris",
title = "Inheritance of rewrite rule structures applied to
symbolic computation",
crossref = "ACM:1994:IPI",
pages = "318--323",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p318-harris/",
abstract = "This paper defines and presents a method of
inheritance for structures that are defined by rewrite
rules. This method is natural in the sense that it can
be easily and cleanly implemented in rewrite rules
themselves. This framework of inheritance is not that
of classical Object-Oriented Programming. It is shown
that this inheritance has particular application to
structures implemented in rewrite rules and, more
generally, to symbolic computation. The treatment is
practical, and examples are presented in {\em
Mathematica\/} for concreteness.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Phys. and Astron., Canterbury Univ.,
Christchurch, New Zealand",
classification = "C4210L (Formal languages and computational
linguistics); C6110F (Formal methods); C6120 (File
organisation)",
keywords = "Abstract data type; Algebraic specification;
algorithms; Inheritance; Natural method; Rewrite rule
structures; Rewriting; Structure; Symbolic computation;
Symbolic specification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica. {\bf D.1.5} Software, PROGRAMMING
TECHNIQUES, Object-oriented Programming.",
thesaurus = "Algebraic specification; Inheritance; Rewriting
systems; Symbol manipulation",
}
@InProceedings{Hasegawa:1994:PMM,
author = "R. Hasegawa and M. Koshimura",
title = "An {AND} Parallelization Method for {MGTP} and Its
Evaluation",
crossref = "Hong:1994:FIS",
pages = "194--203",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hill:1994:VM,
author = "J. M. D. Hill and K. M. Clarke and R. Bornat",
title = "The Vectorisation Monad",
crossref = "Hong:1994:FIS",
pages = "204--213",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jacobs:1994:ANA,
author = "David P. Jacobs",
title = "The {Albert} nonassociative algebra system: a progress
report",
crossref = "ACM:1994:IPI",
pages = "41--44",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p41-jacobs/",
abstract = "After four years of experience with the nonassociative
algebra program Albert, we highlight its successes and
drawbacks. Among its successes are the discovery of
several new results in nonassociative algebra. Each of
these results has been independently verified-either
with a traditional mathematical proof or with an
independent computation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Clemson Univ., SC, USA",
classification = "C7310 (Mathematics computing)",
keywords = "Albert; algorithms; Computation; Mathematical proof;
Nonassociative algebra system; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Algebra; Mathematics computing; Symbol manipulation;
Theorem proving",
}
@InProceedings{Jenks:1994:HMA,
author = "Richard D. Jenks and Barry M. Trager",
title = "How to make {AXIOM} into a {Scratchpad}",
crossref = "ACM:1994:IPI",
pages = "32--40",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p32-jenks/",
abstract = "Scratchpad (Griesmer and Jenks, 1971) was a computer
algebra system that had one principal representation
for mathematical formulae based on expression trees.
Its user interface design was based on a
pattern-matching paradigm with infinite rewrite rule
semantics, providing what we believe to be the most
natural paradigm for interactive symbolic problem
solving. Like M and M, however, user programs were
interpreted, often resulting in poor performance
relative to similar facilities coded in standard
programming languages such as FORTRAN and C. Scratchpad
development stopped in 1976 giving way to a new system
design that evolved into AXIOM. AXIOM has a
strongly-typed programming language for building a
library of parameterized types and algorithms, and a
type-inferencing interpreter that accesses the library
and can build any of an infinite number of types for
interactive use. We suggest that the addition of an
expression tree type to AXIOM can allow users to
operate with the same freedom and convenience of
untyped systems without giving up the expressive power
and run-time efficiency provided by the type system. We
also present a design that supports a multiplicity of
programming styles, from the Scratchpad
pattern-matching paradigm to functional programming to
more conventional procedural programming.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C6180 (User interfaces); C7310 (Mathematics
computing)",
keywords = "algorithms; AXIOM; C; Computer algebra system; design;
Expression trees; FORTRAN; Functional programming;
Infinite rewrite rule semantics; languages; Library;
Mathematical formulae; Pattern-matching; performance;
Procedural programming; Run-time efficiency;
Scratchpad; Strongly-typed programming language;
Symbolic problem solving; Type-inferencing interpreter;
Untyped systems; User interface design; User programs",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Pattern matching. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
thesaurus = "Mathematics computing; Pattern matching; Program
interpreters; Programming; Symbol manipulation; User
interfaces",
}
@InProceedings{Kaib:1994:FVG,
author = "M. Kaib",
title = "A fast variant of the {Gaussian} reduction algorithm",
crossref = "Adleman:1994:ANT",
pages = "159",
year = "1994",
bibdate = "Thu Sep 26 05:50:11 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Summary form only given. We propose a fast variant of
the Gaussian algorithm for the reduction of
two-dimensional lattices for the $\ell_1$-, $\ell_2$-
and $\ell_\infty-norm$. The algorithm uses at most
$O(M(B)(n+log B))$ bit operations for the
$\ell_2$-norm, $O(nM(B)\log{}B)$ bit operations for the
$\ell_\infty$-norm and in $O(n \log{}n M (B) \log{}B)$
bit operations for the $\ell_1$-norm on input vectors
$a$, $b$ in $Z^n$ with norm at most $2^B$ where $M(B)$
is a time bound for $B$-bit integer multiplication.
This generalizes Schonhages fast algorithm for monotone
reduction of binary quadratic forms (Proc. ISSAC 1991,
ACM 1991, p. 128--133) to the centered case and to
various norms. The basic idea is to perform most of the
arithmetic on the leading bits of the integers,
following the techniques of the fast gcd-algorithms due
to Lehmer and Schonhage. We extend the techniques to
the classical `centered' case. The Gaussian algorithm
performs reduction steps $(a, b)$ to
$H(\pm(b-\mu{}a),a)$ where the integer $\mu$ is chosen
to minimize $//b-\mu{}a//$. Our new consideration is,
that the core of the Gaussian algorithm operates stable
until the approximation error exceeds $^1/_12 //a//$,
what is valid for arbitrary norms. We use the
characterization of the transformation matrices which
Kaib and Schnorr gave in their sharp worst case
analysis for the number of reduction steps for
arbitrary norms.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math., Frankfurt Univ., Germany",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Approximation error; Arbitrary norms; B-bit integer
multiplication; Binary quadratic forms; Fast
gcd-algorithms; Fast variant; Gaussian algorithm;
Gaussian reduction algorithm; Input vectors; Integers;
Monotone reduction; Transformation matrices;
Two-dimensional lattices",
thesaurus = "Arithmetic; Data reduction; Matrix algebra; Number
theory",
}
@InProceedings{Kakas:1994:PAL,
author = "A. C. Kakas and G. A. Papadopoulos",
title = "Parallel Abduction in Logic Programming",
crossref = "Hong:1994:FIS",
pages = "214--224",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:1994:AFS,
author = "Erich Kaltofen",
title = "Asymptotically fast solution of {Toeplitz-like}
singular linear systems",
crossref = "ACM:1994:IPI",
pages = "297--304",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p297-kaltofen/",
abstract = "The Toeplitz likeness of a matrix (T. Kailath et al.,
1979) is the generalization of the notion that a matrix
is Toeplitz. Block matrices with Toeplitz blocks, such
as the Sylvester matrix corresponding to the resultant
of two univariate polynomials, are Toeplitz-like, as
are products and inverses of Toeplitz-like matrices.
The displacement rank of a matrix is a measure for the
degree of being Toeplitz-like. For example, an $r*s$
block matrix with Toeplitz blocks has displacement rank
$r+s$ whereas a generic $N*N$ matrix has displacement
rank $N$. A matrix of displacement rank $\alpha$ can be
implicitly represented by a sum of $\alpha$ matrices,
each of which is the product of a lower triangular and
an upper triangular Toeplitz matrix. Such a $\Sigma LU$
representation can usually be obtained efficiently. We
consider the problem of computing a solution to a
possibly singular linear system $Ax=b$ with
coefficients in an arbitrary field, where $A$ is an
$N\times{}N$ matrix of displacement rank $\alpha$ given
in $\Sigma LU$ representation. By use of randomization
we show that if the system is solvable we can find a
vector that is uniformly sampled from the solution
manifold in $O(\alpha ^2N(logN)^2 loglogN)$ expected
arithmetic operations in the field of entries. In case
no solution exists, this fact is discovered by our
algorithm. In asymptotically the same time we can also
compute the rank of $A$ and the determinant of a
nonsingular $A$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity); C6130 (Data handling techniques); C7310
(Mathematics computing)",
keywords = "$\Sigma$ LU representation; Arithmetic operations;
Asymptotically fast solution; Block matrices;
Determinant; Displacement rank; Randomization; Singular
linear system; Solution manifold; Sylvester matrix;
theory; Toeplitz blocks; Toeplitz like singular linear
systems; Toeplitz likeness; Univariate polynomials;
Vector; verification",
subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo). {\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods). {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Linear systems; Symbol
manipulation; Toeplitz matrices",
}
@InProceedings{Kaltofen:1994:FHP,
author = "Erich Kaltofen and Austin Lobo",
title = "Factoring high-degree polynomials by the black box
{Berlekamp} algorithm",
crossref = "ACM:1994:IPI",
pages = "90--98",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p90-kaltofen/",
abstract = "Modern techniques for solving structured linear
systems over finite fields, which use the coefficient
matrix as a black box and require an efficient
algorithm for multiplying this matrix by a vector, are
applicable to the classical algorithm for factoring a
univariate polynomial over a finite field by Berlekamp
(1967 and 1970). The present authors report on a
computer implementation of this idea that is based on
the parallel block Wiedemann linear system solver,
Coppersmith (1994) and Kaltofen (1993 and 1995). The
program uses randomization and they also study the
expected run time behavior of their method. The
asymptotically fastest known algorithm for factoring a
polynomial over a finite field is by von zur Gathen and
Shoup (1992). Shoup (1993) has subsequently implemented
the equal degree part of that algorithm making use of
FFT-based polynomial arithmetic. The present authors
show that a sequential version of the black box
Berlekamp algorithm is strongly related to their method
and allows for the same asymptotic speed-ups, at least
within a logarithmic factor. It is also possible to
realize the Niederreiter approach, Niederreiter and
Gijttfert (1994) by black box linear algebra.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
keywords = "algorithms; Black box Berlekamp algorithm; Coefficient
matrix; Factoring; Finite field; High-degree
polynomials; languages; Matrix multiplication;
Polynomial factorization; Structured linear system;
theory; Univariate polynomial",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods).",
thesaurus = "Algorithm theory; Matrix multiplication; Polynomial
matrices; Polynomials; Symbol manipulation",
}
@InProceedings{Kaltofen:1994:PST,
author = "E. Kaltofen and V. Pan",
title = "Parallel Solution of {Toeplitz} and {Toeplitz}-Like
Linear Systems Over Fields of Small Positive
Characteristic",
crossref = "Hong:1994:FIS",
pages = "225--233",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kapur:1994:AGR,
author = "Deepak Kapur and Tushar Saxena and Lu Yang",
title = "Algebraic and geometric reasoning using {Dixon}
resultants",
crossref = "ACM:1994:IPI",
pages = "99--107",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p99-kapur/",
abstract = "Dixon's method for computing multivariate resultants
by simultaneously eliminating many variables is
reviewed. The method is found to be quite restrictive
because often the Dixon matrix is singular, and the
Dixon resultant vanishes identically yielding no
information about solutions for many algebraic and
geometry problems. We extend Dixon's method for the
case when the Dixon matrix is singular, but satisfies a
condition. An efficient algorithm is developed based on
the proposed extension for extracting conditions for
the existence of affine solutions of a finite set of
polynomials. Using this algorithm, numerous geometric
and algebraic identities are derived for examples which
appear intractable with other techniques of
triangulation such as the successive resultant method,
the Gr{\"o}bner basis method, Macaulay resultants and
Characteristic set method. Experimental results suggest
that the resultant of a set of polynomials which are
symmetric in the variables is relatively easier to
compute using the extended Dixon's method.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1110 (Algebra); C1230 (Artificial intelligence);
C4260 (Computational geometry); C7310 (Mathematics
computing)",
keywords = "algorithms; experimentation; Geometric reasoning;
Dixon resultants; Multivariate resultants; Gr{\"o}bner
basis method; Macaulay resultants; Characteristic set
method; Polynomials",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Polynomials; Spatial reasoning; Symbol manipulation",
}
@InProceedings{Kaser:1994:HPR,
author = "O. Kaser and C. R. Ramakrishnan and R. C. Sekar",
title = "A High Performance Runtime System for Parallel
Evaluation of Lazy Languages",
crossref = "Hong:1994:FIS",
pages = "234--243",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kesseler:1994:RGC,
author = "M. Kesseler",
title = "Reducing Graph Copying Costs --- Time to Wrap it up",
crossref = "Hong:1994:FIS",
pages = "244--253",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Konno:1994:PMC,
author = "K. Konno and M. Nagatsuka and N. Kobayashi and S.
Matsuoka",
title = "{PARCS}: An {MPP}-Oriented {CLP} Language",
crossref = "Hong:1994:FIS",
pages = "254--263",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krandick:1994:BEI,
author = "W. Krandick and T. Jebelean",
title = "Bidirectional Exact Integer Division",
crossref = "Hong:1994:FIS",
pages = "264--272",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{LakshmanYN:1994:CSS,
author = "{Lakshman Y. N.} and B. David Saunders",
title = "On computing sparse shifts for univariate
polynomials",
crossref = "ACM:1994:IPI",
pages = "108--113",
year = "1994",
bibdate = "Sat Apr 25 12:53:49 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p108-lakshman/",
abstract = "In this paper, we consider the problem of computing
$t$-sparse shifts for univariate polynomials. Given a
polynomial $f(x)$ in $F(x)$ of degree $d$ (where $F$ is
a field of characteristic $O$), consider the
representation of $f(x)$ in the basis
$1,x-\alpha,(x-\alpha)^2,\ldots{}$ for some $\alpha$ in
$K$, an extension of $F$, i.e.,
$f(x)=\sum_{i=0}^d{}F_i(x-\alpha)^i$. Let $t$ be a
positive integer $<=I d$. We say that $\alpha$ is a
$t$-sparse shift for $f(x)$ (or, $f(x)$ is $t$-sparse
in the shifted basis
$1,x-\alpha,(x-\alpha)^2,\ldots{}$) if at most $t$ of
the coefficients $F_i$ are non-zero. The main problem
that we address is: given an $f(x)$ and $t$ as above,
can we efficiently compute a $t$-sparse shift for
$f(x)$ if one exists? We construct an efficient
algorithm for solving this problem and answer several
related questions of interest.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
keywords = "algorithms; Polynomial; Sparse shifts; theory;
Univariate polynomials",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{LaScala:1994:AC,
author = "R. La Scala",
title = "An algorithm for complexes",
crossref = "ACM:1994:IPI",
pages = "264--268",
year = "1994",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For computing free resolutions over a polynomial ring,
the usual approach consists in iterating B.
Buchberger's (1985) algorithm for each module in the
resolution. We propose one single algorithm which can
be viewed as a generalization of Buchberger's to chain
complexes. The algorithm is based on the use of
syzygies, due to H. M. Moller, T. Mora and C. Traverso
(1992), as criteria for avoiding useless computation of
S-polynomials. Some strategies for the pairs selection
in complexes are studied and tested in some
experiments.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Pisa Univ., Italy",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C7310 (Mathematics computing)",
keywords = "Free resolutions; Polynomial ring; Chain complexes;
Syzygies; S-polynomials; Pairs selection; Gr{\"o}bner
bases",
thesaurus = "Large-scale systems; Polynomials; Programming theory;
Symbol manipulation",
}
@InProceedings{Leung:1994:CSD,
author = "H.-F. Leung and K. L. Clark",
title = "Constraint Solving in Distributed Concurrent Logic
Programming",
crossref = "Hong:1994:FIS",
pages = "273--283",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Licciardi:1994:IHC,
author = "Sandra Licciardi and Teo Mora",
title = "Implicitization of hypersurfaces and curves by the
{Primbasissatz} and basis conversion",
crossref = "ACM:1994:IPI",
pages = "191--196",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p191-licciardi/",
abstract = "An algorithm for implicitizing curves and
hypersurfaces is proposed which reduces the problem to
a 0-dimensional one by the Primbasissatz and solves it
by FGLM. Also, a high-dimensional FGLM algorithm is
discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Inf. e Sci. dell'Inf., Genoa Univ.,
Italy",
classification = "C4130 (Interpolation and function approximation);
C4260 (Computational geometry)",
keywords = "0-Dimensional problem; algorithms; Basis conversion;
Curves; FGLM; High-dimensional FGLM algorithm;
Hypersurfaces; Primbasissatz; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations.",
thesaurus = "Computational geometry; Curve fitting; Polynomials;
Surface fitting",
}
@InProceedings{LopezGarcia:1994:TGB,
author = "P. {Lopez Garcia} and M. Hermenegildo and S. K.
Debray",
title = "Towards Granularity Based Control of Parallelism in
Logic Programs",
crossref = "Hong:1994:FIS",
pages = "133--144",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Luks:1994:CNP,
author = "Eugene M. Luks and Ferenc R{\'a}k{\'o}czi and Charles
R. B. Wright",
title = "Computing normalizers in permutation $p$-groups",
crossref = "ACM:1994:IPI",
pages = "139--146",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p139-luks/",
abstract = "Let $G$ and $H$ be subgroups of a finite $p$-group of
permutations. We describe the theory and implementation
of a polynomial-time algorithm for computing the
normalizer of $H$ in $G$. The method employs the
imprimitivity structure and an associated canonical
chief series to reduce to linear problems with fast
solutions. An implementation in GAP exhibits marked
speedups over general-purpose methods applied to the
same groups. There are analogous procedures and timings
for the problem of testing conjugacy of subgroups of
$p$-groups, and implementations are planned. It is an
easy matter, also, to extend the application to general
nilpotent groups.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Oregon Univ., Eugene,
OR, USA",
classification = "C4240C (Computational complexity); C7310
(Mathematics computing)",
keywords = "algorithms; Canonical chief series; Conjugacy of
subgroups; Nilpotent groups; Permutation $p$-groups;
Polynomial-time algorithm; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.2.1}
Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Permutations and combinations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Computational complexity; Group theory;
Renormalisation; Series [mathematics]; Symbol
manipulation",
}
@InProceedings{Man:1994:FPD,
author = "Yiu-Kwong Man and Francis J. Wright",
title = "Fast polynomial dispersion computation and its
application to indefinite summation",
crossref = "ACM:1994:IPI",
pages = "175--180",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p175-man/",
abstract = "An algorithm for computing the dispersion of one or
two polynomials is described, based on irreducible
factorization. It is demonstrated that in practice it
is faster than the `conventional' resultant-based
algorithm, at least for small problems. It can be
applied to algorithms for indefinite summation and
closed-form solution of linear difference equations. A
brief survey of existing mostly resultant-based
dispersion algorithms is given and the complexity of
the resultant involved is analysed. The effectiveness
of the proposed algorithm applied to indefinite
summation is demonstrated by some examples that are not
easily summed by the standard facilities in several
computer algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Queen Mary and Westfield Coll.,
London, UK",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
keywords = "algorithms; Closed-form solution; Complexity; Computer
algebra systems; Fast polynomial dispersion
computation; Indefinite summation; Irreducible
factorization; languages; Linear difference equations;
performance; Resultant-based algorithm; Resultant-based
dispersion algorithms; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
REDUCE.",
thesaurus = "Computational complexity; Difference equations;
Polynomials; Symbol manipulation",
}
@InProceedings{Mandache:1994:GBA,
author = "Ana Maria Mandache",
title = "The {Gr{\"o}bner} basis algorithm and subresultant
theory",
crossref = "ACM:1994:IPI",
pages = "123--128",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p123-mandache/",
abstract = "We investigate the possibility of constructing for
Gr{\"o}bner bases a concept similar to the one provided
by subresultants for polynomial remainder sequences.
Namely, we try to express the Gr{\"o}bner basis
polynomials obtained during the algorithm in terms of
matrices having on each row the coefficients of a
polynomial from the input basis, shifted by
multiplication with a power product. We prove that for
the general form of Buchberger's algorithm, the
Gr{\"o}bner basis polynomials not only cannot be
expressed as determinant polynomials but, in general,
they cannot even be obtained by a Gaussian
elimination-like process from such matrices. For the
Gr{\"o}bner basis polynomials that can be expressed as
determinant polynomials we show that we can detect
common factors of the coefficients without computing
gcd's. For achieving this we generalize Bareiss' matrix
triangularization method.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1110 (Algebra); C7310 (Mathematics computing)",
keywords = "algorithms; theory; verification; Gr{\"o}bner basis;
Subresultant theory; Gr{\"o}bner basis polynomials;
Matrix triangularization; Buchberger's algorithm;
Determinant polynomials",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Manocha:1994:CSS,
author = "Dinesh Manocha",
title = "Computing selected solutions of polynomial equations",
crossref = "ACM:1994:IPI",
pages = "1--8",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p1-manocha/",
abstract = "We present efficient and accurate algorithms to
compute solutions of zero-dimensional multivariate
polynomial equations in a given domain. Earlier methods
for solving polynomial equations are based on iterative
methods, homotopy methods or symbolic elimination. The
total number of solutions correspond to the Bezout
bound for dense polynomial systems or the BKK bound for
sparse systems. In most applications the actual number
of solutions in the domain of interest is much lower
than the Bezout or BKK bound. Our approach is based on
global formulation of the problem using resultants and
matrix computations and localizing it to find selected
solutions only. The problem of finding roots is reduced
to computing eigenvalues of a generalized companion
matrix and we use the structure of the matrix to
compute the solutions in the domain of interest only.
The resulting algorithm is iterative in nature and we
discuss its performance on a number of applications.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., North Carolina Univ., Chapel
Hill, NC, USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "algorithms; Bezout bound; BKK bound; Eigenvalues;
Generalized companion matrix; Global formulation;
Iterative; Matrix computations; Multivariate polynomial
equations; performance; Polynomial equations;
Resultants; Roots; Zero-dimensional",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues and
eigenvectors (direct and iterative methods).",
thesaurus = "Eigenvalues and eigenfunctions; Iterative methods;
Polynomials",
}
@InProceedings{Marti:1994:CSS,
author = "P. Marti and M. Rucher",
title = "A Cooperative Scheme for Solving Constraints over the
Reals",
crossref = "Hong:1994:FIS",
pages = "284--293",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Massey:1994:OCM,
author = "B. Massey and E. Tick",
title = "Optimizing Clause Matching Automata in
Committed-Choice Languages",
crossref = "Hong:1994:FIS",
pages = "294--303",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:1994:SFA,
author = "Michael B. Monagan and Gaston H. Gonnet",
title = "Signature functions for algebraic numbers",
crossref = "ACM:1994:IPI",
pages = "291--296",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p291-monagan/",
abstract = "J. T. Schwartz (1980) gave a fast probabilistic method
which tests if a matrix of polynomials over $Z$ is
singular or not. The method is based on the idea of
signature functions which are mappings of mathematical
expressions into finite rings. In Schwartz's paper,
they were polynomials over $Z$ into $\mbox{GF}(p)$.
Because computation in $\mbox{GF}(p)$ is very fast
compared with computing with polynomials, Schwartz's
method yields an enormous speedup both in theory and in
practice. Therefore it is desirable to extend the class
of expressions for which we can find effective
signature functions. G. H. Gonnet (1984; 1986) extended
the class of expressions for which signature functions
could be found, to include a restricted class of
elementary functions and integer roots. We present and
compare methods for constructing signature functions
for expressions containing algebraic numbers. Some
experimental results are given.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
classification = "C1140Z (Other topics in statistics); C4130
(Interpolation and function approximation); C6130 (Data
handling techniques); C7310 (Mathematics computing)",
keywords = "Algebraic numbers; algorithms; Elementary functions;
experimentation; Fast probabilistic method; Finite
rings; Integer roots; Mathematical expressions; Matrix;
Polynomials; Restricted class; Signature functions;
theory",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Functions; Polynomials; Probability; Symbol
manipulation",
}
@InProceedings{Murao:1994:MAS,
author = "H. Murao and T. Fujise",
title = "Modular Algorithm for Sparse Multivariate Polynomial
Interpolation and its Parallel Implementation",
crossref = "Hong:1994:FIS",
pages = "304--315",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Oaku:1994:AFS,
author = "Toshinori Oaku",
title = "Algorithms for finding the structure of solutions of a
system of linear partial differential equations",
crossref = "ACM:1994:IPI",
pages = "216--223",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p216-oaku/",
abstract = "We consider a system of linear partial differential
equations $M: P_1u=P_2u=\ldots{} P_su=0$ for an unknown
function $u$, where $P_1,\ldots{},P_s$, are linear
partial differential operators with polynomial
coefficients. Systems of differential equations for
various hypergeometric functions of several variables
are typical examples. The aim of this paper is to
present algorithms for finding the structure of the
space of solutions of such a system of differential
equations. Our method consists of the following three
steps: 1. Find the dimension of the space of the
solutions (i.e. the rank) of the system M. 2. Find the
singular locus of $M$ (i.e. the set of points where a
solution of $M$ can be singular). 3. Characterize the
asymptotic behavior of the solutions of $M$ near its
singular locus. We discuss mainly the second and the
third steps. We give an algorithm to solve the first
and the second steps at the same time, and algorithms
to solve the third step partially, i.e., under the
condition that $M$ is Fuchsian (or with regular
singularities) along its singular locus. Our methods
are based on the notion of Gr{\"o}bner base and the
Buchberger algorithm applied to rings of differential
operators. We use a standard term ordering for the
first and the second steps, but we introduce term
orderings of a new kind for the third step, which are
associated with a filtration. The algorithms presented
have been implemented on a computer algebra system
risa/asir.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Yokohama City Univ., Japan",
classification = "B0290P (Differential equations); C4170 (Differential
equations); C7310 (Mathematics computing)",
keywords = "algorithms; theory; Linear partial differential
equations; Unknown function; Polynomial coefficients;
Hypergeometric functions; Gr{\"o}bner base; Buchberger
algorithm; Computer algebra system; Risa/asir",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.8} Mathematics of Computing,
NUMERICAL ANALYSIS, Partial Differential Equations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems.",
thesaurus = "Partial differential equations; Symbol manipulation",
}
@InProceedings{Petitjean:1994:ACS,
author = "Sylvain Petitjean",
title = "Automating the construction of stationary
multiple-point classes",
crossref = "ACM:1994:IPI",
pages = "9--14",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p9-petitjean/",
abstract = "In this paper, we describe an algorithm to compute
arbitrary stationary multiple-point formulas. We report
its full implementation in Maple and show some examples
matching formulas found by hand computation. We also
present an application to the enumeration of lines
having specified contact with a projective surface.",
acknowledgement = ack-nhfb,
affiliation = "CRIN, CNRS, Vandoeuvre-les-Nancy, France",
classification = "C4260 (Computational geometry); C7310 (Mathematics
computing)",
keywords = "algorithms; Enumeration of lines; languages; Maple;
Multiple-point classes; Multiple-point formulas;
Projective surface; Stationary multiple-point formulas;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Computational geometry; Symbol manipulation",
}
@InProceedings{Rayes:1994:PGS,
author = "Mohamed Omar Rayes and P. S. Wang",
title = "Parallel {GCD} for Sparse Multivariate Polynomials on
Shared Memory Multiprocessors",
crossref = "Hong:1994:FIS",
pages = "326--335",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rayes:1994:PSM,
author = "Mohamed Omar Rayes and Paul S. Wang and Kenneth
Weber",
title = "Parallelization of the sparse modular {GCD} algorithm
for multivariate polynomials on shared memory
multiprocessors",
crossref = "ACM:1994:IPI",
pages = "66--73",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p66-rayes/",
abstract = "Reported are experiences and practical results from
parallelizing the modular GCD algorithm for sparse
multivariate polynomials. The strategy is to identify
key computation steps in the sequential algorithm and
implement them in parallel. The two major steps of the
sequential algorithm---computing the GCD modulo several
primes and applying the Chinese Remainder Algorithm on
the integer coefficients---are easily partitioned into
independent subtasks. The subtask of computing the GCD
modulo one prime can be subdivided further. Several
parallel strategies for the multivariate GCD modulo a
prime are presented. Actual timings on a Sequent
Balance with 26 processors are presented.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C5440
(Multiprocessing systems); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "algorithms; Chinese remainder algorithm; Computation
steps; GCD module; Integer coefficients; Multivariate
polynomials; Parallelization; Sequent Balance;
Sequential algorithm; Shared memory multiprocessors;
Sparse modular GCD algorithm",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Mathematics computing; Polynomials; Shared memory
systems; Symbol manipulation",
}
@InProceedings{Recio:1994:SIG,
author = "T. Recio and M. J. Gonz{\'a}lez-L{\'o}pez",
title = "On the symbolic insimplification of the general
$6{R}$-manipulator kinematic equations",
crossref = "ACM:1994:IPI",
pages = "354--358",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p354-recio/",
abstract = "When symbolically solving inverse kinematic problems
for robot classes, we deal with computations on ideals
representing these robot's geometry. Therefore, such
ideals must be considered over a base field {\em K\/},
where the parameters of the class (and also the
possible relations among them) are represented. In this
framework we shall prove that the ideal corresponding
to the general 6R manipulator is real and prime over
{\em K\/}. The practical interest of our result is that
it confirms that the usual inverse kinematic equations
of this robot class do not add redundant solutions and
that this ideal cannot be ``factorized'', establishing
therefore, Kov{\'a}cs [7] conjecture. We prove also
that this root class has six degrees of freedom (i.e.
the corresponding ideal is six-dimensional), even over
the extended field {\em K\/}, which is the algebraic
counterpart to the fact that the 6R manipulator is
completely general. Our proof uses, as intermediate
step, some dimensionality analysis of the Elbow
manipulator, which is a specialization of the {\em
6R\/}.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Matematicas, Estadistica y Comput., Cantabria
Univ., Santander, Spain",
classification = "C3390M (Manipulators)",
keywords = "algorithms; Elbow manipulator; General 6R manipulator
kinematic equations; Ideal; Inverse kinematic problems;
Kinematics; Kovacs conjecture; Robot class; Robot
theory; Robotics; Six degrees of freedom; Symbolic
computation; Symbolic insimplification; Symbolically
solving; theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf I.2.9}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Robotics, Manipulators. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Manipulator kinematics; Symbol manipulation",
}
@InProceedings{Richardson:1994:IPE,
author = "Dan Richardson and John Fitch",
title = "The identity problem for elementary functions and
constants",
crossref = "ACM:1994:IPI",
pages = "285--290",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p285-richardson/",
abstract = "A solution for a version of the identity problem is
proposed for a class of functions including the
elementary functions. Given $f(x)$, $g(x)$, defined at
some point $\beta$ we decide whether or not $f(x)$
identical to $g(x)$ in some neighbourhood of $\beta$.
This problem is first reduced to a problem about zero
equivalence of elementary constants. Then a semi
algorithm is given to solve the elementary constant
problem. This semi algorithm is guaranteed to give the
correct answer whenever it terminates, and it
terminates unless the problem being considered contains
a counter example to Schanuel's conjecture (J. Ax,
1971).",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1100 (Mathematical techniques); C4240 (Programming
and algorithm theory); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "Algorithm termination; algorithms; Computer algebra;
Elementary constants; Elementary functions; Identity
problem; Schanuel conjecture; Semi algorithm; theory;
verification; Zero equivalence",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Constants; Functions; Programming theory; Symbol
manipulation",
}
@InProceedings{Roach:1994:SNE,
author = "Kelly Roach",
title = "Symbolic-numeric nonlinear equation solving",
crossref = "ACM:1994:IPI",
pages = "278--284",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p278-roach/",
abstract = "A numerical equation solving algorithm employing
differentiation and interval arithmetic is presented
which finds all solutions of $f(z)=0$ on an interval
$I$ when $f$ is holomorphic and has simple zeros. A two
dimensional generalization of this algorithm is
discussed. Finally, aspects of a broader symbolic
numeric algorithm which uses the first algorithm as a
foundation are considered.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C4150 (Nonlinear and functional equations); C4160
(Numerical integration and differentiation); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algorithms; Broader symbolic numeric algorithm;
Differentiation; Holomorphic; Interval arithmetic;
languages; Numerical equation solving algorithm; Simple
zeros; Symbolic numeric nonlinear equation solving;
Symbolic-numeric nonlinear equation solving; Two
dimensional generalization",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Differentiation; Nonlinear equations; Symbol
manipulation",
}
@InProceedings{RuizS:1994:AGG,
author = "O. E. {Ruiz S.} and P. M. Ferreira",
title = "Algebraic geometry and group theory in geometric
constraint satisfaction",
crossref = "ACM:1994:IPI",
pages = "224--233",
year = "1994",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The determination of a set of geometric entities that
satisfy a series of geometric relations (constraints)
constitutes the Geometric Constraint Satisfaction or
Scene Feasibility (GCS/SF) problem. This problem
appears in different forms in Assembly Planning,
Constraint Driven Design, Computer Vision, etc. Its
solution is related to the existence of roots to
systems of polynomial equations. Previous attempts
using exclusively numerical (geometry) or symbolic
(topology) solutions for this problem present
shortcomings regarding characterization of solution
space, incapability to deal with geometric and
topological inconsistencies, and very high
computational expenses. In this investigation
Gr{\"o}bner Bases are used for the characterization of
the algebraic variety of the ideal generated by the set
of polynomials. Properties of Gr{\"o}bner Bases provide
a theoretical framework responding to questions about
consistency, ambiguity, and dimension of the solution
space. It also allows for the integration of geometric
and topological reasoning. The high computational cost
of Buchberger's algorithm for the Gr{\"o}bner Basis is
compensated by the choice of a non redundant set of
variables, determined by the characterization of
constraints based on the subgroups of the group of
Euclidean displacements SE(3). Examples have shown the
advantage of using group based variables. One of those
examples is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. and Ind. Eng., Illinois Univ., Urbana,
IL, USA",
classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
intelligence); C4260 (Computational geometry)",
keywords = "Group theory; Geometric constraint satisfaction;
Algebraic geometry; Geometric entities; Polynomial
equations; Gr{\"o}bner Bases; Buchberger algorithm;
Euclidean displacements; Spatial reasoning",
thesaurus = "Computational geometry; Constraint theory; Group
theory; Spatial reasoning",
}
@InProceedings{S:1994:AGG,
author = "Oscar E. Ruiz S. and Placid M. Ferreira",
title = "Algebraic geometry and group theory in geometric
constraint satisfaction",
crossref = "ACM:1994:IPI",
pages = "224--233",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p224-ruiz_s./",
abstract = "The determination of a set of geometric entities that
satisfy a series of geometric relations (constraints)
constitutes the Geometric Constraint Satisfaction or
Scene Feasibility (GCS/SF) problem. This problem
appears in different forms in Assembly Planning,
Constraint Driven Design, Computer Vision, etc. Its
solution is related to the existence of roots to
systems of polynomial equations. Previous attempts
using exclusively numerical (geometry) or symbolic
(topology) solutions for this problem present
shortcomings regarding characterization of solution
space, incapability to deal with geometric and
topological inconsistencies, and very high
computational expenses. In this investigation
Gr{\"o}bner Bases are used for the characterization of
the algebraic variety of the ideal generated by the set
of polynomials. Properties of Gr{\"o}bner Bases provide
a theoretical framework responding to questions about
consistency, ambiguity, and dimension of the solution
space. It also allows for the integration of geometric
and topological reasoning. The high computational cost
of Buchberger's algorithm for the Gr{\"o}bner Basis is
compensated by the choice of a non redundant set of
variables, determined by the characterization of
constraints based on the subgroups of the group of
Euclidean displacements {\em SE(3)\/}. Examples have
shown the advantage of using group based variables. One
of those examples is discussed.",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf J.6}
Computer Applications, COMPUTER-AIDED ENGINEERING,
Computer-aided design (CAD).",
}
@InProceedings{Saenz:1994:SMP,
author = "F. Saenz and J. J. Ruz and W. Hans and S. Winkler",
title = "A Stack-based Machine for Parallel Execution of
{Babel} Programs",
crossref = "Hong:1994:FIS",
pages = "336--345",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Scala:1994:AC,
author = "Roberto La Scala",
title = "An algorithm for complexes",
crossref = "ACM:1994:IPI",
pages = "264--268",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p264-la_scala/",
abstract = "For computing free resolutions over a polynomial ring
the usual approach consists in iterating the
Buchburger's algorithm for each module in the
resolution. In this paper, we propose one single
algorithm which can be viewed as a generalization of
Buchberger's to chain complexes. The algorithm is based
on the use of syzygies, due to M{\"o}ller, Mora and
Traverso, as criteria for avoiding useless computation
of S-polynomials. Some strategies for the pairs
selection in complexes are studied and tested in some
experiments.",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Schonert:1994:FBI,
author = "Martin Sch{\"o}nert and {\'A}kos Seress",
title = "Finding blocks of imprimitivity in small-base groups
in nearly linear time",
crossref = "ACM:1994:IPI",
pages = "154--157",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p154-schonert/",
abstract = "The purpose of this note is to describe a new
algorithm for finding blocks of imprimitivity for a
permutation group $G$, operating on a domain $\Omega$.
It runs in
$O(n\log^3\bmod{}G\bmod{}+ns\log\bmod{}G\bmod{})$ time,
where a is the size of $R$ and $s$ is the number of
generators for G. In many situations it is therefore
faster than Atkinson's method, which runs in $O(n^2s)$
time. A base of $G$ is a subset $B$ contained in
$\Omega$ such that only the identity of $G$ fixes $B$
pointwise. We call a family of groups small-base groups
if they admit bases of size $O(\log^c n)$ for some
fixed constant $c$. If $G$ belongs to a family of
small-base groups, our algorithm runs in nearly linear
time, namely in $O(ns\log^{c'}a)$. Beals recently gave
an algorithm with the same worst case estimate. Our
algorithm is simpler to implement and we expect faster
practical performance.",
acknowledgement = ack-nhfb,
affiliation = "Tech. Hochschule Aachen, Germany",
classification = "C1110 (Algebra); C4240C (Computational complexity)",
keywords = "algorithms; Imprimitivity; Nearly linear time;
Permutation group; Small-base groups; theory;
verification; Worst case estimate",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf E.1} Data, DATA STRUCTURES, Arrays.",
thesaurus = "Computational complexity; Group theory",
xxnote = "Check title??",
}
@InProceedings{Schreiner:1994:PPI,
author = "W. Schreiner",
title = "A Para-Functional Programming Interface for a Parallel
Computer Algebra Package",
crossref = "Hong:1994:FIS",
pages = "346--355",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Siegl:1994:PFT,
author = "K. Siegl",
title = "A Parallel Factorization Tree {Gr{\"o}bner} Basis
Algorithm",
crossref = "Hong:1994:FIS",
pages = "356--362",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sodan:1994:SAP,
author = "A. Sodan and H. Bi",
title = "A Semi-Automatic Approach for Parallelizing Symbolic
Processing Programs",
crossref = "Hong:1994:FIS",
pages = "363--372",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sommeling:1994:CCI,
author = "Ron Sommeling",
title = "Characteristic classes for irregular singularities",
crossref = "ACM:1994:IPI",
pages = "163--168",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p163-sommeling/",
abstract = "For an endomorphism in a finite dimensional vector
space, one can define its characteristic polynomial and
rational Jordan normal form. In this article something
analogous is done for differential operators in a
finite dimensional vector space. An overview of
(partial) algorithms to compute these invariants is
also given. Proofs and more results and details can be
found in (Sommeling, 1993) on which this article is
based.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Nijmegen Univ., Netherlands",
classification = "C4140 (Linear algebra); C4170 (Differential
equations)",
keywords = "algorithms; Characteristic classes; Characteristic
polynomial; Differential operators; Endomorphism;
Finite dimensional vector space; Irregular
singularities; Rational Jordan normal form; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Differential equations; Polynomial matrices",
}
@InProceedings{Takesue:1994:PSP,
author = "M. Takesue",
title = "Parallel Symbolic Processing with the Distributed
Lists",
crossref = "Hong:1994:FIS",
pages = "373--381",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Todd:1994:SSA,
author = "Philip H. Todd and Robin J. Y. McLeod and Marcia
Harris",
title = "A system for the symbolic analysis of problems in
engineering mechanics",
crossref = "ACM:1994:IPI",
pages = "84--89",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p84-todd/",
abstract = "In this paper, we present a system for the symbolic
solution of problems in engineering mechanics. Of
critical importance is a sub-system for maintaining and
manipulating quantities containing unevaluated
intermediate variables. Without this subsystem,
intermediate expression expansion makes symbolic
mechanics impractical for all but trivial problems.
With the subsystem, readable symbolic solutions may be
derived for mechanics problems of textbook complexity
and above. More complex symbolic solutions in a form
amenable to code generation may be derived for
mechanics problems of the complexity found in a
practical engineering context.",
acknowledgement = ack-nhfb,
affiliation = "Saltire Software, Beaverton, OR, USA",
classification = "C4240C (Computational complexity); C6130 (Data
handling techniques); C7310 (Mathematics computing);
C7400 (Engineering computing)",
keywords = "algorithms; Code generation; Complexity; Engineering
mechanics; Intermediate expression expansion;
Intermediate variables; Symbolic analysis; Symbolic
mechanics; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational complexity; Engineering computing;
Mathematics computing; Symbol manipulation",
}
@InProceedings{Tong:1994:IDC,
author = "B.-M. Tong and H.-F. Leung",
title = "Implementation of a Data-Parallel Concurrent
Constraint Programming System",
crossref = "Hong:1994:FIS",
pages = "382--393",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:1994:CPR,
author = "Mark {van Hoeij}",
title = "Computing parameterizations of rational algebraic
curves",
crossref = "ACM:1994:IPI",
pages = "187--190",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p187-van_hoeij/",
abstract = "In this paper I want to present a new method for
computing parametrizations of algebraic curves.
Basically this method is a direct application of
integral basis computation. Examples show that this
method is faster than older methods.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Nijmegen Univ., Netherlands",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; Integral basis computation; languages;
Parametrizations; Rational algebraic curves; Rational
functions; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
thesaurus = "Curve fitting; Functions; Integral equations",
xxtitle = "Computing parametrizations of rational algebraic
curves",
}
@InProceedings{Villard:1994:FPC,
author = "Gilles Villard",
title = "Fast parallel computation of the {Smith} normal form
of polynomial matrices",
crossref = "ACM:1994:IPI",
pages = "312--317",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p312-villard/",
abstract = "The author establishes that the Smith normal form of a
polynomial matrix in $F(x)^{n*n}$, where $F$ is an
arbitrary commutative field, can be computed in
$\mbox{NC}_F$.",
acknowledgement = ack-nhfb,
affiliation = "Lab. LMC, IMAG, Grenoble, France",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240P
(Parallel programming and algorithm theory)",
keywords = "Algorithm theory; algorithms; Arbitrary commutative
field; Computability; Fast parallel computation;
Parallel algorithm; Polynomial matrices; Polynomial
matrix; Smith normal form; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Algorithm theory; Computability; Parallel algorithms;
Polynomial matrices",
}
@InProceedings{Wang:1994:PPO,
author = "P. S. Wang",
title = "Parallel Polynomial Operations: {A} Progress Report
(Invited Tutorial)",
crossref = "Hong:1994:FIS",
pages = "394--404",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Watt:1994:FRA,
author = "Stephen M. Watt and Peter A. Broadbery and Samuel S.
Dooley and Pietro Iglio and Scott C. Morrison and
Jonathan M. Steinbach and Robert S. Sutor",
title = "A first report on the ${A}^{\mbox{Hash}}$ compiler",
crossref = "ACM:1994:IPI",
pages = "25--31",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p25-watt/",
abstract = "The $A^{\mbox{Hash}}$ compiler allows users of
computer algebra to develop programs in a context where
multiple programming languages are employed. The
compiler translates programs written in the
$A^{\mbox{Hash}}$ programming language to a low level
intermediate language, Foam (Watt et al., 1994) from
which it can generate stand-alone programs, native
object libraries to be linked with other applications,
or code to be read into closed environments. In
addition, Foam code may be directly executed using an
interpreter provided with the $A^{\mbox{Hash}}$
compiler.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C6150C (Compilers, interpreters and other
processors); C7310 (Mathematics computing)",
keywords = "$A^{\mbox{Hash}}$ compiler; algorithms; Computer
algebra; design; Foam; Interpreter; languages; Multiple
programming languages; Object libraries; performance;
Program generation; Program translation; Stand-alone
programs",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Compilers. {\bf
F.3.3} Theory of Computation, LOGICS AND MEANINGS OF
PROGRAMS, Studies of Program Constructs, Type
structure. {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Optimization. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
LISP.",
thesaurus = "Program compilers; Program interpreters; Software
libraries; Symbol manipulation",
}
@InProceedings{Weber:1994:ATI,
author = "Andreas Weber",
title = "Algorithms for type inference with coercions",
crossref = "ACM:1994:IPI",
pages = "324--329",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p324-weber/",
abstract = "The paper presents algorithms that perform a type
inference for a type system occurring in the context of
computer algebra. The type system permits various
classes of coercions between types and the algorithms
are complete for the precisely defined system, which
can be seen as a formal description of an important
subset of the type system supported by the computer
algebra program AXIOM. Previously only algorithms for
much more restricted cases of coercions have been
described or the frameworks used have been so general
that the corresponding type inference problems were
known to be undecidable.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
Germany",
classification = "C4240 (Programming and algorithm theory); C6130
(Data handling techniques)",
keywords = "algorithms; Algorithms; AXIOM computer algebra
program; Coercions; Computer algebra; Formal
description; languages; Precisely defined system;
theory; Type inference; Type system; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.3.3} Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Type structure. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Algorithm theory; Symbol manipulation; Type theory",
}
@InProceedings{Weber:1994:PIA,
author = "K. Weber",
title = "Parallel Implementation of the Accelerated Integer
{GCD} Algorithm",
crossref = "Hong:1994:FIS",
pages = "405--411",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Weil:1994:USS,
author = "Jacques-Arthur Weil",
title = "The use of the special semi-groups for solving
differential equations",
crossref = "ACM:1994:IPI",
pages = "341--347",
year = "1994",
bibdate = "Sat Apr 25 12:54:38 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p341-weil/",
abstract = "In general, there is no method for finding closed form
first integrals or solutions of ordinary differential
equations with non constant coefficients. Thus, one
usually performs heuristics, but this involves
fastidious computations. The aim of the paper is to
propose strategies that computerize such heuristics to
help the analysis. We formulate our questions in terms
of differential algebra. Then, we are able to derive
algebraic constructive criteria for the search for
closed form solutions of differential equations of the
type
$s(x,y,\ldots{},y^{(n-1)})y^{(n)}+t(x,y,\ldots{},y^{(n-1)})=0$
(sections 2 and 3). In particular, we focus on the
so-called special polynomials (or Darboux curves). We
show how our tools link the expression of the solutions
to that of the first integrals, and how it gives a
strategy to compute them. Then, we show how these
techniques permit one to derive algorithmic methods to
find solutions of order $n-1$ for linear differential
equations of order $n$; we specifically detail the
second order case.",
acknowledgement = ack-nhfb,
affiliation = "GAGE/Centre de Math., Ecole Polytech., Palaiseau,
France",
classification = "C1160 (Combinatorial mathematics); C4160 (Numerical
integration and differentiation); C4170 (Differential
equations); C7310 (Mathematics computing)",
keywords = "Algebraic constructive criteria; Algorithmic methods;
algorithms; Closed form first integrals; Closed form
solutions; Darboux curves; Differential algebra;
Differential equations; Linear differential equations;
Non constant coefficients; Ordinary differential
equations; Second order case; Special polynomials;
Special semi group; Special semi-groups; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations.",
thesaurus = "Differentiation; Group theory; Linear differential
equations; Symbol manipulation",
}
@InProceedings{Weispfenning:1994:QER,
author = "Volker Weispfenning",
title = "Quantifier elimination for real algebra-the cubic
case",
crossref = "ACM:1994:IPI",
pages = "258--263",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p258-weispfenning/",
abstract = "We present a special purpose quantifier elimination
method that eliminates a quantifier $\exists x$ in
formulas $\exists x(\phi)$ where $\phi$ is a Boolean
combination of polynomial inequalities of degree $<=3$
with respect to $x$. The method extends the virtual
substitution of parametrized test points developed by
V. Weispfenning (1988) and R. Loos and V. Weispfenning
(1993) for the linear case and by V. Weispfenning
(1993) for the quadratic case. It has similar upper
complexity bounds and offers similar advantages
(relatively large preprocessing part, explicit
parametric solutions). Small examples suggest that the
method will be of practical significance.",
acknowledgement = ack-nhfb,
affiliation = "Passau Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C4210 (Formal logic); C4240C (Computational
complexity); C6130 (Data handling techniques); C7310
(Mathematics computing)",
keywords = "Boolean combination; Cubic case; Explicit parametric
solutions; Large preprocessing part; Parametrized test
points; Polynomial inequalities; Quadratic case; Real
algebra; Special purpose quantifier elimination method;
theory; Upper complexity bounds; verification; Virtual
substitution",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Mechanical theorem proving.",
thesaurus = "Boolean algebra; Computational complexity;
Polynomials; Symbol manipulation",
}
@InProceedings{Wikstroem:1994:DPE,
author = "C. Wikstroem",
title = "Distributed Programming in {Erlang}",
crossref = "Hong:1994:FIS",
pages = "412--421",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhang:1994:CSD,
author = "H. Zhang and M. P. Bonacina",
title = "Cumulating Search in a Distributed Computing
Environment: {A} Case Study in Parallel
Satisfiability",
crossref = "Hong:1994:FIS",
pages = "422--431",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:1995:ISR,
author = "S. A. Abramov",
title = "Indefinite sums of rational functions",
crossref = "Levelt:1995:IPI",
pages = "303--308",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p303-abramov/",
abstract = "We propose a new algorithm for indefinite rational
summation which, given a rational function $F(x)$,
extracts a rational part $R(s)$ from the indefinite sum
of $F(x): \sum F(x)=R(x)+ \sum H(x)$. If $H(x)$ is not
equal to $0$ then the denominator of this rational
function has the lowest possible degree. We then solve
the same problem in the $q$-difference case.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C1100 (Mathematical techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Denominator;
Indefinite rational summation; Indefinite sums;
Q-difference, ISSAC; Rational functions; symbolic
computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2}
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Rational approximation. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Functions; Mathematics computing",
}
@InProceedings{Abramov:1995:PSL,
author = "Sergei A. Abramov and Manuel Bronstein and Marko
Petkov{\v{s}}ek",
title = "On polynomial solutions of linear operator equations",
crossref = "Levelt:1995:IPI",
pages = "290--296",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p290-abramov/",
abstract = "Let $K$ be a field of characteristic $0$ and $L: K(x)$
to $K(x)$ an endomorphism of the $K$ linear space of
univariate polynomials over $K$. We consider the
following computational tasks concerning $L$: (i)
homogeneous equation $Ly=0$: compute a basis of
$\mbox{Ker} L$ in $K(x)$; (ii) inhomogeneous equation
$Ly=f$: given $f$ in $K(x)$, compute a basis of the
affine space $L^{-l}(f)$ in $K(x)$; (iii) parametric
inhomogeneous equation $Ly=\sum^m_{i=1}\lambda{}_if_i$:
given $f_1, f_2, \ldots{}, f_m$ in $K(x)$, compute a
basis of $\mbox{Ker} L'$ where $L':(K(x)(+)K^m)$ to
$K(x)$ and $L':(y, \lambda)$ to
$Ly-\sum^m_{i=1}\lambda{}_if_i$, for $y$ in $K(x)$,
$\lambda$ in $K^m$. Many problems and algorithms in
differential and difference algebra contain these tasks
as subproblems which, however conceptually simple,
often account for a fair share of the overall computing
time.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C1110 (Algebra); C1120 (Mathematical analysis);
C4130 (Interpolation and function approximation); C4170
(Differential equations); C7310 (Mathematics
computing)",
keywords = "$K$ linear space; Affine space; algebraic computation;
algorithms; Computational tasks; Difference algebra;
Endomorphism; Homogeneous equation; Inhomogeneous
equation; Linear operator equations; Parametric
inhomogeneous equation; Polynomial solutions;
Subproblems, ISSAC; symbolic computation; theory;
Univariate polynomials; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
systems (direct and iterative methods). {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Difference equations; Mathematics computing;
Polynomials",
}
@InProceedings{Abramov:1995:RSL,
author = "S. A. Abramov",
title = "Rational solutions of linear difference and
$q$-difference equations with polynomial coefficients",
crossref = "Levelt:1995:IPI",
pages = "285--289",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p285-abramov/",
abstract = "We propose a simple algorithm to construct a
polynomial divisible by the denominator of any rational
solution of a linear difference equation
$a_n(x)y(x+n)+\ldots{} +a_0(x)y(x)=b(x)$ with
polynomial coefficients and a polynomial right-hand
side. Then we solve the same problem for $q$-difference
equations. Nonhomogeneous equations with hypergeometric
righthand sides are considered as well.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "B0290F (Interpolation and function approximation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4170 (Differential
equations)",
keywords = "algebraic computation, Rational solutions; algorithms;
Denominator; ISSAC; Linear difference; Linear
difference equation; Nonhomogeneous equations;
Polynomial coefficients; Q-difference equations;
Rational solution; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Difference equations; Polynomials",
}
@Article{Anonymous:1995:IA,
author = "Anonymous",
title = "{ISSAC} '95: Announcement",
journal = j-SIGNUM,
volume = "30",
number = "2",
pages = "12--??",
year = "1995",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Fri Jan 5 07:58:42 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1995:IIS,
author = "Anonymous",
title = "{ISSAC '96: International Symposium on Symbolic and
Algebraic Computation}",
journal = j-SIGSAM,
volume = "29",
number = "3\&4",
pages = "19--19",
month = dec,
year = "1995",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
bibdate = "Fri Sep 06 07:11:07 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Avitzur:1995:HIP,
author = "Ron Avitzur and Olaf Bachmann and Norbert Kajler",
title = "From honest to intelligent plotting",
crossref = "Levelt:1995:IPI",
pages = "32--41",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p32-avitzur/",
abstract = "Adaptive and honest plotting are two techniques to
improve the quality of curve and surface visualization
packages. Beyond honest plotting, we investigate a
number of alternative techniques in order to improve
correctness and completeness of 2D and 3D plotting, to
increase efficiency, and to achieve better usability.
We refer to these techniques as intelligent plotting as
most of them transparently take advantage of the
numerical and/or symbolic capabilities available from
some mathematical engine in order to provide better and
faster graphical displays. We implemented these
techniques inside two very different packages: the
Graphing Calculator and IZIC which we used as testbeds
for our experiments.",
acknowledgement = ack-nhfb,
affiliation = "RIACA, Amsterdam, Netherlands",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Completeness;
Correctness; Curve visualization packages;
experimentation; Graphing Calculator; Honest plotting;
Intelligent plotting; IZIC, ISSAC; languages;
reliability; Surface visualization packages; Symbolic
capabilities; symbolic computation",
subject = "{\bf I.3.4} Computing Methodologies, COMPUTER
GRAPHICS, Graphics Utilities, Graphics packages. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica. {\bf I.3.5} Computing Methodologies,
COMPUTER GRAPHICS, Computational Geometry and Object
Modeling, Curve, surface, solid, and object
representations.",
thesaurus = "Symbol manipulation",
}
@InProceedings{Ballarin:1995:TAI,
author = "Clemens Ballarin and Karsten Homann and Jacques
Calmet",
title = "Theorems and Algorithms: An Interface between
{Isabelle} and {Maple}",
crossref = "Levelt:1995:IPI",
pages = "150--157",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "Compendex database; http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p150-ballarin/",
abstract = "Solving sophisticated mathematical problems often
requires algebraic algorithms and theorems. However,
there are no environments integrating theorem provers
and computer algebra systems which consistently provide
the inference capabilities of the former and the
powerful arithmetic of the latter systems. As an
example of such a mechanized mathematics environment,
we describe a prototype implementation of an interface
between Isabelle and Maple. It is achieved by extending
the simplifier of Isabelle through the introduction of
a new class of simplification rules called `evaluation
rules', in order to make selected operations of Maple
available, and without any modification to the computer
algebra system. Additionally, we specify syntax
translations for the concrete syntax of Maple which
enables the communication between both systems. This is
illustrated by some examples that can be solved by
theorems and algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "721.1; 722.2; 723.1.1; 921; 921.1; 921.2; C4210
(Formal logic); C6150E (General utility programs);
C6170K (Knowledge engineering techniques); C7310
(Mathematics computing)",
conference = "Proceedings of the 1995 International Symposium on
Symbolic and Algebraic Computation",
keywords = "Algebra; Algebraic algorithms; algebraic computation;
Algorithms; algorithms; Arithmetic; Artificial
intelligence; Calculations; Computer algebra system;
Computer programming languages; Digital arithmetic;
Evaluation rules; Inference capabilities; Integration;
Interface; Interfaces (computer); Isabelle; languages;
Logical languages; Maple; Mathematical techniques;
Mechanized mathematics environment; Problem solving;
Procedural algebraic knowledge; Prototype
implementation; Simplification rules; Simplifier;
Symbolic calculations; symbolic computation; Syntax
translations; Syntax translations, ISSAC; Theorem
prover; Theorem proving; theory; verification",
meetingaddress = "Montreal, Can",
meetingdate = "Jul 10--12 1995",
meetingdate2 = "07/10--12/95",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic. {\bf I.1.4} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Applications.",
thesaurus = "Application program interfaces; Arithmetic; Inference
mechanisms; Mathematics computing; Symbol manipulation;
Theorem proving",
}
@InProceedings{Barkatou:1995:RVM,
author = "A. Barkatou",
title = "A rational version of {Moser}'s algorithm",
crossref = "Levelt:1995:IPI",
pages = "297--302",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p297-barkatou/",
abstract = "It is important to know whether a linear system of
differential equations has a regular or an irregular
singularity at a given point $x_0$ of the complex
domain C. Moser (1960) has given an algorithm to solve
this problem. His algorithm needs to compute with the
individual singularities of the system and requires
computations in algebraic extensions of the constant
field for the coefficients of the system. This may
represent an important drawback from a practical point
of view. This paper describes a rational version of
Moser's algorithm which has been implemented in the
Maple computer algebra system for systems of
differential equations with coefficients in $Q(x)$. It
never needs to compute with the individual
singularities of the system and avoids any algebraic
extensions. In addition, our algorithm reduces a linear
system of differential equations with coefficients in
$Q(x)$ to an `irreducible' form which is particularly
convenient if one wishes to compute invariants at
singularities.",
acknowledgement = ack-nhfb,
affiliation = "LMC-IMAG, Grenoble, France",
classification = "C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "algebraic computation; Algebraic extensions;
algorithms; Computer algebra system, ISSAC; Irregular
singularity; Linear differential equations; Maple;
Regular singularity; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Linear differential equations; Mathematics computing;
Symbol manipulation",
}
@InProceedings{Boulier:1995:RRF,
author = "F. Boulier and F. Ollivier and D. Lazard and M.
Petitot",
title = "Representation for the radical of a finitely generated
differential ideal",
crossref = "Levelt:1995:IPI",
pages = "158--166",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p158-boulier/",
abstract = "We give an algorithm which represents the radical $J$
of a finitely generated differential ideal as an
intersection of radical differential ideals. The
computed representation provides an algorithm for
testing membership in $J$. This algorithm works over
either an ordinary or a partial differential polynomial
ring of characteristic zero. It has been programmed. We
also give a method to obtain a characteristic set of
$J$, if the ideal is prime.",
acknowledgement = ack-nhfb,
affiliation = "LIFL, Lille I Univ., Villeneuve d'Ascq, France",
classification = "C1110 (Algebra); C1120 (Mathematical analysis);
C1160 (Combinatorial mathematics)",
keywords = "algebraic computation; algorithms; Characteristic set;
Differential algebra, ISSAC; Finitely generated
differential ideal; Membership testing algorithm;
Partial differential polynomial ring; Prime ideal;
Programming; Radical differential ideals intersection;
Radical representation; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial). {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Algebra; Differential geometry; Polynomials; Set
theory",
xxauthor = "F. Boulier and D. Lazard and F. Ollivier and M.
Petitot",
xxnote = "Check author order: Ollivier and Lazard, or Lazard and
Ollivier??",
}
@InProceedings{Broadbery:1995:IDE,
author = "P. A. Broadbery and T. G{\'o}mez-D{\'\i}az and S. M.
Watt",
title = "On the Implementation of Dynamic Evaluation",
crossref = "Levelt:1995:IPI",
pages = "77--84",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p77-broadbery/",
abstract = "Dynamic evaluation is a technique for producing
multiple results according to a decision tree which
evolves with program execution. Sometimes we need to
produce results for all possible branches in the
decision tree, while on other occasions it may be
sufficient to compute a single result which satisfies
certain properties. This technique finds use in
computer algebra where computing the correct result
depends on recognising and properly handling special
cases of parameters. In previous work, programs using
dynamic evaluation have explored all branches of
decision trees by repeating the computations prior to
decision points. The paper presents two new
implementations of dynamic evaluation which avoid
recomputing intermediate results. The first approach
uses Scheme `continuations' to record the state for
resuming program execution. The second implementation
uses the Unix `fork' operation to form new processes to
explore alternative branches in parallel. These
implementations are based on modifications to Lisp- and
C-based run-time systems for the Axiom Version 2
extension language (previously known as
$A^{\mbox{Hash}}$). This allows the same high-level
source code to be compared using the `re-evaluation',
the `continuation', and the `fork' implementations.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Algorithms Group Ltd., Oxford, UK",
classification = "C1140E (Game theory); C1160 (Combinatorial
mathematics); C6130 (Data handling techniques); C6150G
(Diagnostic, testing, debugging and evaluating
systems); C6150J (Operating systems)",
keywords = "algebraic computation, Dynamic evaluation; algorithms;
Axiom Version 2 extension language; C-based run-time
systems; Computer algebra; Decision points; Decision
tree; High-level source code; ISSAC; languages;
Lisp-based run-time systems; Multiple results; Program
execution; Re-evaluation; Scheme continuations; State
recording; symbolic computation; Unix fork operation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, SCHEME. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Decision theory; Symbol manipulation; System
monitoring; Trees [mathematics]; Unix",
}
@InProceedings{Bubeck:1995:DSC,
author = "T. Bubeck and M. Hiller and W. Kuechlin and W.
Rosenstiel",
title = "Distributed Symbolic Computation with {DTS}",
crossref = "Ferreira:1995:PAI",
pages = "231--248",
year = "1995",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chaffy:1995:ACP,
author = "Claudine Chaffy",
title = "The analytic continuation process: From computer
algebra to numerical analysis",
crossref = "Levelt:1995:IPI",
pages = "216--222",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p216-chaffy/",
abstract = "Presents an implementation of the Weierstrass process
of analytic continuation to compute the solution to the
holomorphic Cauchy problem: $f'(z)=H(z,f(z)),f(0)=a_0$,
along a path in the complex plane. This theoretical
process uses power series expansions of the solution at
successive points $z_k$ of this path: in practice,
these expansions have to be truncated; moreover, in the
general case, their coefficients are not exactly known.
But in fact, they can be computed from the holomorphic
function $H$. To do this, we use a computer algebra
system: it provides expressions that are evaluated at a
finite number of points $(z_k,t_k)$, where $t_k$ is an
approached value of the solution at the point $z_k$.
$t_k$ depends on
$z_0,z_1,\ldots{},z_{k-1},z_k,a_0,t_0,t_1,t_{k-1}$.
These expressions may also be transformed by using
convergence acceleration techniques in order to produce
better approximations. The method looks like the method
of Euler, with polynomials of degree greater than 1 or
even rational functions at each step, but in fact, the
two points of view essentially differ: to improve the
numerical results, instead of increasing the number of
steps, we let it be fixed and prefer to increase the
order of approximation at each step. Experiments have
been done with circular paths, especially to detect
many-valued functions.",
acknowledgement = ack-nhfb,
affiliation = "LMC, Grenoble, France",
classification = "C1110 (Algebra); C4100 (Numerical analysis); C7310
(Mathematics computing)",
keywords = "algebraic computation; algorithms; Analytic
continuation; Approximation order; Circular paths;
Complex plane; Computer algebra; Convergence
acceleration techniques; Euler method; Holomorphic
Cauchy problem; Holomorphic function; Inexactly known
coefficients; Many-valued functions, ISSAC; Numerical
analysis; Polynomials; Power series expansions;
Rational functions; symbolic computation; theory;
Truncated expansions; Weierstrass process",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Functions; Numerical analysis; Series [mathematics];
Symbol manipulation",
}
@InProceedings{Cooperman:1995:CMG,
author = "Gene Cooperman and Larry Finkelstein and Michael
Tselman",
title = "Computing with Matrix Groups using Permutation
Representations",
crossref = "Levelt:1995:IPI",
pages = "259--264",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p259-cooperman/",
abstract = "Permutation representations constructed from matrix
groups defined over finite fields often have very high
degree. New techniques are presented for performing
effective computations with the resulting permutation
group. These techniques are designed to work in an
environment in which the degree of the permutation
group is considered too large to permit the use of
standard permutation algorithms for solving problems
such as computing the order of the group and testing
simplicity. The theory has been successfully tested on
a representation of the sporadic simple group Ly. A
permutation representation was constructed for Ly of
degree 9, 606, 125 on a conjugacy class of subgroups of
order 3. Using this permutation representation and no
specific knowledge of the group, we are able to apply
our methods to construct a base of at most four points
for the resulting permutation group, compute its order
and verify simplicity. Monte Carlo algorithms for group
membership presented previously are used to improve the
performance of these algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo
methods); C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Finite fields;
Group membership, ISSAC; Matrix groups; Monte Carlo
algorithms; performance; Permutation algorithms;
Permutation representations; Sporadic simple group;
symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Representations (general and
polynomial). {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices.",
thesaurus = "Monte Carlo methods; Symbol manipulation",
}
@InProceedings{Cooperman:1995:SBP,
author = "Gene Cooperman",
title = "{STAR\slash MPI}: binding a parallel library to
interactive symbolic algebra systems",
crossref = "Levelt:1995:IPI",
pages = "126--132",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p126-cooperman/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Special-purpose algebraic systems. {\bf D.1.3}
Software, PROGRAMMING TECHNIQUES, Concurrent
Programming, Parallel programming. {\bf D.2.2}
Software, SOFTWARE ENGINEERING, Design Tools and
Techniques, Software libraries.",
}
@InProceedings{Cooperman:1995:SMB,
author = "G. Cooperman",
title = "{STAR\slash MPI}: Binding a Parallel Library to
Interactive Symbolic Algebra Systems",
crossref = "Levelt:1995:IPI",
pages = "126--132",
year = "1995",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This work is aimed at making parallel programming more
accessible to users of symbolic algebra systems and to
users of interactive languages in general. This is done
by integrating MPI (Message Passing Interface), a
portable, parallel message-passing library, with two
interactive languages: GCL (GNU Common LISP), and GAP.
The GAP system includes a general purpose language for
mathematical group theory, and LISP is the basis for
several general-purpose symbolic algebra systems. In
addition, a simple master-slave abstraction is written,
so that end-users need not learn any of the details of
the MPI function calls. This work is distinct from past
studies in that it provides the ability to
interactively create, test and modify a distributed
environment using the original interactive language and
a portable parallel library.",
abstract2 = "Many users of symbolic algebra systems have felt the
need for greater CPU power. Yet few of them have
ventured into parallel programming due to the steep
learning curve and the unfamiliar programming
environment entailed by such an effort. In an attempt
to remedy that situation, the parallel library MPI has
been integrated into both GCL (GNU Common LISP) and GAP
(a general purpose language for mathematical group
theory). These implementations are examples that extend
bindings of MPI to interactive languages. (MPI already
has bindings to the compiled languages C and FORTRAN.)
Further, this binding to an interactive language
retains the interactive environment during execution.
Further, STAR/MPI represents a blueprint for binding
MPI to other interactive languages besides GCL and GAP,
from which comes the name STAR/MPI, or */MPI. STAR/MPI
includes a simple SPMD architecture on top of this MPI
binding. An important class of sequential algorithms is
described that can be parallelized with little effort
using STAR/MPI architecture. Since GAP is
representative of systems for discrete mathematics and
LISP is the basis for several symbolic algebra systems
with strengths in nondiscrete mathematics, it is hoped
to gain broad feedback on the issues involved. Although
vendor-specific, interactive, parallel languages exist,
this appears to be the first attempt at defining a
binding of a vendor-independent, portable, parallel
library to arbitrary interactive languages.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ.",
affiliationaddress = "Boston, MA, USA",
classification = "721.1; 722.2; 722.4; 723.1; 723.5; 921.1; C6110B
(Software engineering techniques); C6110P (Parallel
programming); C6115 (Programming support); C7310
(Mathematics computing)",
conference = "Proceedings of the 1995 International Symposium on
Symbolic and Algebraic Computation",
journalabr = "Int Symp Symbol Algebraic Comput ISSAC Proc",
keywords = "Algebra; algebraic computation; Computational methods;
Computer programming; Computer programming languages;
Computer simulation; Computer software; GCL; GNU Common
LISP; Interactive computer systems; Interactive
languages; Interactive symbolic algebra systems;
Interfaces (computer); ISSAC; Mathematical group
theory; Mathematical techniques; Message passing
interface; Parallel library; Parallel processing
systems; STAR/MPI; Symbolic algebra; symbolic
computation; User interfaces",
meetingaddress = "Montreal, Can",
meetingdate = "Jul 10--12 1995",
meetingdate2 = "07/10--12/95",
thesaurus = "Parallel programming; Software libraries; Symbol
manipulation",
}
@InProceedings{Corless:1995:SVD,
author = "Robert M. Corless and Patrizia M. Gianni and Barry M.
Trager and Stephen M. Watt",
title = "The Singular Value Decomposition for Polynomial
Systems",
crossref = "Levelt:1995:IPI",
pages = "195--207",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p195-corless/",
abstract = "Introduces singular value decomposition (SVD)
algorithms for some standard polynomial computations,
in the case where the coefficients are inexact or
imperfectly known. We first give an algorithm for
computing univariate greatest common divisors (GCDs)
which gives exact results for interesting nearby
problems, and give efficient algorithms for computing
precisely how nearby. We generalize this to
multivariate GCD computation. Next, we adapt Lazard's
(1981) 21-resultant algorithm for the solution of
overdetermined systems of polynomial equations to the
inexact-coefficient case. We also briefly discuss an
application of the modified Lazard's method to the
location of singular points on approximately known
projections of algebraic curves.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1110 (Algebra)",
keywords = "21-Resultant algorithm; algebraic computation;
Algebraic curves, ISSAC; algorithms; Approximately
known projections; Imperfectly known coefficients;
Inexact coefficients; Multivariate greatest common
divisors; Nearby problems; Overdetermined systems;
Polynomial equation systems; Singular point location;
Singular value decomposition; symbolic computation;
theory; Univariate greatest common divisors;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues and
eigenvectors (direct and iterative methods). {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Equations; Polynomials; Singular value decomposition",
}
@InProceedings{Covic:1995:SFC,
author = "V. Covic and S. Markovic",
title = "Symbolic Form Computation of the Complete Dynamics of
Robotic Systems with the Closed Chains Structure",
crossref = "Aityan:1995:PNP",
pages = "125--128",
year = "1995",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Daberkow:1995:CRE,
author = "M. Daberkow and M. Pohst",
title = "Computations with relative extensions of number fields
with an application to the construction of {Hilbert}
class fields",
crossref = "Levelt:1995:IPI",
pages = "68--76",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p68-daberkow/",
abstract = "We present new and improved algorithms for
computations with relative extensions of algebraic
number fields. Especially, the tasks of relative normal
forms, relative bases, detection of subfields, and
embedding of these subfields are discussed. The new
methods are then used to compute Hilbert class fields
of totally real cubic and quartic fields for the first
time.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math., Tech. Univ. Berlin, Germany",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C4240
(Programming and algorithm theory); C7310 (Mathematics
computing)",
keywords = "algebraic computation; Algorithms; algorithms;
Computations; Embedded subfields; Hilbert class field
construction; languages; Relative algebraic number
field extensions; Relative bases; Relative normal
forms; Subfield detection; symbolic computation;
Totally real cubic fields; Totally real quartic fields,
ISSAC",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Algorithm theory; Hilbert spaces; Number theory;
Polynomials; Symbol manipulation",
}
@InProceedings{Diaz:1995:CGC,
author = "Angel D{\'\i}az and Erich Kaltofen",
title = "On Computing Greatest Common Divisors with Polynomials
Given By Black Boxes for Their Evaluations",
crossref = "Levelt:1995:IPI",
pages = "232--239",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p232-diaz/",
abstract = "The black box representation of a multivariate
polynomial is a function that takes as input a value
for each variable and then produces the value of the
polynomial. We revisit the problem of computing the
greatest common divisor (GCD) in black box format of
several multivariate polynomials that themselves are
given by black boxes. To this end an improved version
of the algorithm sketched by E. Kaltofen and B. Trager
(1990) is described. Also the full analysis of the
improved algorithm is given. Our algorithm constructs
in random polynomial-time a procedure that will
evaluate a fixed associate of the GCD at an arbitrary
point (supplied as its input) in polynomial time. The
randomization of the black box construction is of the
Monte-Carlo kind, that is with controllably high
probability the procedures evaluating the GCD are
correct at all input points. Finally, a Maple prototype
implementation as well as our plans for developing a
subsystem for manipulating multivariate polynomials and
rational functions in black box representation are
presented.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
keywords = "algebraic computation; algorithms; Black box format;
Black boxes; Greatest common divisor; Greatest common
divisors; languages; Maple prototype implementation;
Monte-Carlo method; Multivariate polynomials;
Polynomials; Random polynomial-time; Randomization;
Rational functions, ISSAC; symbolic computation;
theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Representations (general and
polynomial). {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Doffou:1995:SCD,
author = "M. J. Doffou and R. L. Grossman",
title = "The Symbolic Computation of Differential Invariants of
Polynomial Vector Field Systems Using Trees",
crossref = "Levelt:1995:IPI",
pages = "26--31",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p26-doffou/",
abstract = "Let $K$ denote a field of characteristic 0, and let
$V=K^N$ denote the vector space over $K$ of dimension
$N$. Let $R$ denote the $K$-algebra of polynomials over
$V:r=\sum_{j1=1}^Na_{j1}x^{j1}+\sum_{j1,j2=1}^N{}a_{j1,j2}x^{j1}x^{j2}+\ldots{},a_{j1},a_{j1,j2},\ldots{}$
in $K$. Consider the algebra $D$ of derivations of $R$.
Given a derivation $E$ in $D$, we are interested in
symbolic algorithms for computing its invariants. To be
more precise, the action of $GL(V)$ on $V$ induces an
action on the space of coefficients $C$ of the
derivations. A polynomial over $C$ is called invariant
in case it is invariant under this action. Our approach
to computing differential invariants is to define an
algebraic structure on the space of rooted, labeled
trees $T$ and introduce an algebra homomorphism from
$C$ to $T$. Differential invariants are naturally
expressed and easily computed in terms of a few basic
operations on the space of trees. Our main result
provides a simple and direct combinatorial means of
computing differential invariants. The algorithm has
been implemented in C++. We illustrate these ideas by
computing all the differential invariants of vector
field systems in the plane $V=K^2$.",
acknowledgement = ack-nhfb,
affiliation = "Lab. for Adv. Comput., Illinois Univ., Chicago, IL,
USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics computing)",
keywords = "Algebra; algebraic computation; Algebraic structure;
algorithms; C++; Differential invariants;
experimentation; languages; Polynomial vector field
systems; Rooted labeled trees; Symbolic algorithms;
Symbolic computation; symbolic computation; theory;
Trees; Vector field systems, ISSAC; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Polynomials; Symbol manipulation; Trees
[mathematics]",
}
@InProceedings{Einwohner:1995:STI,
author = "T. H. Einwohner and Richard J. Fateman",
title = "Searching techniques for integral tables",
crossref = "Levelt:1995:IPI",
pages = "133--139",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p133-einwohner/",
abstract = "We describe the design of data structures and a
computer program for storing a table of symbolic
indefinite or definite integrals and retrieving
user-requested integrals on demand. Typical times are
so short that a preliminary look-up attempt prior to
any algorithmic integration approach seems justified.
In one such test for a table with around 700 entries,
matches were found requiring an average of 2.8
milliseconds per request, on a Hewlett Packard 9000/712
workstation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electr. Eng. and Comput. Sci., California
Univ., Berkeley, CA, USA",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; Algorithmic integration, ISSAC;
algorithms; Data structures; design; Integral tables;
performance; symbolic computation; Symbolic indefinite
integrals",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Pattern matching. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Sorting and searching.",
thesaurus = "Data structures; Integration; Symbol manipulation;
Table lookup",
}
@InProceedings{Estevez:1995:CAE,
author = "L. W. Estevez and N. D. Kehtarnavaz",
title = "Computer assisted enhancement of mammograms for
detection of microcalcifications",
crossref = "IEEE:1995:PEI",
pages = "16--23",
year = "1995",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The presence of microcalcifications in mammograms
provides an early indication of possible breast cancer.
Because of the difficulty associated with visual
identification of microcalcifications and the large
volume of mammograms read per day, the radiologist
stands a good chance of missing some small
microcalcification clusters. Although several
computer-assisted programs have been developed for the
automatic detection of microcalcifications in
mammograms, they often generate too many false
positives. This paper presents a computer-assisted
enhancement technique which is capable of coping with
false positive samples. More specifically, a
general-purpose clustering algorithm, called Issac
(Interactive Selective and Adaptive Clustering), has
been developed which achieves a compromise between
sensitivity and generalization attributes of existing
clustering algorithms. Issac comprises two parts: (i)
selective clustering and (ii) interactive adaptation.
The first part reduces the number of false positives by
identifying sensitive sample domains in the feature
space. The second part allows the radiologist to
improve results by interactively identifying additional
false positive or true negative samples. The clinical
evaluation of the results has indicated that the
developed enhancement technique has the potential of
being an effective mechanism to bring
microcalcification areas to the attention of the
radiologist during a routine reading session of
mammograms. Further clinical evaluation is being
carried out for the purpose of full-scale clinical
deployment.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electr. Eng., Texas A and M Univ., College
Station, TX, USA",
classification = "B6140C (Optical information, image and video signal
processing); B7510B (Radiation and radioactivity
applications in biomedicine); C5260B (Computer vision
and image processing techniques); C7330 (Biology and
medical computing)",
keywords = "Breast cancer; Clinical evaluation; Computer-assisted
mammogram enhancement; False positive samples;
General-purpose clustering algorithm; Generalization;
Interactive adaptation; Interactive Selective and
Adaptive Clustering; Issac; Microcalcification
detection; Radiology; Routine reading session;
Selective clustering; Sensitive sample domains;
Sensitivity; Visual identification",
thesaurus = "Generalisation [artificial intelligence]; Interactive
systems; Medical image processing; Object detection;
Radiology",
}
@InProceedings{Giesbrecht:1995:FCS,
author = "Mark Giesbrecht",
title = "Fast Computation of the {Smith Normal Form} of an
Integer Matrix",
crossref = "Levelt:1995:IPI",
pages = "110--118",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p110-giesbrecht/",
abstract = "We present two new probabilistic algorithms for
computing the Smith normal form of an $A$ in $(Z^m*n)$.
The first requires an expected number of
$O(m^2n.M(m\log{}//A//))$ bit operations (ignoring
logarithmic factors) and is of the Las Vegas
type/vol/ahml/issac95/eind/Giesbrecht; that is, it
never produces an incorrect answer. Here
$//A//=max_{ij}/\bmod{}A_{ij} mod$ and $h/l(l)$ bit
operations are sufficient to multiply two I-bit
integers ($M(1) 12$ using standard arithmetic). This
improves on the previously best known (deterministic)
algorithm of Hafner and McCurley, which requires about
$O(m^3n \log{}//A//. M(m \log{}//A//))$ bit operations.
We also present an even faster, more space efficient
algorithm which requires an expected number of
$O((m^3n\log{}//A//+m^3\log^2//A//).\log(1/\epsilon))$
bit operations using standard integer arithmetic. This
algorithm is of the Monte Carlo type: it returns the
correct result with probability at least $1- \epsilon$
for a user specified tolerance $\epsilon >0$. This
algorithm also requires only $O(nm \log{}//A//)$ bits
of storage, versus $O(nm^2 \log{}//A//)$ bits required
by other known algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
Canada",
classification = "B0290H (Linear algebra); C4140 (Linear algebra);
C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Integer matrix;
Monte Carlo type, ISSAC; Smith normal form; symbolic
computation; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.3}
Mathematics of Computing, PROBABILITY AND STATISTICS,
Probabilistic algorithms (including Monte Carlo).",
thesaurus = "Matrix algebra; Symbol manipulation",
}
@InProceedings{Gonzalez-Vega:1995:IPC,
author = "L. Gonz{\'a}lez-Vega and G. Trujillo",
title = "Implicitization of parametric curves and surfaces by
using symmetric functions",
crossref = "Levelt:1995:IPI",
pages = "180--186",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p180-gonzalez-vega/",
abstract = "This paper presents a new algorithm to compute the
implicit equation of a parametric plane curve and
several classes of parametric surfaces in the
three-dimensional Euclidean space. This algorithm does
not require the computation of any symbolic determinant
or Gr{\"o}bner basis, these tools being replaced by the
computation of some symmetric functions, in particular
the Newton sums on the solution set of a very precise
zero-dimensional ideal.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Math., Cantabria Univ., Santander, Spain",
classification = "C1110 (Algebra); C7310 (Mathematics computing)",
keywords = "3D Euclidean space; algebraic computation; algorithms;
Implicit equation computation; Implicitization; ISSAC;
Newton sums; Parametric plane curve; Parametric
surfaces; Precise zero-dimensional ideal; Solution set;
symbolic computation; Symmetric functions; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Equations; Functions; Symbol manipulation",
}
@InProceedings{Grigoriev:1995:ACS,
author = "Dima Yu. Grigoriev and {Lakshman Y. N.}",
title = "Algorithms for Computing Sparse Shifts for
Multivariate Polynomials",
crossref = "Levelt:1995:IPI",
pages = "96--103",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p96-grigoriev/",
abstract = "We build on the results of two earlier papers,
(Grigoriev-Karpinski, 1993; Lakshman-Saunders, 1994),
and we make use of techniques used to deal with
zero-dimensional Gr{\"o}bner bases. The main
contributions are: deriving sufficient conditions for
uniqueness of sparse shifts for multivariate
polynomials; computing tight bounds on the degree of
the polynomial being interpolated in terms of the
sparsity bound and a bound on the size of the
coefficients of the polynomial in the standard
representation; two new efficient algorithms for
computing sparse shifts for a multivariate
polynomial.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Pennsylvania State Univ.,
University Park, PA, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4240C
(Computational complexity)",
keywords = "Sparse shift computation; Multivariate polynomials;
Algorithms; Zero-dimensional Gr{\"o}bner bases;
Interpolation; Sparsity bound; Polynomial coefficient
size bounds, ISSAC; symbolic computation; algebraic
computation; algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse,
structured, and very large systems (direct and
iterative methods). {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Computational complexity; Polynomial matrices; Sparse
matrices",
}
@InProceedings{Kapur:1995:CVM,
author = "Deepak Kapur and Tushar Saxena",
title = "Comparison of Various Multivariate Resultant
Formulations",
crossref = "Levelt:1995:IPI",
pages = "187--194",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p187-kapur/",
abstract = "Three of the most important resultant formulations are
the Macaulay, Dixon and sparse resultant formulations.
For most polynomial systems, however, the matrices
constructed in these formulations become singular and
the projection operator vanishes identically. In such
cases, perturbation techniques for the Macaulay
formulation, such as generalized characteristic
polynomial (GCP) and a method based on rank submatrix
computation (RSC), applicable to all three
formulations, can be used, giving four methods
(Macaulay/GCP, Macaulay/RSC, Dixon/RSC and Sparse/RSC)
for computing nontrivial projection operators. In this
paper, these four methods are compared. It is shown
that the Dixon matrix is (by a factor up to $O(e^n)$
for a certain class) smaller than the sparse resultant
matrix, which is (by a factor up to $O(e^n)$ for a
certain class) smaller than the Macaulay matrix.
Empirical results confirm that Dixon/RSC is the most
efficient, followed by Sparse/RSC, then Macaulay/RSC,
and finally Macaulay/GCP, which is found to be almost
impractical. All four methods are found to generate
extraneous factors in the projection operator.
Efficient heuristics for interpolation, used to expand
the resultant matrices, are also discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4240C
(Computational complexity)",
keywords = "algebraic computation; algorithms; Dixon formulation;
Efficiency; Extraneous factors; Generalized
characteristic polynomial; Interpolation heuristics,
ISSAC; Macaulay formulation; Multivariate resultant
formulations; Perturbation techniques; Polynomial
systems; Projection operators; Rank submatrix
computation; Singular matrices; Sparse formulation;
symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Computational complexity; Interpolation; Matrix
algebra; Perturbation techniques; Polynomials; Sparse
matrices",
}
@InProceedings{Krishnan:1995:NAE,
author = "Shankar Krishnan and Dinesh Manocha",
title = "Numeric-symbolic algorithms for evaluating
one-dimensional algebraic sets",
crossref = "Levelt:1995:IPI",
pages = "59--67",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p59-krishnan/",
abstract = "We present efficient algorithms based on a combination
of numeric and symbolic techniques for evaluating
one-dimensional algebraic sets in a subset of the real
domain. Given a description of a one-dimensional
algebraic set, we compute its projection using
resultants. We represent the resulting plane curve as a
singular set of a matrix polynomial as opposed to roots
of a bivariate polynomial. Given the matrix
formulation, we make use of algorithms from numerical
linear algebra to compute start points on all the
components, partition the domain such that each
resulting region contains only one component and
evaluate it accurately using marching methods. We also
present techniques to handle singularities for
well-conditioned inputs. The resulting algorithm is
iterative and its complexity is output sensitive. It
has been implemented in floating-point arithmetic and
we highlight its performance in the context of
computing intersection of high-degree algebraic
surfaces.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., North Carolina Univ., Chapel
Hill, NC, USA",
classification = "B0290H (Linear algebra); C4140 (Linear algebra);
C4240C (Computational complexity); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Bivariate
polynomial; Complexity; Floating-point arithmetic;
High-degree algebraic surfaces, ISSAC; Marching
methods; Matrix polynomial; Numeric-symbolic
algorithms; Numerical linear algebra; One-dimensional
algebraic sets; Plane curve; Real domain; symbolic
computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Eigenvalues and eigenvectors (direct
and iterative methods).",
thesaurus = "Computational complexity; Linear algebra; Symbol
manipulation",
}
@InProceedings{Liao:1995:EHP,
author = "Hsin-Chao Liao and Richard J. Fateman",
title = "Evaluation of the heuristic polynomial {GCD}",
crossref = "Levelt:1995:IPI",
pages = "240--247",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p240-liao/",
abstract = "The heuristic polynomial GCD procedure (GCDHEU) is
used by the Maple computer algebra system, but no
other. Because Maple has an especially efficient kernel
that provides fast integer arithmetic, but a relatively
slower interpreter for non-kernel code, the GCDHEU
routine is especially effective in that it moves much
of the computation into `bignum' arithmetic and hence
executes primarily in the kernel. We speculated that in
other computer algebra systems an implementation of
GCDHEU would not be advantageous. In particular, if all
the system code is compiled to run at `full speed' in a
(presumably more bulky) kernel that is entirely written
in C or compiled Lisp, then there would seem to be no
point in recasting the polynomial GCD problem into a
bignum GCD problem. Manipulating polynomials that are
vectors of coefficients would seem to be equivalent
computationally to manipulating vectors of big digits.
Yet our evidence suggests that one can take advantage
of the GCDHEU in a Lisp system as well. Given a good
implementation of bignums, for most small problems and
many large ones, a substantial speedup can be obtained
by the appropriate choice of GCD algorithm, including
often enough, the GCDHEU approach. Another major winner
seem to be the subresultant polynomial remainder
sequence algorithm. Because more sophisticated sparse
algorithms are relatively slow on small problems and
only occasionally emerge as superior (on larger
problems) it seems the choice of a fast GCD algorithm
is tricky.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C6140D (High level
languages); C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; C language;
Compiled Lisp; Computer algebra systems; Heuristic
polynomial GCD; Integer arithmetic; ISSAC; languages;
Maple computer algebra system; Sparse algorithms;
symbolic computation; System code",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Number-theoretic computations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple.",
thesaurus = "C language; LISP; Polynomials; Symbol manipulation",
}
@InProceedings{Lisle:1995:ADS,
author = "I. G. Lisle and G. J. Reid and A. Boulton",
title = "Algorithmic determination of structure of infinite
{Lie} pseudogroups of symmetries of {PDEs}",
crossref = "Levelt:1995:IPI",
pages = "1--6",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p1-lisle/",
abstract = "We describe a method which uses a finite number of
differentiations and linear operations to determine the
Cartan structure coefficients of a structurally
transitive Lie pseudogroup from its infinitesimal
defining equations. If the defining system is of first
order and the pseudogroup has no scalar invariants, the
structure coefficients can be simply extracted from the
coefficients of the infinitesimal system. We give an
algorithm which reduces the higher order case to the
first order case. The reduction process uses only
differentiation and linear eliminations, for which
several well-known algorithms are available. Our method
makes feasible the calculation of the Cartan structure
of infinite Lie pseudogroups of symmetries of
differential equations. Examples including the KP
equation and Liouville's equation are given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., British Columbia Univ., Vancouver, BC,
Canada",
classification = "C4160 (Numerical integration and differentiation);
C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Cartan structure
coefficients; Differentiation; KP equation; languages;
Lie pseudogroups; Linear eliminations; Liouville's
equation, ISSAC; PDEs; Reduction; Structurally
transitive Lie pseudogroup; symbolic computation;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Differentiation; Lie groups; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Majewski:1995:SEG,
author = "Bohdan S. Majewski and George Havas",
title = "A solution to the extended gcd problem",
crossref = "Levelt:1995:IPI",
pages = "248--253",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p248-majewski/",
abstract = "An improved method for expressing the greatest common
divisor of $n$ numbers as an integer linear combination
of the numbers is presented and analyzed, both
theoretically and practically. The performance of this
algorithm is compared with other methods, indicating
substantial improvements in the size of the solution.
The results are given in the light of the current
knowledge about the complexity of extended gcd
computations. Thus, finding optimal sets of multipliers
has been proved to be an NP-complete problem. We
present a relatively efficient approximation algorithm
with excellent performance. This problem is interesting
in its own right. Furthermore, it has important
applications, for example in computing canonical normal
forms of integer matrices.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Queensland Univ., Brisbane,
Qld., Australia",
classification = "C1160 (Combinatorial mathematics); C4240C
(Computational complexity); C4260 (Computational
geometry)",
keywords = "algebraic computation; algorithms; Canonical normal
forms; Complexity; Extended gcd problem; Greatest
common divisor; Integer linear combination; Integer
matrices, ISSAC; NP-complete problem; performance;
symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations.",
thesaurus = "Computational complexity; Computational geometry",
}
@InProceedings{Marinari:1995:GDM,
author = "Maria Grazia Marinari and Teo Mora and Hans Michael
M{\"o}ller",
title = "{Gr{\"o}bner} Duality and Multiplicities in Polynomial
System Solving",
crossref = "Levelt:1995:IPI",
pages = "167--179",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p167-marinari/",
abstract = "This paper deals with the description of the solutions
of zero-dimensional systems of polynomial equations.
Based on different models for describing solutions, we
consider suitable representations of a multiple root,
or more precisely suitable descriptions of the primary
component of the system at a root. We analyse the
complexity of finding the representations. We also
discuss the current approach to the representation of
real roots.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Genoa Univ., Italy",
classification = "C1110 (Algebra); C4240C (Computational complexity)",
keywords = "Gr{\"o}bner duality; Multiplicities; Polynomial system
solving; Zero-dimensional systems; Polynomial
equations; Solution description models; Multiple root;
Primary component; Complexity; Real roots, ISSAC;
symbolic computation; algebraic computation;
algorithms; theory; verification",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Representations (general and
polynomial). {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational complexity; Duality [mathematics];
Equations; Polynomials",
}
@InProceedings{Marje:1995:NLA,
author = "Prabhav Marje",
title = "A nearly linear algorithm for {Sylow} subgroups in
small-base groups",
crossref = "Levelt:1995:IPI",
pages = "270--277",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p270-marje/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Minkwitz:1995:COI,
author = "Torsten Minkwitz",
title = "On the Computation of Ordinary Irreducible
Representations of Finite Groups",
crossref = "Levelt:1995:IPI",
pages = "278--284",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p278-minkwitz/",
abstract = "This article describes a method to compute ordinary
matrix representations afforded by all the irreducible
characters of a finite group. It can be shown to work
for any solvable group and a number of other classes of
groups. However, it is a method to construct
irreducible representations $P$ of any finite group
$G$, provided that $G$ contains a subgroup $H$ with an
irreducible character that is contained with
multiplicity one in the character of the restriction of
$p$ to $H$. The improvements in comparison with known
methods are algorithmic rather than in mathematical
principle.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "B0290H (Linear algebra); C4140 (Linear algebra);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Finite groups;
Irreducible characters; languages; Mathematical
principle, ISSAC; Ordinary irreducible representations;
Ordinary matrix representations; performance; Solvable
group; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Representations (general and
polynomial). {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices.",
thesaurus = "Matrix algebra; Symbol manipulation",
}
@InProceedings{Morje:1995:NLA,
author = "P. Morje",
title = "A nearly linear algorithm for {Sylow} subgroups in
small-base groups",
crossref = "Levelt:1995:IPI",
pages = "270--277",
year = "1995",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $G$ be a permutation group acting on a finite set
$\Omega$ and assume that no composition factor of $G$
is an exceptional group of Lie type. Let $p$ be a
prime. New Monte Carlo algorithms are presented for the
construction and conjugation of Sylow $p$-subgroups of
G. The running time of the algorithms is
$O(sn\log^c\bmod{}G\bmod{})$ for some explicitly
computable constant $c$ where $n$ is the size of
$\Omega$ and $s$ is the number of generators for $G$.
This running time is nearly linear for small-base
groups. The method employs a reduction to the case of
permutation representations of finite simple groups,
where we invoke the classification of finite simple
groups and design algorithms for the alternating and
classical families of simple groups.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Ohio State Univ., Columbus, OH, USA",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; Finite simple groups; Lie type;
Monte Carlo algorithms; Nearly linear algorithm;
Permutation group; Permutation representations; Simple
groups, ISSAC; Small-base groups; Sylow subgroups;
symbolic computation",
thesaurus = "Symbol manipulation",
}
@InProceedings{Nam:1995:HSM,
author = "Tr{\^{\`a}}n Quo{\^{\'a}}c Nam",
title = "A Hybrid Symbolic-Numerical Method for Tracing
Surface-to-Surface Intersections",
crossref = "Levelt:1995:IPI",
pages = "51--58",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p51-nam/",
abstract = "We present a hybrid symbolic-numerical algorithm for
approximation and representation of surface-to-surface
intersections-the fundamental and difficult problem in
computer aided geometric design (CAGD) and solid
modelling. Reliability and efficiency of intersection
algorithms are two basic prerequisites for their
effective use in any practical system. Typically, a
numerical algorithm is efficient, but it is not fully
robust and may fail in certain cases; On the other
hand, algorithms based on exact arithmetic are fully
robust and accurate, but are normally slow and require
a lot of memory space. Perhaps the goals of efficiency
and reliability cannot be met simultaneously without
some compromises. In this paper, we negotiate those
compromises judiciously. The key step of the algorithm
is based upon a new technique of the author, namely the
`extended Newton method' for determining the roots of
an arbitrary system of equations iteratively, where the
equations can be nonlinear algebraic or
transcendental.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4260
(Computational geometry); C6130B (Graphics
techniques)",
keywords = "algebraic computation; algorithms; Computer aided
geometric design; experimentation; Extended Newton
method, ISSAC; Hybrid symbolic-numerical method;
Intersection algorithms; Memory space; reliability;
Solid modelling; Surface-to-surface intersections
tracing; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf J.6} Computer Applications,
COMPUTER-AIDED ENGINEERING, Computer-aided design
(CAD).",
thesaurus = "Computational geometry; Engineering graphics;
Polynomials; Solid modelling",
}
@InProceedings{Quere:1995:ARL,
author = "M. P. Qu{\'e}r{\'e} and G. Villard",
title = "An algorithm for the reduction of linear {DAE}",
crossref = "Levelt:1995:IPI",
pages = "223--231",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p223-quere/",
abstract = "Studies linear differential algebraic equations (DAE)
with time-varying coefficients. Such equations,
$B(t)x(t)=A(t)x(t)+f(t)$, have been intensively studied
from a numerical point of view. Canonical forms have
been proposed to find conditions under which the
equation admits a solution, to find the set of
consistent initial conditions and to determine
conditions under which there is a unique solution.
However, since the situation where the system admits
infinitely many solutions for one initial value is not
really tractable in a numerical framework, few
algorithms may be found in this latter case. Among
them, we find the method of P. Kunkel and V. Mehrmann
(1992), who proposed a new set of local characterizing
quantities for the treatment of the system. This leads
to a generalization of the global index. Nevertheless,
these latter characterizing quantities impose too
restrictive conditions on the input equations. We
propose new definitions for them that lead to a new
algorithm which puts the initial system into a reduced
form without making any assumption on it. This allows
us to propose a new generalization of the global index
and a definition for the singularities of the initial
system. The questions of existence and uniqueness of
solutions are solved in all intervals which do not
contain a singularity. Finally, since from a practical
point of view the general case of analytic functions is
difficult to handle, we focus on the polynomial case.
We propose an effective algorithm that has been
implemented and report some experiments.",
acknowledgement = ack-nhfb,
affiliation = "LITP-IBP, Paris VI Univ., France",
classification = "C1110 (Algebra); C1120 (Mathematical analysis);
C4140 (Linear algebra); C4170 (Differential equations);
C7310 (Mathematics computing)",
keywords = "algebraic computation, Linear differential algebraic
equations; algorithms; Analytic functions; Canonical
forms; Consistent initial conditions; Equation solution
conditions; Global index generalization; Infinitely
many solutions; Initial system singularities; ISSAC;
Linear DAE reduction algorithm; Local characterizing
quantities; Numerical framework; Polynomial; Solution
existence; Solution uniqueness; symbolic computation;
theory; Time-varying coefficients; Unique solution;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Differential equations; Initial value problems; Linear
algebra; Symbol manipulation",
}
@InProceedings{Rakoczi:1995:FRN,
author = "Ferenc R{\'a}k{\'o}czi",
title = "Fast Recognition of the Nilpotency of Permutation
Groups",
crossref = "Levelt:1995:IPI",
pages = "265--269",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p265-rakoczi/",
abstract = "Let $G$ be a subgroup of the symmetric group on $n$
points, given by a set of generators, $S$. We describe
algorithms that decide whether or not $G$ is nilpotent,
and whether or not $G$ is a $p$-group for some prime
$p$. The algorithms utilize the imprimitivity structure
of such groups. The running time of the algorithms is
$O(\log{}n \alpha (n, 4\bmod{}S\bmod{}n))$, where
$\alpha(x,y)$ denotes the time required for $x$ Union
and $y$ Find operations in a Union-Find data structure,
the asymptotically best implementation of which runs in
time $O(y \log* (x+y))$. Standard methods for answering
the question require the computation of a point
stabilizer series, that takes
$O(\bmod{}S\bmod{}n^2+n^5)$ time. Implementation of the
algorithms in GAP shows that these algorithms run
faster than the built-in ones, except for very small
cases. For the nilpotence test this is the case even if
we just measure the time after the computation of the
point stabilizer series.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Oregon Univ., Eugene,
OR, USA",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Asymptotically best
implementation; Imprimitivity structure; Nilpotency of
permutation groups; P-group; Point stabilizer series,
ISSAC; Set of generators; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Symbol manipulation",
}
@InProceedings{Richardson:1995:SMR,
author = "Daniel Richardson",
title = "A simplified method of recognizing zero among
elementary constants",
crossref = "Levelt:1995:IPI",
pages = "104--109",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p104-richardson/",
abstract = "In ISSAC '94, a method was given for deciding whether
or not an elementary constant, given as a polynomial
image of a solution of a system of exponential
polynomial equations, represents the famous object
zero. In this article the technique is considerably
simplified and-speeded up. The main improvement has
been to integrate the numerical and symbolic
computations in such a way that unnecessary branches of
the symbolic computation are avoided.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Bath Univ., UK",
classification = "C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Elementary
constants; Exponential polynomial equations; symbolic
computation; Symbolic computations, ISSAC; theory;
verification; Zero",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf G.1.2}
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation.",
thesaurus = "Symbol manipulation",
}
@InProceedings{Schwartz:1995:SOO,
author = "F. Schwartz",
title = "Symmetries of $2^{\mbox{nd}}$ and $3^{\mbox{rd}}$
order {ODEs}",
crossref = "Levelt:1995:IPI",
pages = "16--25",
year = "1995",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Starting from Lie's classification of point groups of
the plane, all possible symmetry groups of
$2^{\mbox{nd}}$ and $3^{\mbox{rd}}$ order ordinary
differential equations are determined. It turns out
that for a $3^{\mbox{rd}}$ order equation a group of
any size within Lie's bound $r=7$ may occur as opposed
to $2^{\mbox{nd}}$ order equations. In order to
determine the group of a given equation, the Janet
bases for the determining system are constructed and
studied in detail for two-parameter groups. A theorem
is proved which allows one to identify the type of a
two-parameter group from the coefficients of the Janet
basis for its determining system. This is an important
step for finding explicit solutions of the original
differential equation.",
acknowledgement = ack-nhfb,
affiliation = "Inst. SCAI, GMD, Sankt Augustin, Germany",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
keywords = "algebraic computation; ISSAC; Janet bases; Lie's
classification; Ordinary differential equations; Point
groups; symbolic computation; Symmetry groups;
Two-parameter group; Two-parameter groups",
thesaurus = "Differential equations",
xxauthor = "F. Schwarz",
}
@InProceedings{Schwarz:1995:SSS,
author = "Fritz Schwarz",
title = "Symmetries of {$2^{\em nd}$} and $3^{\rm rd}$ order
{ODE}'s",
crossref = "Levelt:1995:IPI",
pages = "16--25",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p16-schwarz/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.8} Mathematics of Computing,
NUMERICAL ANALYSIS, Partial Differential Equations.
{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Semmler:1995:NUH,
author = "Klaus-Dieter Semmler and Mika Sepp{\"a}l{\"a}",
title = "Numerical uniformization of hyperelliptic curves",
crossref = "Levelt:1995:IPI",
pages = "208--215",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p208-semmler/",
abstract = "We develop algorithms which allow us to uniformize
numerically any given real hyperelliptic plane M-curve.
Starting from an equation for such a curve, we get
floating point approximations for the generators of a
discontinuous group of Mobius transformations
uniformizing the given M-curve. Furthermore, we show
how to compute an equation for a Riemann surface given
by such a group. For real hyperelliptic plane curves
having maximal number of real components, this
construction gives a complete answer to the problem of
numerical uniformization. Some of the algorithms
described have already been coded. The programs are to
be made publicly available through the WWW home page of
the HCM network `Computational conformal geometry'.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Math., Ecole Polytech. Federale de Lausanne,
Switzerland",
classification = "B0290F (Interpolation and function approximation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4170 (Differential
equations); C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Computational
conformal geometry, ISSAC; Discontinuous group;
Floating point approximations; Generators; HCM network
home page; Mobius transformations; Numerical
uniformization; Publicly available programs; Real
hyperelliptic plane M-curves; Riemann surface equation;
symbolic computation; theory; World Wide Web",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Number-theoretic
computations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Elliptic equations; Floating point arithmetic;
Function approximation; Mathematics computing; Public
domain software",
xxauthor = "Klaus-Dieter Semmler and Mika Se{\"a}l{\"a}",
}
@InProceedings{Soiffer:1995:MTM,
author = "Neil Soiffer",
title = "Mathematical typesetting in {Mathematica}",
crossref = "Levelt:1995:IPI",
pages = "140--149",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "Compendex database; http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p140-soiffer/",
abstract = "Mathematica's user interface has been significantly
enhanced in Mathematica Version 3. This paper focuses
on the new mathematical typesetting capabilities in the
user interface, with the aim of discussing not only
what they are, but also the rationale behind the design
and also how the capabilities can be used.",
acknowledgement = ack-nhfb,
affiliation = "Wolfram Res. Inc., Champaign, IL, USA",
classification = "722.2; 723.1.1; 723.2; 921; 921.1; C6180 (User
interfaces); C7108 (Desktop publishing); C7310
(Mathematics computing)",
conference = "Proceedings of the 1995 International Symposium on
Symbolic and Algebraic Computation",
journalabr = "Int Symp Symbol Algebraic Comput ISSAC Proc",
keywords = "Algebra; algebraic computation; algorithms; Computer
programming languages; Data structures; design; Design
rationale, ISSAC; Display devices; Encoding (symbols);
languages; Mathematica Version 3; Mathematical
techniques; Mathematical typesetting; String based
systems; symbolic computation; Syntax; Tree based
systems; User interface enhancement; User interfaces",
meetingaddress = "Montreal, Can",
meetingdate = "Jul 10--12 1995",
meetingdate2 = "07/10--12/95",
subject = "{\bf G.4} Mathematics of Computing, MATHEMATICAL
SOFTWARE, Mathematica. {\bf I.7.2} Computing
Methodologies, DOCUMENT AND TEXT PROCESSING, Document
Preparation, Photocomposition/typesetting. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf H.5.2}
Information Systems, INFORMATION INTERFACES AND
PRESENTATION, User Interfaces, Interaction styles.",
thesaurus = "Computer controlled typesetting; Mathematics
computing; Software packages; Symbol manipulation; User
interfaces",
}
@InProceedings{Sorenson:1995:ALE,
author = "Jonathan Sorenson",
title = "An analysis of {Lehmer}'s {Euclidean} {GCD}
algorithm",
crossref = "Levelt:1995:IPI",
pages = "254--258",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p254-sorenson/",
abstract = "Let $u$ and $v$ be positive integers. We show that a
slightly modified version of D. H. Lehmer's greatest
common divisor algorithm will compute $\gcd(u, v)$
(with $u>v$) using at most
$O((\log{}u\log{}v)/k+k\log{}v+\log{}u+k^2)$ bit
operations and $O(\log{}u+k2^{2k})$ space, where $k$ is
the number of bits in the multiprecision base of the
algorithm. This is faster than Euclid's algorithm by a
factor that is roughly proportional to $k$. Letting $n$
be the number of bits in $u$ and $v$, and setting
$k=((\log{}n)/4)$, we obtain a subquadratic running
time of $O(n^2/\log{}n)$ in linear space.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Butler Univ.,
Indianapolis, IN, USA",
classification = "C1160 (Combinatorial mathematics); C4260
(Computational geometry)",
keywords = "algebraic computation, Lehmer's Euclidean GCD
algorithm; algorithms; Greatest common divisor
algorithm; ISSAC; Linear space; Multiprecision base;
Positive integers; Subquadratic running time; symbolic
computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Number-theoretic
computations.",
thesaurus = "Computational geometry",
}
@InProceedings{Storjohann:1995:PRP,
author = "Arne Storjohann and George Labahn",
title = "Preconditioning of Rectangular Polynomial Matrices for
Efficient {Hermite Normal Form} Computation",
crossref = "Levelt:1995:IPI",
pages = "119--125",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p119-storjohann/",
abstract = "We present a Las Vegas probabalistic algorithm for
reducing the computation of Hermite normal forms of
rectangular polynomial matrices. In particular, the
problem of computing the Hermite normal form of a
rectangular m*n matrix (with $m>n$) reduces to that of
computing the Hermite normal form of a matrix of size
$(n+1)*n$ having entries of similar coefficient size
and degree. The main cost of the reduction is the same
as the cost of fraction-free Gaussian elimination of an
$m*n$ polynomial matrix. As an application, the
reduction allows for the efficient computation of
one-sided GCDs of two matrix polynomials along with the
solution of the matrix diophantine equation associated
to such a GCD.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C4140 (Linear algebra); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; Hermite normal form
computation; Las Vegas probabalistic algorithm; Matrix
diophantine equation, ISSAC; Matrix polynomials;
Polynomial matrices; Rectangular polynomial matrices;
symbolic computation; theory; verification",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
G.3} Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo). {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Matrix algebra; Polynomial matrices; Symbol
manipulation",
}
@InProceedings{vanHoeij:1995:ACW,
author = "Mark {van Hoeij}",
title = "An algorithm for computing the {Weierstrass} normal
form",
crossref = "Levelt:1995:IPI",
pages = "90--95",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p90-van_hoeij/",
abstract = "The paper describes an algorithm for computing a
normal form $y^2+x^3+ax+b$ for algebraic curves with
genus 1. The corresponding isomorphism of
function-fields is also computed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Nijmegen Univ., Netherlands",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C6130 (Data handling techniques)",
keywords = "algebraic computation, Algorithm; Algebraic curves;
algorithms; Function field isomorphism; Genus 1; ISSAC;
symbolic computation; theory; verification; Weierstrass
normal form computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Algebra; Algorithm theory; Symbol manipulation",
}
@InProceedings{Wolf:1995:PAS,
author = "Thomas Wolf",
title = "Programs for applying symmetries of {PDEs}",
crossref = "Levelt:1995:IPI",
pages = "7--15",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p7-wolf/",
abstract = "In this paper the programs APPLYSYM, QUASILINPDE and
DETRAFO are described which aim at the utilization of
infinitesimal symmetries of differential equations. The
purpose of QUASILINPDE is the general solution of
quasilinear PDEs. This procedure is used by APPLYSYM
for the application of point symmetries for either:
calculating similarity variables to perform a point
transformation which lowers the order of an ODE or
effectively reduces the number of explicitly occurring
independent variables in a PDE(-system) or for
generalizing given special solutions of ODEs/PDEs with
new constant parameters. The program DETRAFO performs
arbitrary point- and contact-transformations of
ODEs/PDEs and is applied if similarity and symmetry
variables have been found. The program APPLYSYM is used
in connection with the program LIE-PDE for formulating
and solving the conditions for point- and
contact-symmetries. The actual problem solving is done
in all these programs through a call to the package
CRACK for solving overdetermined PDE systems.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Queen Mary and Westfield Coll.,
London, UK",
classification = "C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "algebraic computation; algorithms; APPLYSYM; CRACK;
DETRAFO; Differential equations; Infinitesimal
symmetries; languages; ODEs; Overdetermined PDE
systems, ISSAC; PDEs; QUASILINPDE; symbolic
computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Special-purpose algebraic systems.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Yokoyama:1995:FRU,
author = "Kazuhiro Yokoyama and Ziming Li and Istv{\'a}n Nemes",
title = "Finding Roots of Unity among Quotients of the Roots of
an Integral Polynomial",
crossref = "Levelt:1995:IPI",
pages = "85--89",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p85-yokoyama/",
abstract = "We present an efficient algorithm for testing whether
a given integral polynomial has two distinct roots
$\alpha / \beta$ such that $\alpha / \beta$ is a root
of unity. The test is based on results obtained by
investigation of the structure of the splitting field
of the polynomial. By this investigation, we found also
an improved bound for the least common multiple of the
orders of roots of unity appearing as quotients of
distinct roots.",
acknowledgement = ack-nhfb,
affiliation = "ISIS, Fujitsu Labs. Ltd., Shizuoka, Japan",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C6130 (Data handling techniques)",
keywords = "algebraic computation; algorithms; Distinct roots;
Efficient algorithm; experimentation; Integral
polynomial root quotient; Root order least common
multiple bound, ISSAC; Splitting field; symbolic
computation; Testing; theory; Unity roots;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials; Sequences; Symbol manipulation",
}
@InProceedings{Zima:1995:SOT,
author = "Eugene V. Zima",
title = "Simplification and Optimization Transformations of
Chains of Recurrences",
crossref = "Levelt:1995:IPI",
pages = "42--50",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p42-zima/",
abstract = "The problem of expediting the evaluation of
closed-form functions at regular intervals is
considered. The chain of recurrences technique to
expedite computations is extended by rational
simplifications and examined as a form of internal
representation, oriented towards fast evaluation.
Optimizing transformations of chains of recurrences are
proposed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Math. and Cybern., Moscow State
Univ., Russia",
classification = "B0260 (Optimisation techniques); C1180 (Optimisation
techniques); C7310 (Mathematics computing)",
keywords = "algebraic computation; algorithms; Chains of
recurrences; Closed-form functions; Internal
representation, ISSAC; languages; Optimization
transformations; Rational simplifications; Regular
intervals; symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
thesaurus = "Optimisation; Symbol manipulation",
}
@InProceedings{Abramov:1996:DSI,
author = "Sergei A. Abramov and Eugene V. Zima",
title = "{D'Alembertian} solutions of inhomogeneous linear
equations (differential, difference, and some other)",
crossref = "LakshmanYN:1996:IPI",
pages = "232--240",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p232-abramov/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
}
@InProceedings{Ahrendt:1996:FHC,
author = "Timm Ahrendt",
title = "Fast High-Precision Computations of Complex Square
Roots",
crossref = "LakshmanYN:1996:IPI",
pages = "142--149",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; measurement;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Bounded-action devices.
{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Iterative
methods. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
xxtitle = "Fast high-precision computation of complex square
roots",
}
@InProceedings{Amrhein:1996:CSM,
author = "Beatrice Amrhein and Oliver Gloor and Wolfgang
K{\"u}chlin",
title = "A Case Study of Multi-Threaded {Gr{\"o}bner} Basis
Completion",
crossref = "LakshmanYN:1996:IPI",
pages = "95--102",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p95-amrhein/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; experimentation;
ISSAC; performance; SIGNUM; SIGSAM; symbolic
computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf D.1.3}
Software, PROGRAMMING TECHNIQUES, Concurrent
Programming, Parallel programming. {\bf C.1.2} Computer
Systems Organization, PROCESSOR ARCHITECTURES, Multiple
Data Stream Architectures (Multiprocessors), Parallel
processors**.",
}
@InProceedings{Bacher:1996:AGO,
author = "Rainer Bacher",
title = "Automatic Generation of Optimization Code Based on
Symbolic Non-Linear Domain Formulation",
crossref = "LakshmanYN:1996:IPI",
pages = "283--291",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p283-bacher/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse,
structured, and very large systems (direct and
iterative methods). {\bf G.1.6} Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization. {\bf
G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS,
Graph Theory, Network problems. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple.",
}
@InProceedings{Bachmann:1996:MFD,
author = "Olaf Bachmann and Hans Sch{\"o}nemann and Simon Gray",
title = "{MPP}: {A} Framework for Distributed Polynomial
Computations",
crossref = "LakshmanYN:1996:IPI",
pages = "103--112",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p103-bachmann/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; design; ISSAC;
languages; SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Binder:1996:FCL,
author = "Franz Binder",
title = "Fast Computations in the Lattice of Polynomial
Rational Function Fields",
crossref = "LakshmanYN:1996:IPI",
pages = "43--48",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p43-binder/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Number-theoretic
computations.",
}
@InProceedings{Buendgen:1996:MAP,
author = "R. Buendgen and M. Goebel and W. Kuechlin",
title = "A Master-Slave Approach to Parallel Term Rewriting on
a Hierarchical Multiprocessor",
crossref = "Calmet:1996:DIS",
pages = "183--194",
year = "1996",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Caboara:1996:MHF,
author = "Massimo Caboara and Gabriel {de Dominicis} and Lorenzo
Robbiano",
title = "Multigraded {Hilbert} Functions and {Buchberger}
Algorithm",
crossref = "LakshmanYN:1996:IPI",
pages = "72--78",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p72-caboara/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; performance;
SIGNUM; SIGSAM; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Cesari:1996:PFA,
author = "G. Cesari and R. Maeder",
title = "Parallel $3$-Primes {FFT} Algorithm",
crossref = "Calmet:1996:DIS",
pages = "174--182",
year = "1996",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Clark:1996:DOO,
author = "K. L. Clark and F. G. McCabe",
title = "Distributed and Object Oriented Symbolic Programming
in {April}",
crossref = "Briot:1996:OBP",
pages = "104--124",
year = "1996",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Collins:1996:TMP,
author = "George E. Collins and Werner Krandick",
title = "A Tangent-Secant Method for Polynomial Complex Root
Calculation",
crossref = "LakshmanYN:1996:IPI",
pages = "137--141",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p137-collins/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; performance;
SIGNUM; SIGSAM; symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Cooperman:1996:NSP,
author = "Gene Cooperman and Michael Tselman",
title = "New Sequential and Parallel Algorithms for Generating
High Dimension {Hecke} Algebras using the Condensation
Technique",
crossref = "LakshmanYN:1996:IPI",
pages = "155--160",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p155-cooperman/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf E.2} Data, DATA STORAGE
REPRESENTATIONS, Hash-table representations.",
}
@InProceedings{Eberly:1996:EDA,
author = "W. Eberly and M. Giesbrecht",
title = "Efficient Decomposition of Associative Algebras",
crossref = "LakshmanYN:1996:IPI",
pages = "170--178",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p170-eberly/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Erlingsson:1996:GGO,
author = "{\'U}lfar Erlingsson and Erich Kaltofen and David
Musser",
title = "Generic {Gram--Schmidt} Orthogonalization by Exact
Division",
crossref = "LakshmanYN:1996:IPI",
pages = "275--282",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p275-erlingsson/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
performance; SIGNUM; SIGSAM; symbolic computation;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C++. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Fateman:1996:SMS,
author = "Richard J. Fateman",
title = "Symbolic mathematics system evaluators (extended
abstract)",
crossref = "LakshmanYN:1996:IPI",
pages = "86--94",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p86-fateman/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; design; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Evaluation strategies. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, AXIOM. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Mathematica.",
}
@InProceedings{Fujise:1996:PDD,
author = "Tetsuro Fujise and Hirokazu Murao",
title = "Parallel Distinct Degree Factorization Algorithm",
crossref = "LakshmanYN:1996:IPI",
pages = "18--25",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p18-fujise/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; experimentation;
ISSAC; SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
}
@InProceedings{Grigoriev:1996:TSP,
author = "D. Grigoriev",
title = "Testing Shift-Equivalence of Polynomials Using Quantum
Machines",
crossref = "LakshmanYN:1996:IPI",
pages = "49--54",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p49-grigoriev/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.3}
Mathematics of Computing, PROBABILITY AND STATISTICS,
Probabilistic algorithms (including Monte Carlo). {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields.",
}
@InProceedings{Hong:1996:GBU,
author = "Hoon Hong",
title = "{Gr{\"o}bner} basis under composition {II}",
crossref = "LakshmanYN:1996:IPI",
pages = "79--85",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p79-hong/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Hubert:1996:GSO,
author = "Evelyne Hubert",
title = "The General Solution of an Ordinary Differential
Equation",
crossref = "LakshmanYN:1996:IPI",
pages = "189--195",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p189-hubert/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@Article{Kaltofen:1996:ISC,
author = "E. Kaltofen",
title = "{ISSAC} Steering Committee Bylaws",
journal = j-SIGSAM,
volume = "30",
number = "1",
pages = "31--33",
month = mar,
year = "1996",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
bibdate = "Fri Sep 06 07:11:07 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:1996:RPT,
author = "E. Kaltofen and A. Lobo",
title = "On Rank Properties of {Toeplitz} Matrices over Finite
Fields",
crossref = "LakshmanYN:1996:IPI",
pages = "241--249",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p241-kaltofen/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods). {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations in
finite fields.",
}
@InProceedings{Karmarkar:1996:APG,
author = "N. Karmarkar and {Lakshman Y. N.}",
title = "Approximate Polynomial Greatest Common Divisors and
Nearest Singular Polynomials",
crossref = "LakshmanYN:1996:IPI",
pages = "35--39",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p35-karmarkar/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
}
@InProceedings{Kavian:1996:MPR,
author = "Masoud Kavian and R. G. McLenaghan and K. O. Geddes",
title = "{MapleTensor}: Progress Report on a New System for
Performing Indicial and Component Tensor Calculations
Using Symbolic Computation",
crossref = "LakshmanYN:1996:IPI",
pages = "204--211",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p204-kavian/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; design; ISSAC;
languages; SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C++. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Koenhagen:1996:OAC,
author = "Ulla Koenhagen and Ernst W. Mayr",
title = "An optimal algorithm for constructing the reduced
{Gr{\"o}bner} basis of binomial ideals",
crossref = "LakshmanYN:1996:IPI",
pages = "55--62",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p55-koppenhagen/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes, Reducibility and completeness. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Koppenhagen:1996:OAC,
author = "U. Koppenhagen and E. W. Mayr",
title = "An Optimal Algorithm for Constructing the Reduced
{Gr{\"o}bner} Basis of Binomial Ideals",
crossref = "LakshmanYN:1996:IPI",
pages = "55--62",
year = "1996",
bibdate = "Sat May 10 10:28:09 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; ISSAC; SIGNUM; SIGSAM; symbolic
computation",
}
@InProceedings{Kuhnle:1996:ESC,
author = "Klaus K{\"u}hnle and Ernst W. Mayr",
title = "Exponential space computation of {Gr{\"o}bner} bases",
crossref = "LakshmanYN:1996:IPI",
pages = "63--71",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p63-kuhnle/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Mikhalev:1996:APE,
author = "Alexander A. Mikhalev and Andrej A. Zolotykh",
title = "Algorithms for Primitive Elements of Free {Lie}
Algebras and {Lie} Superalgebras",
crossref = "LakshmanYN:1996:IPI",
pages = "161--169",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p161-mikhalev/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf J.2} Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Physics. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Norman:1996:MTA,
author = "Arthur Norman and John Fitch",
title = "Memory Tracing of Algebraic Calculations",
crossref = "LakshmanYN:1996:IPI",
pages = "113--119",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p113-norman/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; measurement;
performance; SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and
Techniques.",
}
@InProceedings{Pottier:1996:EAD,
author = "Lo{\"\i}c Pottier",
title = "The {Euclidean} algorithm in dimension $n$",
crossref = "LakshmanYN:1996:IPI",
pages = "40--42",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p40-pottier/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Number-theoretic computations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
}
@InProceedings{Reinhart:1996:DHD,
author = "Georg M. Reinhart and William Sit",
title = "Differentially Homogeneous Differential Polynomials",
crossref = "LakshmanYN:1996:IPI",
pages = "212--218",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p212-reinhart/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations.",
}
@InProceedings{Richardson:1996:AEE,
author = "Daniel Richardson and Bruno Salvy and John Shackell
and Joris {Van der Hoeven}",
title = "Asymptotic Expansions of $\exp$--$\log$ Functions",
crossref = "LakshmanYN:1996:IPI",
pages = "309--313",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p309-richardson/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
xxpages = "309--312",
}
@InProceedings{Richardson:1996:SES,
author = "Daniel Richardson",
title = "Solution of elementary systems of equations in a box
in {$R^n$}",
crossref = "LakshmanYN:1996:IPI",
pages = "120--126",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p120-richardson/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Roach:1996:HFR,
author = "Kelly Roach",
title = "Hypergeometric Function Representations",
crossref = "LakshmanYN:1996:IPI",
pages = "301--308",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p301-roach/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, MACSYMA. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Mathematica.",
}
@InProceedings{Roy:1996:CCS,
author = "Marie-Fran{\c{c}}oise Roy and Nicolai Vorobjov",
title = "Computing the complexification of a semi-algebraic
set",
crossref = "LakshmanYN:1996:IPI",
pages = "26--34",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p26-roy/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Complexity Measures and Classes.",
}
@InProceedings{Schwarz:1996:JBO,
author = "Fritz Schwarz",
title = "Janet bases of 2nd order ordinary differential
equations",
crossref = "LakshmanYN:1996:IPI",
pages = "179--188",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p179-schwarz/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf G.1.8}
Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
}
@InProceedings{Stetter:1996:AZC,
author = "Hans J. Stetter",
title = "Analysis of Zero Clusters in Multivariate Polynomial
Systems",
crossref = "LakshmanYN:1996:IPI",
pages = "127--136",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p127-stetter/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
}
@InProceedings{Storjohann:1996:AFC,
author = "Arne Storjohann and George Labahn",
title = "Asymptotically Fast Computation of the {Hermite Normal
Forms} of Integer Matrices",
crossref = "LakshmanYN:1996:IPI",
pages = "259--266",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p259-storjohann/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra.",
}
@InProceedings{Storjohann:1996:NOA,
author = "Arne Storjohann",
title = "Near optimal algorithms for computing {Smith} normal
forms of integer matrices",
crossref = "LakshmanYN:1996:IPI",
pages = "267--274",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p267-storjohann/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
}
@InProceedings{Thomas:1996:SCI,
author = "G. Thomas",
title = "Symbolic Computation of the Index of Quasilinear
Differential-Algebraic Equations",
crossref = "LakshmanYN:1996:IPI",
pages = "196--203",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p196-thomas/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Thuemmel:1996:CCT,
author = "A. Thuemmel",
title = "Computing Character Tables of $p$-Groups",
crossref = "LakshmanYN:1996:IPI",
pages = "150--154",
year = "1996",
bibdate = "Sat May 10 10:28:09 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; ISSAC; SIGNUM; SIGSAM; symbolic
computation",
}
@InProceedings{Thummel:1996:CCT,
author = "Andreas Th{\"u}mmel",
title = "Computing character tables of $p$-groups",
crossref = "LakshmanYN:1996:IPI",
pages = "150--154",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p150-thummel/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Computations on
discrete structures. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices. {\bf E.1} Data, DATA STRUCTURES, Graphs and
networks.",
}
@InProceedings{Tsarev:1996:ACE,
author = "S. P. Tsarev",
title = "An Algorithm for Complete Enumeration of All
Factorizations of a Linear Ordinary Differential
Operator",
crossref = "LakshmanYN:1996:IPI",
pages = "226--231",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p226-tsarev/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems.",
}
@InProceedings{vanHoeij:1996:RSM,
author = "Mark {van Hoeij}",
title = "Rational Solutions of the Mixed Differential Equation
and Its Application to Factorization of Differential
Operators",
crossref = "LakshmanYN:1996:IPI",
pages = "219--225",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p219-van_hoeij/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General. {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Eigenvalues and eigenvectors (direct and
iterative methods). {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices.",
}
@InProceedings{Villard:1996:CPH,
author = "G. Villard",
title = "Computing {Popov} and {Hermite} Forms of Polynomial
Matrices",
crossref = "LakshmanYN:1996:IPI",
pages = "250--258",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p250-villard/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; SIGNUM;
SIGSAM; symbolic computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods).",
}
@InProceedings{VonzurGathen:1996:AFP,
author = "Joachim {von zur Gathen} and J{\"u}rgen Gerhard",
title = "Arithmetic and factorization of polynomial over {${\bf
F}_2$} (extended abstract)",
crossref = "LakshmanYN:1996:IPI",
pages = "1--9",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p1-von_zur_gathen/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; experimentation;
ISSAC; performance; SIGNUM; SIGSAM; symbolic
computation",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations. {\bf G.1.5}
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Polynomials, methods for. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields.",
}
@InProceedings{vonzurGathen:1996:FMP,
author = "Joachim {von zur Gathen} and Silke Hartlieb",
title = "Factoring modular polynomials (extended abstract)",
crossref = "LakshmanYN:1996:IPI",
pages = "10--17",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p10-von_zur_gathen/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; performance;
SIGNUM; SIGSAM; symbolic computation; theory;
verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf G.3} Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo).",
}
@InProceedings{Zhao:1996:MPM,
author = "Yanjie Zhao and Tetsuya Sakurai and Hiroshi Sugiura
and Tatsuo Torii",
title = "A Methodology of Parsing Mathematical Notation for
Mathematical Computation",
crossref = "LakshmanYN:1996:IPI",
pages = "292--300",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p292-zhao/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; languages;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems, Grammar types. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems, Parsing. {\bf
F.4.3} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Formal Languages.",
}
@InProceedings{Abate:1997:ADS,
author = "Jason Abate and Christian Bischof and Lucas Roh and
Alan Carle",
title = "Algorithms and design for a second-order automatic
differentiation module",
crossref = "Kuchlin:1997:PPS",
pages = "149--155",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p149-abate/",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:1997:MCF,
author = "Sergei A. Abramov and Eugene V. Zima",
title = "Minimal completely factorable annihilators",
crossref = "Kuchlin:1997:PPS",
pages = "290--297",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p290-abramov/",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:1997:MIS,
author = "Sergei A. Abramov and Mark {van Hoeij}",
title = "A method for the integration of solutions of {{\O}re}
equations",
crossref = "Kuchlin:1997:PPS",
pages = "172--175",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p172-abramov/",
acknowledgement = ack-nhfb,
}
@InProceedings{Adamchik:1997:CLI,
author = "Victor Adamchik",
title = "A class of logarithmic integrals",
crossref = "Kuchlin:1997:PPS",
pages = "1--8",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p1-adamchik/",
acknowledgement = ack-nhfb,
}
@InProceedings{Andradas:1997:ROR,
author = "Carlos Andradas and Tom{\'a}s Recio and J. Rafael
Sendra",
title = "A relatively optimal rational space curve
reparametrization algorithm through canonical
divisors",
crossref = "Kuchlin:1997:PPS",
pages = "349--355",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p349-andradas/",
acknowledgement = ack-nhfb,
}
@InProceedings{Bachmann:1997:PSD,
author = "Olaf Bachmann and Hans Sch{\"o}nemann and Simon Gray",
title = "A proposal for syntactic data integration math
protocols",
crossref = "Kuchlin:1997:PPS",
pages = "165--175",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p165-bachmann/",
acknowledgement = ack-nhfb,
keywords = "design; languages",
subject = "{\bf D.2.6} Software, SOFTWARE ENGINEERING,
Programming Environments. {\bf D.2.2} Software,
SOFTWARE ENGINEERING, Design Tools and Techniques. {\bf
E.1} Data, DATA STRUCTURES, Trees. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
E.1} Data, DATA STRUCTURES, Arrays. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra.",
}
@InProceedings{Basu:1997:UQE,
author = "Saugata Basu",
title = "Uniform quantifier elimination and constraint query
processing",
crossref = "Kuchlin:1997:PPS",
pages = "21--27",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p21-basu/",
acknowledgement = ack-nhfb,
}
@InProceedings{Beckermann:1997:FCM,
author = "Bernhard Beckermann and Stan Cabay and George Labahn",
title = "Fraction-free computation of matrix {Pad{\'e}}
systems",
crossref = "Kuchlin:1997:PPS",
pages = "125--132",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p125-beckermann/",
acknowledgement = ack-nhfb,
}
@InProceedings{Bernardin:1997:MMP,
author = "Laurent Bernardin",
title = "{Maple} on a massively parallel, distributed memory
machine",
crossref = "Kuchlin:1997:PPS",
pages = "217--222",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p217-bernardin/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages; performance",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf C.1.2} Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors**. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Bonacina:1997:ESS,
author = "Maria Paola Bonacina",
title = "Experiments with subdivisions of search in distributed
theorem proving",
crossref = "Kuchlin:1997:PPS",
pages = "88--100",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p88-bonacina/",
acknowledgement = ack-nhfb,
keywords = "experimentation; performance; verification",
subject = "{\bf I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving, Deduction.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Bronstein:1997:SPD,
author = "Manuel Bronstein and Thom Mulders and Jacques-Arthur
Weil",
title = "On symmetric powers of differential operators",
crossref = "Kuchlin:1997:PPS",
pages = "156--163",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p156-bronstein/",
acknowledgement = ack-nhfb,
}
@InProceedings{Buchberger:1997:STP,
author = "Bruno Buchberger and Tudor Jebelean and Franz Kriftner
and Mircea Marin and Elena Tomu{\c{t}}a and Daniela
V{\=a}saru",
title = "A survey of the theorema project",
crossref = "Kuchlin:1997:PPS",
pages = "384--391",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p384-buchberger/",
acknowledgement = ack-nhfb,
}
@InProceedings{Caboara:1997:FIS,
author = "Massimo Caboara and Lorenzo Robbiano",
title = "Families of ideals in statistics",
crossref = "Kuchlin:1997:PPS",
pages = "404--410",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p404-caboara/",
acknowledgement = ack-nhfb,
}
@InProceedings{Cannon:1997:CCC,
author = "John Cannon and Bernd Souvignier",
title = "On the computation of conjugacy classes in permutation
groups",
crossref = "Kuchlin:1997:PPS",
pages = "392--399",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p392-cannon/",
acknowledgement = ack-nhfb,
}
@InProceedings{Cesari:1997:CCA,
author = "Giovanni Cesari",
title = "{CALYPSO}: a computer algebra library for parallel
symbolic computation",
crossref = "Kuchlin:1997:PPS",
pages = "204--216",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p204-cesari/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; experimentation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
}
@InProceedings{Chistov:1997:PTA,
author = "Alexander Chistov and G{\'a}bor Ivanyos and Marek
Karpinski",
title = "Polynomial time algorithms for modules over finite
dimensional algebras",
crossref = "Kuchlin:1997:PPS",
pages = "68--74",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p68-chistov/",
acknowledgement = ack-nhfb,
}
@InProceedings{Colin:1997:RRP,
author = "Antoine Colin",
title = "Relative resolvents and partition tables in {Galois}
group computations",
crossref = "Kuchlin:1997:PPS",
pages = "78--84",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p78-colin/",
acknowledgement = ack-nhfb,
}
@InProceedings{Corless:1997:RSF,
author = "Robert M. Corless and Patrizia M. Gianni and Barry M.
Trager",
title = "A reordered {Schur} factorization method for
zero-dimensional polynomial systems with multiple
roots",
crossref = "Kuchlin:1997:PPS",
pages = "133--140",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p133-corless/",
acknowledgement = ack-nhfb,
}
@InProceedings{Corless:1997:SSL,
author = "Robert M. Corless and David J. Jeffrey and Donald E.
Knuth",
title = "A sequence of series for the {Lambert} ${W}$
function",
crossref = "Kuchlin:1997:PPS",
pages = "197--204",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p197-corless/",
acknowledgement = ack-nhfb,
}
@InProceedings{Costa:1997:EPL,
author = "V{\'\i}tor Santos Costa and Ricardo Bianchini and
In{\^e}s de Castro Dutra",
title = "Evaluating parallel logic programming systems on
scalable multiprocessors",
crossref = "Kuchlin:1997:PPS",
pages = "58--67",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p58-santos_costa/",
acknowledgement = ack-nhfb,
keywords = "performance",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems, Parallel rewriting systems. {\bf F.1.2} Theory
of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes
of Computation, Parallelism and concurrency. {\bf
C.1.2} Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors**. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
}
@InProceedings{Dalmas:1997:OI,
author = "St{\'e}phane Dalmas and Marc Ga{\"e}tano and Stephen
Watt",
title = "An {OpenMath} 1.0 implementation",
crossref = "Kuchlin:1997:PPS",
pages = "241--248",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p241-dalmas/",
acknowledgement = ack-nhfb,
}
@InProceedings{Dolzmann:1997:GEP,
author = "Andreas Dolzmann and Thomas Sturm",
title = "Guarded expressions in practice",
crossref = "Kuchlin:1997:PPS",
pages = "376--383",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p376-dolzmann/",
acknowledgement = ack-nhfb,
}
@InProceedings{Dora:1997:ANA,
author = "J. Della Dora and F. Richard-Jung",
title = "About the {Newton} algorithm for non-linear ordinary
differential equations",
crossref = "Kuchlin:1997:PPS",
pages = "298--304",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p298-dora/",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:1997:PEP,
author = "Wayne Eberly",
title = "Processor-efficient parallel matrix inversion over
abstract fields: two extensions",
crossref = "Kuchlin:1997:PPS",
pages = "38--45",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p38-eberly/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods). {\bf G.1.0} Mathematics
of Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
}
@InProceedings{Eberly:1997:RLA,
author = "Wayne Eberly and Erich Kaltofen",
title = "On randomized {Lanczos} algorithms",
crossref = "Kuchlin:1997:PPS",
pages = "176--183",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p176-eberly/",
acknowledgement = ack-nhfb,
}
@InProceedings{Edneral:1997:CEC,
author = "Victor F. Edneral",
title = "Computer evaluation of cyclicity in planar cubic
system",
crossref = "Kuchlin:1997:PPS",
pages = "305--309",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p305-edneral/",
acknowledgement = ack-nhfb,
}
@InProceedings{Egner:1997:DPC,
author = "Sebastian Egner and Markus P{\"u}schel and Thomas
Beth",
title = "Decomposing a permutation into a conjugated tensor
product",
crossref = "Kuchlin:1997:PPS",
pages = "101--108",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p101-egner/",
acknowledgement = ack-nhfb,
}
@InProceedings{Emiris:1997:SSR,
author = "Ioanis Z. Emiris and Victor Y. Pan",
title = "The structure of sparse resultant matrices",
crossref = "Kuchlin:1997:PPS",
pages = "189--196",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p189-emiris/",
acknowledgement = ack-nhfb,
}
@InProceedings{Encarnacion:1997:ANM,
author = "Mark J. Encarnaci{\'o}n",
title = "The average number of modular factors in {Trager}'s
polynomial factorization algorithm",
crossref = "Kuchlin:1997:PPS",
pages = "278--281",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p278-encarnacion/",
acknowledgement = ack-nhfb,
}
@InProceedings{Encarnacion:1997:FPA,
author = "Mark J. Encarnaci{\'o}n",
title = "Factoring polynomials over algebraic number fields via
norms",
crossref = "Kuchlin:1997:PPS",
pages = "265--270",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p265-encarnacion/",
acknowledgement = ack-nhfb,
}
@InProceedings{Fang:1997:WCI,
author = "Xin Gui Fang and George Havas",
title = "On the worst-case complexity of integer {Gaussian}
elimination",
crossref = "Kuchlin:1997:PPS",
pages = "28--31",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p28-fang/",
acknowledgement = ack-nhfb,
}
@InProceedings{Fateman:1997:NSS,
author = "Richard J. Fateman",
title = "Network servers for symbolic mathematics",
crossref = "Kuchlin:1997:PPS",
pages = "249--256",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p249-fateman/",
acknowledgement = ack-nhfb,
}
@InProceedings{Fujimura:1997:MSS,
author = "Masayo Fujimura and Kiyoko Nishizawa",
title = "Moduli spaces and symmetry loci of polynomial maps",
crossref = "Kuchlin:1997:PPS",
pages = "342--348",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p342-fujimura/",
acknowledgement = ack-nhfb,
}
@InProceedings{Galligo:1997:NAP,
author = "Andr{\'e} Galligo and Stephen Watt",
title = "A numerical absolute primality test for bivariate
polynomials",
crossref = "Kuchlin:1997:PPS",
pages = "217--224",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p217-galligo/",
acknowledgement = ack-nhfb,
}
@InProceedings{Gautier:1997:NCG,
author = "Thierry Gautier and Jean-Louis Roch",
title = "{{\sc NC$^2$}} computation of gcd-free basis and
alication to parallel algebraic numbers computation",
crossref = "Kuchlin:1997:PPS",
pages = "31--37",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p31-gautier/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@InProceedings{Gemignani:1997:GPB,
author = "Luca Gemignani",
title = "{GCD} of polynomials and {B{\'e}zout} matrices",
crossref = "Kuchlin:1997:PPS",
pages = "271--277",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p271-gemignani/",
acknowledgement = ack-nhfb,
}
@InProceedings{Gianni:1997:ICN,
author = "Patrizia Gianni and Barry Trager",
title = "Integral closure of {Noetherian} rings",
crossref = "Kuchlin:1997:PPS",
pages = "212--216",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p212-gianni/",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:1997:EPS,
author = "Mark Giesbrecht",
title = "Efficient parallel solution of sparse systems of
linear {Diophantine} equations",
crossref = "Kuchlin:1997:PPS",
pages = "1--10",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p1-giesbrecht/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods). {\bf G.1.3} Mathematics
of Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Sparse, structured, and very large systems
(direct and iterative methods). {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Parallel algorithms. {\bf G.3} Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo).",
}
@InProceedings{Glauert:1997:OGR,
author = "John Glauert",
title = "Object graph rewriting: an experimental parallel
implementation",
crossref = "Kuchlin:1997:PPS",
pages = "119--128",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p119-glauert/",
acknowledgement = ack-nhfb,
keywords = "experimentation; languages",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming, Parallel programming. {\bf E.1}
Data, DATA STRUCTURES, Trees. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic. {\bf F.4.2} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
Other Rewriting Systems. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Standard ML.",
}
@InProceedings{Graaf:1997:CFM,
author = "W. A. de Graaf",
title = "Constructing faithful matrix representations of {Lie}
algebras",
crossref = "Kuchlin:1997:PPS",
pages = "54--59",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p54-de_graaf/",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:1997:EDD,
author = "Gopal Gupta and Enrico Pontelli",
title = "Extended dynamic dependent {And}-parallelism in
{ACE}",
crossref = "Kuchlin:1997:PPS",
pages = "68--79",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p68-gupta/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; performance",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming, Parallel programming. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Prolog. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Optimization.",
}
@InProceedings{Haridi:1997:ODD,
author = "Seif Haridi and Peter {Van Roy} and Gert Smolka",
title = "An overview of the design of {Distributed Oz}",
crossref = "Kuchlin:1997:PPS",
pages = "176--187",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p176-haridi/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Concurrent, distributed, and parallel languages. {\bf
D.3.1} Software, PROGRAMMING LANGUAGES, Formal
Definitions and Theory, Semantics. {\bf C.2.4} Computer
Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
Distributed Systems, Distributed applications. {\bf
I.3.4} Computing Methodologies, COMPUTER GRAPHICS,
Graphics Utilities, Graphics editors.",
}
@InProceedings{Hermenegildo:1997:WSC,
author = "M. Hermenegildo",
title = "Workshop 19: Symbolic Computation",
crossref = "Lengauer:1997:EPP",
pages = "1167--1168",
year = "1997",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Huang:1997:FRM,
author = "Xiaohan Huang and Victor Y. Pan",
title = "Fast rectangular matrix multiplications and improving
parallel matrix computations",
crossref = "Kuchlin:1997:PPS",
pages = "11--23",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p11-huang/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance; theory; verification",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods). {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms.",
}
@InProceedings{Jebelean:1997:PID,
author = "Tudor Jebelean",
title = "Practical integer division with {Karatsuba}
complexity",
crossref = "Kuchlin:1997:PPS",
pages = "339--341",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p339-jebelean/",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeffrey:1997:ISP,
author = "D. J. Jeffrey and G. Labahn and M. {Von Mohrenschildt}
and A. D. Rich",
title = "Integration of the signum, piecewise and related
functions",
crossref = "Kuchlin:1997:PPS",
pages = "324--330",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p324-jeffrey/",
acknowledgement = ack-nhfb,
}
@InProceedings{Johnson:1997:PRR,
author = "J. R. Johnson and Werner Krandick",
title = "Polynomial real root isolation using approximate
arithmetic",
crossref = "Kuchlin:1997:PPS",
pages = "225--232",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p225-johnson/",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:1997:FPF,
author = "Erich Kaltofen and Victor Shoup",
title = "Fast polynomial factorization over high algebraic
extensions of finite fields",
crossref = "Kuchlin:1997:PPS",
pages = "184--188",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p184-kaltofen/",
acknowledgement = ack-nhfb,
}
@InProceedings{Kapur:1997:EFD,
author = "Deepak Kapur and Tushar Saxena",
title = "Extraneous factors in the {Dixon} resultant
formulation",
crossref = "Kuchlin:1997:PPS",
pages = "141--148",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p141-kapur/",
acknowledgement = ack-nhfb,
}
@InProceedings{Kato:1997:PIC,
author = "Shohei Kato and Hirohisa Seki and Hidenori Itoh",
title = "A parallel implementation of cost-based abductive
reasoning",
crossref = "Kuchlin:1997:PPS",
pages = "111--118",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p111-kato/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory",
subject = "{\bf I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving, Deduction.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic. {\bf C.1.2}
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Parallel processors**. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Prolog.",
}
@InProceedings{kavian:1997:AGA,
author = "M. kavian and R. G. McLenaghan and K. O. Geddes",
title = "Application of genetic algorithms to the algebraic
simplification of tensor polynomials",
crossref = "Kuchlin:1997:PPS",
pages = "93--100",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p93-kavian/",
acknowledgement = ack-nhfb,
}
@InProceedings{Lam:1997:MPP,
author = "Monica Lam",
title = "Maximizing performance on parallel machines
(abstract)",
crossref = "Kuchlin:1997:PPS",
pages = "129--129",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p129-lam/",
acknowledgement = ack-nhfb,
keywords = "performance",
subject = "{\bf C.1.2} Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors**. {\bf D.3.4}
Software, PROGRAMMING LANGUAGES, Processors,
Optimization.",
}
@InProceedings{Lehobey:1997:RCR,
author = "Fr{\'e}d{\'e}ric Lehobey",
title = "Resolvent computations by resultants without
extraneous powers",
crossref = "Kuchlin:1997:PPS",
pages = "85--92",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p85-lehobey/",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:1997:MAC,
author = "Ziming Li and Istv{\'a}n Nemes",
title = "A modular algorithm for computing greatest common
right divisors of {{\O}re} polynomials",
crossref = "Kuchlin:1997:PPS",
pages = "282--289",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p282-li/",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:1997:MGB,
author = "Qiang Li and Yi-ke Guo and Tetsuo Ida and John
Darlington",
title = "The minimised geometric {Buchberger} algorithm: an
optimal algebraic algorithm for integer programming",
crossref = "Kuchlin:1997:PPS",
pages = "331--338",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p331-li/",
acknowledgement = ack-nhfb,
}
@InProceedings{McKay:1997:FRA,
author = "John McKay and Richard Stauduhar",
title = "Finding relations among the roots of an irreducible
polynomial",
crossref = "Kuchlin:1997:PPS",
pages = "75--77",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p75-mckay/",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:1997:TPM,
author = "Michael B. Monagan and Gladys Monagan",
title = "A toolbox for program manipulation and efficient code
generation with an application to a problem in computer
vision",
crossref = "Kuchlin:1997:PPS",
pages = "257--264",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p257-monagan/",
acknowledgement = ack-nhfb,
}
@InProceedings{Montelius:1997:EPS,
author = "Johan Montelius and Seif Haridi",
title = "An evaluation of {Penny}: a system for fine grain
implicit parallelism",
crossref = "Kuchlin:1997:PPS",
pages = "46--57",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p46-montelius/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; performance",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming, Parallel programming. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Concurrent, distributed, and parallel
languages. {\bf C.1.2} Computer Systems Organization,
PROCESSOR ARCHITECTURES, Multiple Data Stream
Architectures (Multiprocessors), Parallel processors**.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Murao:1997:TEI,
author = "Hirokazu Murao and Tetsuro Fujise",
title = "Towards an efficient implementation of a fast
algorithm for multipoint polynomial evaluation and its
parallel processing",
crossref = "Kuchlin:1997:PPS",
pages = "24--30",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p24-murao/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf C.1.2}
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Parallel processors**. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Norman:1997:CPP,
author = "Arthur Norman and John Fitch",
title = "{CABAL}: polynomial and power series algebra on a
parallel computer",
crossref = "Kuchlin:1997:PPS",
pages = "196--203",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p196-norman/",
acknowledgement = ack-nhfb,
keywords = "design; experimentation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf C.1.2} Computer Systems Organization,
PROCESSOR ARCHITECTURES, Multiple Data Stream
Architectures (Multiprocessors), Parallel processors**.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
}
@InProceedings{Noro:1997:CRF,
author = "Masayuki Noro and John McKay",
title = "Computation of replicable functions on {Risa\slash
Asir}",
crossref = "Kuchlin:1997:PPS",
pages = "130--138",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p130-noro/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; performance;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms.",
}
@InProceedings{Nussbaum:1997:RPP,
author = "Doron Nussbaum",
title = "Rectilinear $p$-piercing problems",
crossref = "Kuchlin:1997:PPS",
pages = "316--323",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p316-nussbaum/",
acknowledgement = ack-nhfb,
}
@InProceedings{Ohno:1997:IMC,
author = "Kazuhiko Ohno and Masahiko Ikawa and Shin-ichiro Mori
and Hiroshi Nakashima and Shinji Tomita and Masahiro
Goshima",
title = "Improvement of message communication in concurrent
logic language",
crossref = "Kuchlin:1997:PPS",
pages = "156--164",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p156-ohno/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; performance",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Concurrent, distributed, and parallel
languages. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic. {\bf F.3.3} Theory of Computation, LOGICS AND
MEANINGS OF PROGRAMS, Studies of Program Constructs,
Type structure.",
}
@InProceedings{Pflugel:1997:ACE,
author = "Eckhard Pfl{\"u}gel",
title = "An algorithm for computing exponential solutions of
first order linear differential systems",
crossref = "Kuchlin:1997:PPS",
pages = "164--171",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p164-pflugel/",
acknowledgement = ack-nhfb,
}
@InProceedings{Pontelli:1997:PSC,
author = "E. Pontelli and G. Gupta",
title = "Parallel symbolic computation in {ACE}",
crossref = "Baral:1997:LPN",
pages = "359--396",
year = "1997",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Reischert:1997:AFC,
author = "Daniel Reischert",
title = "Asymptotically fast computation of subresultants",
crossref = "Kuchlin:1997:PPS",
pages = "233--240",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p233-reischert/",
acknowledgement = ack-nhfb,
}
@InProceedings{Roach:1997:MGF,
author = "Kelly Roach",
title = "{Meijer} ${G}$ functions representations",
crossref = "Kuchlin:1997:PPS",
pages = "205--211",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p205-roach/",
acknowledgement = ack-nhfb,
}
@InProceedings{Rust:1997:RPD,
author = "C. J. Rust and G. J. Reid",
title = "Rankings of partial derivatives",
crossref = "Kuchlin:1997:PPS",
pages = "9--16",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p9-rust/",
acknowledgement = ack-nhfb,
}
@InProceedings{Sims:1997:CSA,
author = "Charles C. Sims",
title = "Computing with subgroups of automorphism groups of
finite groups",
crossref = "Kuchlin:1997:PPS",
pages = "400--403",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p400-sims/",
acknowledgement = ack-nhfb,
}
@InProceedings{Sperber:1997:DPE,
author = "Michael Sperber and Peter Thiemann and Hervert
Klaeren",
title = "Distributed partial evaluation",
crossref = "Kuchlin:1997:PPS",
pages = "80--87",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p80-sperber/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; performance",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Optimization. {\bf D.1.1} Software,
PROGRAMMING TECHNIQUES, Applicative (Functional)
Programming. {\bf I.2.2} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Automatic Programming, Program
transformation. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Compilers.",
}
@InProceedings{Stetter:1997:SPS,
author = "Hans J. Stetter",
title = "Stabilization of polynomial systems solving with
{Gr{\"o}bner} bases",
crossref = "Kuchlin:1997:PPS",
pages = "117--124",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p117-stetter/",
acknowledgement = ack-nhfb,
}
@InProceedings{Stiller:1997:SCO,
author = "Peter F. Stiller",
title = "Symbolic computation of object\slash image equations",
crossref = "Kuchlin:1997:PPS",
pages = "359--364",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p359-stiller/",
acknowledgement = ack-nhfb,
}
@InProceedings{Storjohann:1997:SEG,
author = "Arne Storjohann",
title = "A solution to the extended {GCD} problem with
applications",
crossref = "Kuchlin:1997:PPS",
pages = "109--116",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p109-storjohann/",
acknowledgement = ack-nhfb,
}
@InProceedings{Szanto:1997:CWR,
author = "{\'A}gnes Sz{\'a}nt{\'o}",
title = "Complexity of the {Wu--Ritt} decomposition",
crossref = "Kuchlin:1997:PPS",
pages = "139--149",
year = "1997",
bibdate = "Fri May 07 12:02:05 1999",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p139-szanto/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Teo:1997:DEP,
author = "Yong Meng Teo and Wei-Ngan Chin and Soon Huat Tan",
title = "Deriving efficient parallel programs for complex
recurrences",
crossref = "Kuchlin:1997:PPS",
pages = "101--110",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p101-teo/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; performance",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming, Parallel programming. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Application Builder. {\bf F.2.0}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, General. {\bf E.1} Data, DATA
STRUCTURES, Lists, stacks, and queues.",
}
@InProceedings{Tsarev:1997:SMI,
author = "S. P. Tsarev",
title = "Symbolic manipulation of integrodifferential
expressions and factorization of linear ordinary
differential operators over transcendental extensions
of a differential field",
crossref = "Kuchlin:1997:PPS",
pages = "310--315",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p310-tsarev/",
acknowledgement = ack-nhfb,
}
@InProceedings{V:1997:MRP,
author = "Eugene V. and Zima",
title = "Mixed representation of polynomials oriented towards
fast parallel shift",
crossref = "Kuchlin:1997:PPS",
pages = "150--155",
year = "1997",
bibdate = "Thu Mar 12 07:28:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p150-zima/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{vanderHoeven:1997:LMF,
author = "Joris {van der Hoeven}",
title = "Lazy multiplication of formal power series",
crossref = "Kuchlin:1997:PPS",
pages = "17--20",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p17-van_der_hoeven/",
acknowledgement = ack-nhfb,
}
@InProceedings{Villard:1997:FAC,
author = "G. Villard",
title = "Further analysis of {Coppersmith}'s block {Wiedemann}
algorithm for the solution of sparse linear systems",
crossref = "Kuchlin:1997:PPS",
pages = "32--39",
year = "1997",
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http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Volcheck:1997:CDP,
author = "Emil Volcheck",
title = "On computing the dual of a plane algebraic curve",
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pages = "356--358",
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}
@InProceedings{vonzurGathen:1997:FAT,
author = "Joachim von zur Gathen and J{\"u}rgen Gerhard",
title = "Fast algorithms for {Taylor} shifts and certain
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crossref = "Kuchlin:1997:PPS",
pages = "40--47",
year = "1997",
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http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Wang:1997:TPD,
author = "Paul S. Wang",
title = "Tools for parallel\slash distributed mathematical
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acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf C.1.2} Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors**. {\bf D.1.3}
Software, PROGRAMMING TECHNIQUES, Concurrent
Programming, Parallel programming. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP.",
}
@InProceedings{Weispfenning:1997:CUE,
author = "Wolker Weispfenning",
title = "Complexity and uniformity of elimination in
{Presburger} arithmetic",
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}
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author = "Horst G. Zimmer",
title = "{SIMATH} --- a computer algebra system for number
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author = "Andrij A. Zolotykh",
title = "Tensor product decomposition and other algorithms for
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author = "Olaf Bachmann and Hans Sch{\"o}nemann",
title = "Monomial representations for {Gr{\"o}bner} bases
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author = "M. A. Barkatou and E. Pfl{\"u}gel",
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author = "Saugata Basu and Richard Pollack and
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title = "Complexity of computing semi-algebraic descriptions of
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author = "Fr{\'e}d{\'e}ric Beringer and Fran{\c{c}}oise Jung",
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author = "Laurent Bernardin",
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author = "Didier Bondyfalat and Bernard Mourrain and Victor Y.
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author = "Angel D{\'\i}az and Erich Kaltofen",
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author = "Hans J. Stetter and G{\"u}nther H. Thallinger",
title = "Singular systems of polynomials",
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author = "Akmal A. Vakhidov and Irina V. Tupikova",
title = "Application of computer algebra methods to the
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author = "Mark {van Hoeij}",
title = "Rational solutions of linear difference equations",
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author = "Sergei A. Abramov and Mark van Hoeij",
title = "Desingularization of linear difference operators with
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author = "Marc Giusti and {\'E}ric Schost",
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author = "C.-P. Jeannerod and E. Pfl{\"u}gel",
title = "A reduction algorithm for matrices depending on a
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author = "Erich Kaltofen and Michael B. Monagan",
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author = "V. Kislenkov and V. Mitrofanov and E. Zima",
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author = "Y. O. Macutan",
title = "Formal solutions of scalar singularly-perturbed linear
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author = "Scott McCallum",
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author = "Schuichi Moritsugu and Kazuko Kuriyama",
title = "On multiple zeros of systems of algebraic equations",
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author = "Thom Mulders and Arne Storjohann",
title = "{Diophantine} linear system solving",
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author = "Igor Pak and Sergey Bratus",
title = "On sampling generating sets of finite groups and
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pages = "91--96",
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title = "Existence and uniqueness theorems for formal power
series solutions of analytic differential systems",
crossref = "Dooley:1999:IJS",
pages = "105--112",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Shackell:1999:SPR,
author = "John Shackell",
title = "Star products and the representation of asymptotic
growth",
crossref = "Dooley:1999:IJS",
pages = "97--104",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Shoup:1999:ECM,
author = "Victor Shoup",
title = "Efficient computation of minimal polynomials in
algebraic extensions of finite fields",
crossref = "Dooley:1999:IJS",
pages = "53--58",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Tsarev:1999:FNO,
author = "S. P. Tsarev",
title = "On factorization of nonlinear ordinary differential
equations",
crossref = "Dooley:1999:IJS",
pages = "159--164",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Villard:1999:AIA,
author = "Dominique Villard and Michael B. Monagan",
title = "{ADrien}: an implementation of automatic
differentiation in {Maple}",
crossref = "Dooley:1999:IJS",
pages = "221--228",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:1999:CSP,
author = "Joachim von zur Gathen and Michael N{\"o}cker",
title = "Computing special powers in finite fields: extended
abstract",
crossref = "Dooley:1999:IJS",
pages = "83--90",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:1999:DPI,
author = "Paul S. Wang",
title = "Design and protocol for {Internet} accessible
mathematical computation",
crossref = "Dooley:1999:IJS",
pages = "291--298",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Wavrik:1999:CTE,
author = "John J. Wavrik",
title = "Commutativity theorems: examples in search of
algorithms",
crossref = "Dooley:1999:IJS",
pages = "31--36",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Weispfenning:1999:MRI,
author = "Volker Weispfenning",
title = "Mixed real-integer linear quantifier elimination",
crossref = "Dooley:1999:IJS",
pages = "129--136",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Zilic:1999:FMP,
author = "Zeljko Zilic and Katarzyna Radecka",
title = "On feasible multivariate polynomial interpolations
over arbitrary fields",
crossref = "Dooley:1999:IJS",
pages = "67--74",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@InProceedings{Abbott:2000:FSP,
author = "John Abbott and Victor Shoup and Paul Zimmermann",
title = "Factorization in {${\mathbb Z}[x]$}: the searching
phase",
crossref = "Traverso:2000:IAU",
pages = "1--7",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p1-abbott/p1-abbott.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p1-abbott/",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2000:HDO,
author = "Sergei A. Abramov and Manuel Bronstein",
title = "Hypergeometric dispersion and the orbit problem",
crossref = "Traverso:2000:IAU",
pages = "8--13",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p8-abramov/p8-abramov.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p8-abramov/",
acknowledgement = ack-nhfb,
}
@InProceedings{Anai:2000:DLT,
author = "Hirokazu Anai and Volker Weispfenning",
title = "Deciding linear-trigonometric problems",
crossref = "Traverso:2000:IAU",
pages = "14--22",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p14-anai/p14-anai.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p14-anai/",
acknowledgement = ack-nhfb,
}
@InProceedings{Barendegt:2000:RHM,
author = "Henk Barendegt and Arjeh M. Cohen",
title = "Representing and handling mathematical concepts by
humans and machines",
crossref = "Traverso:2000:IAU",
pages = "6--??",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p6-barendegt/",
acknowledgement = ack-nhfb,
}
@InProceedings{Binder:2000:ANR,
author = "Franz Binder and Erhard Aichinger and J{\"u}rgen Ecker
and Christof N{\"o}bauer and Peter Mayr",
title = "Algorithms for near-rings of non-linear
transformations",
crossref = "Traverso:2000:IAU",
pages = "23--29",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p23-binder/p23-binder.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p23-binder/",
acknowledgement = ack-nhfb,
}
@InProceedings{Bodnar:2000:IAR,
author = "G{\'a}bor Bodn{\'a}r and Josef Schicho",
title = "An improved algorithm for the resolution of
singularities",
crossref = "Traverso:2000:IAU",
pages = "30--37",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p30-bodnar/p30-bodnar.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p30-bodnar/",
acknowledgement = ack-nhfb,
}
@InProceedings{Boulier:2000:CCR,
author = "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire",
title = "Computing canonical representatives of regular
differential ideals",
crossref = "Traverso:2000:IAU",
pages = "38--47",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p38-boulier/p38-boulier.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p38-boulier/",
acknowledgement = ack-nhfb,
}
@InProceedings{Brown:2000:IPC,
author = "Christopher W. Brown",
title = "Improved projection for {CAD}'s of {$R^3$}",
crossref = "Traverso:2000:IAU",
pages = "48--53",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p48-brown/p48-brown.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p48-brown/",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheng:2000:AME,
author = "Howard Cheng and Eugene Zima",
title = "On accelerated methods to evaluate sums of products of
rational numbers",
crossref = "Traverso:2000:IAU",
pages = "54--61",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p54-cheng/p54-cheng.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p54-cheng/",
acknowledgement = ack-nhfb,
}
@InProceedings{Chtcherba:2000:CER,
author = "Arthur D. Chtcherba and Deepak Kapur",
title = "Conditions for exact resultants using the {Dixon}
formulation",
crossref = "Traverso:2000:IAU",
pages = "62--70",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p62-chtcherba/p62-chtcherba.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p62-chtcherba/",
acknowledgement = ack-nhfb,
}
@InProceedings{Collins:2000:MFP,
author = "George E. Collins and Werner Krandick",
title = "Multiprecision floating point addition",
crossref = "Traverso:2000:IAU",
pages = "71--77",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p71-collins/p71-collins.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p71-collins/",
acknowledgement = ack-nhfb,
keywords = "FSUM; interval arithmetic; LEDA; MPADD; MPFUN;
polynomial root finding",
}
@InProceedings{Cormier:2000:CGG,
author = "Olivier Cormier and Michael F. Singer and Felix
Ulmer",
title = "Computing the {Galois} group of a polynomial using
linear differential equations",
crossref = "Traverso:2000:IAU",
pages = "78--85",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p78-cormier/p78-cormier.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p78-cormier/",
acknowledgement = ack-nhfb,
}
@InProceedings{Cucker:2000:SPS,
author = "Felipe Cucker",
title = "Solving polynomial systems: a complexity theory
viewpoint",
crossref = "Traverso:2000:IAU",
pages = "??--??",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p-cucker/",
acknowledgement = ack-nhfb,
}
@InProceedings{Dolzmann:2000:LQE,
author = "Andreas Dolzmann and Volker Weispfenning",
title = "Local quantifier elimination",
crossref = "Traverso:2000:IAU",
pages = "86--94",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p86-dolzmann/p86-dolzmann.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p86-dolzmann/",
acknowledgement = ack-nhfb,
}
@InProceedings{Dumas:2000:ISF,
author = "Jean-Guillaume Dumas and B. David Saunders and Gilles
Villard",
title = "Integer {Smith} form via the valence: experience with
large sparse matrices from homology",
crossref = "Traverso:2000:IAU",
pages = "95--105",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p95-dumas/p95-dumas.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p95-dumas/",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:2000:BBF,
author = "Wayne Eberly",
title = "Black box {Frobenius} decompositions over small
fields",
crossref = "Traverso:2000:IAU",
pages = "106--113",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p106-eberly/p106-eberly.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p106-eberly/",
acknowledgement = ack-nhfb,
}
@InProceedings{Fernandez-Ferreiros:2000:MDW,
author = "Pilar Fernandez-Ferreiros and Maria de los Angeles
Gomez-Molleda",
title = "A method for deciding whether the {Galois} group is
abelian",
crossref = "Traverso:2000:IAU",
pages = "114--120",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p114-fernandez-ferreiros/p114-fernandez-ferreiros.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p114-fernandez-ferreiros/",
acknowledgement = ack-nhfb,
}
@InProceedings{Fredet:2000:LDE,
author = "Anne Fredet",
title = "Linear differential equations, iterative logarithms
and orderings on monomial differential extensions",
crossref = "Traverso:2000:IAU",
pages = "121--128",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p121-fredet/p121-fredet.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p121-fredet/",
acknowledgement = ack-nhfb,
}
@InProceedings{Green:2000:CER,
author = "Edward L. Green and Lenwood S. Heath and Craig A.
Struble",
title = "Constructing endomorphism rings via duals",
crossref = "Traverso:2000:IAU",
pages = "129--136",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p129-green/p129-green.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p129-green/",
acknowledgement = ack-nhfb,
}
@InProceedings{Grigoriev:2000:BNV,
author = "Dima Grigoriev and Nicolai Vorobjov",
title = "Bounds on numers of vectors of multiplicities for
polynomials which are easy to compute",
crossref = "Traverso:2000:IAU",
pages = "137--146",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p137-grigoriev/p137-grigoriev.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p137-grigoriev/",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:2000:FPA,
author = "Anshul Gupta and Pankaj Rohatgi and Ramesh Agarwal",
title = "Fast practical algorithms for the
{Boolean-product-witness-matrix} problem",
crossref = "Traverso:2000:IAU",
pages = "146--152",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p146-gupta/p146-gupta.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p146-gupta/",
acknowledgement = ack-nhfb,
}
@InProceedings{Harris:2000:ANM,
author = "Jason Harris",
title = "Advanced notations in {\em Mathematica\/}",
crossref = "Traverso:2000:IAU",
pages = "153--160",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p153-harris/p153-harris.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p153-harris/",
acknowledgement = ack-nhfb,
}
@InProceedings{Holt:2000:CWH,
author = "Derek F. Holt",
title = "Computation in word-hyperbolic groups",
crossref = "Traverso:2000:IAU",
pages = "??--??",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p-holt/",
acknowledgement = ack-nhfb,
}
@InProceedings{Huang:2000:PMP,
author = "Yuzhen Huang and Wenda Wu and Hans J. Stetter and
Lihong Zhi",
title = "Pseudofactors of multivariate polynomials",
crossref = "Traverso:2000:IAU",
pages = "161--168",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p161-huang/p161-huang.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p161-huang/",
acknowledgement = ack-nhfb,
}
@InProceedings{Hur:2000:ERA,
author = "Namhyun Hur and James H. Davenport",
title = "An exact real algebraic arithmetic with equality
determination",
crossref = "Traverso:2000:IAU",
pages = "169--174",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p169-hur/p169-hur.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p169-hur/",
acknowledgement = ack-nhfb,
}
@InProceedings{Ivanyos:2000:FRA,
author = "G{\'a}bor Ivanyos",
title = "Fast randomized algorithms for the structure of matrix
algebras over finite fields (extended abstract)",
crossref = "Traverso:2000:IAU",
pages = "175--183",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p175-ivanyos/p175-ivanyos.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p175-ivanyos/",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeannerod:2000:AEP,
author = "Claude-Pierre Jeannerod",
title = "An algorithm for the eigenvalue perturbation problem:
reduction of a ?-matrix to a {Lidskii} matrix",
crossref = "Traverso:2000:IAU",
pages = "184--191",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p184-jeannerod/",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2000:ETB,
author = "Erich Kaltofen and Wen-shin Lee and Austin A. Lobo",
title = "Early termination in {Ben-Or\slash Tiwari} sparse
interpolation and a hybrid of {Zippel}'s algorithm",
crossref = "Traverso:2000:IAU",
pages = "192--201",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p192-kaltofen/p192-kaltofen.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p192-kaltofen/",
acknowledgement = ack-nhfb,
}
@InProceedings{Landsmann:2000:SPP,
author = "G{\"u}nter Landsmann and Josef Schicho and Franz
Winkler and Erik Hillgarter",
title = "Symbolic parametrization of pipe and canal surfaces",
crossref = "Traverso:2000:IAU",
pages = "202--208",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p202-landsmann/",
acknowledgement = ack-nhfb,
}
@InProceedings{Lecerf:2000:CED,
author = "Gr{\'e}goire Lecerf",
title = "Computing an equidimensional decomposition of an
algebraic variety by means of geometric resolutions",
crossref = "Traverso:2000:IAU",
pages = "209--216",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p209-lecerf/p209-lecerf.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p209-lecerf/",
acknowledgement = ack-nhfb,
}
@InProceedings{Lisonek:2000:MIT,
author = "Petr Lison{\u{e}}k and Robert B. Israel",
title = "Metric invariants of tetrahedra via polynomial
elimination",
crossref = "Traverso:2000:IAU",
pages = "217--219",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p217-lisonek/p217-lisonek.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p217-lisonek/",
acknowledgement = ack-nhfb,
}
@InProceedings{Miyamoto:2000:CNP,
author = "Izumi Miyamoto",
title = "Computing normalizers of permutation groups
efficiently using isomorphisms of association schemes",
crossref = "Traverso:2000:IAU",
pages = "220--224",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p220-miyamoto/p220-miyamoto.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p220-miyamoto/",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:2000:DIB,
author = "Michael B. Monagan and Allan D. Wittkopf",
title = "On the design and implementation of {Brown}'s
algorithm over the integers and number fields",
crossref = "Traverso:2000:IAU",
pages = "225--233",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p225-monagan/p225-monagan.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p225-monagan/",
acknowledgement = ack-nhfb,
}
@InProceedings{Mourrain:2000:SPC,
author = "Bernard Mourrain and Philippe Tr{\'e}buchet",
title = "Solving projective complete intersection faster",
crossref = "Traverso:2000:IAU",
pages = "234--241",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p234-mourrain/p234-mourrain.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p234-mourrain/",
acknowledgement = ack-nhfb,
}
@InProceedings{Mulders:2000:RSS,
author = "Thom Mulders and Arne Storjohann",
title = "Rational solutions of singular linear systems",
crossref = "Traverso:2000:IAU",
pages = "242--249",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p242-mulders/p242-mulders.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p242-mulders/",
acknowledgement = ack-nhfb,
}
@InProceedings{Nocker:2000:SRP,
author = "Michael N{\"o}cker",
title = "Some remarks on parallel exponentiation (extended
abstract)",
crossref = "Traverso:2000:IAU",
pages = "250--257",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/345542/p250-nocker/",
acknowledgement = ack-nhfb,
}
@InProceedings{Norman:2000:FEJ,
author = "Arthur C. Norman",
title = "Further evaluation of {Java} for symbolic
computation",
crossref = "Traverso:2000:IAU",
pages = "258--265",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p258-norman/p258-norman.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p258-norman/",
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}
@InProceedings{Pan:2000:MSP,
author = "Victor Y. Pan",
title = "Matrix structure, polynomial arithmetic, and
erasure-resilient encoding\slash decoding",
crossref = "Traverso:2000:IAU",
pages = "266--271",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p266-pan/",
acknowledgement = ack-nhfb,
}
@InProceedings{Reid:2000:DMS,
author = "Gregory J. Reid and Allan D. Wittkopf",
title = "Determination of maximal symmetry groups of classes of
differential equations",
crossref = "Traverso:2000:IAU",
pages = "272--280",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p272-reid/",
acknowledgement = ack-nhfb,
}
@InProceedings{Reinert:2000:SSL,
author = "Birgit Reinert",
title = "Solving systems of linear one-sided equations in
integer monoid and group rings",
crossref = "Traverso:2000:IAU",
pages = "281--287",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p281-reinert/",
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}
@InProceedings{Rosales:2000:HCI,
author = "Jos{\'e} Carlos Rosales and Pedro A.
Garc{\'\i}a-S{\'a}nchez and Juan Ignacio
Garc{\'\i}a-Garc{\'\i}a",
title = "How to check if a finitely generated commutative
monoid is a principal ideal commutative monoid",
crossref = "Traverso:2000:IAU",
pages = "288--291",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p288-rosales/",
acknowledgement = ack-nhfb,
}
@InProceedings{Schicho:2000:PPS,
author = "Josef Schicho",
title = "Proper parametrization of surfaces with a rational
pencil",
crossref = "Traverso:2000:IAU",
pages = "292--300",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p292-schicho/",
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}
@InProceedings{Zhang:2000:RCC,
author = "Ming Zhang and Ron Goldman",
title = "Rectangular corner cutting and
{Sylvester}-resultants",
crossref = "Traverso:2000:IAU",
pages = "301--308",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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http://www.acm.org/pubs/citations/proceedings/issac/345542/p301-zhang/",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2001:MDI,
author = "Sergei A. Abramov and M. Petkovsek",
title = "Minimal decomposition of indefinite hypergeometric
sums",
crossref = "Mourrain:2001:IJU",
pages = "7--14",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Abramov:2001:SLF,
author = "Sergei A. Abramov and Manuel Bronstein",
title = "On solutions of linear functional systems",
crossref = "Mourrain:2001:IJU",
pages = "1--6",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Adamchik:2001:BF,
author = "V. S. Adamchik",
title = "On the {Barnes} function",
crossref = "Mourrain:2001:IJU",
pages = "15--20",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Aguirre:2001:GIM,
author = "Edith Aguirre and Abdul Salam Jarrah and Reinhard
Laubenbacher",
title = "Generic ideals and {Moreno-Soc{\'\i}as} conjecture",
crossref = "Mourrain:2001:IJU",
pages = "21--23",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Armando:2001:MEP,
author = "Alessandro Armando and Clemens Ballarin",
title = "{Maple}'s evaluation process as constraint contextual
rewriting",
crossref = "Mourrain:2001:IJU",
pages = "32--37",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Boulier:2001:P,
author = "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire and
Marc Moreno Maza",
title = "{PARDI}!",
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pages = "38--47",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Buse:2001:RRP,
author = "Laurent Bus{\'e}",
title = "Residual resultant over the projective plane and the
implicitization problem",
crossref = "Mourrain:2001:IJU",
pages = "48--55",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Caboara:2001:FET,
author = "Massimo Caboara and Lorenzo Robbiano",
title = "Families of estimable terms",
crossref = "Mourrain:2001:IJU",
pages = "56--63",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheng:2001:CAF,
author = "Howard Cheng and George Labahn",
title = "Computing all factorizations in {$\mathbb{Z}_N[x]$}",
crossref = "Mourrain:2001:IJU",
pages = "64--71",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cioffi:2001:CMG,
author = "Francesca Cioffi and Ferruccio Orecchia",
title = "Computation of minimal generators of ideals of fat
points",
crossref = "Mourrain:2001:IJU",
pages = "72--76",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cooperman:2001:SPC,
author = "Gene Cooperman and Victor Grinberg",
title = "Scalable parallel coset enumeration using bulk
definition",
crossref = "Mourrain:2001:IJU",
pages = "77--84",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Corless:2001:TFB,
author = "Robert M. Corless and Mark W. Giesbrecht and Mark van
Hoeij and Ilias S. Kotsireas and Stephen M. Watt",
title = "Towards factoring bivariate approximate polynomials",
crossref = "Mourrain:2001:IJU",
pages = "85--92",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Cormier:2001:LSL,
author = "Olivier Cormier",
title = "On {Liouvillian} solutions of linear differential
equations of order $4$ and $5$",
crossref = "Mourrain:2001:IJU",
pages = "93--100",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DAndrea:2001:HSR,
author = "Carlos D'Andrea and Ioannis Z. Emiris",
title = "Hybrid sparse resultant matrices for bivariate
systems",
crossref = "Mourrain:2001:IJU",
pages = "24--31",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dominguez:2001:MIC,
author = "C{\'e}sar Dom{\'\i}nguez and Julio Rubio",
title = "Modeling inheritance as coercion in a symbolic
computation system",
crossref = "Mourrain:2001:IJU",
pages = "109--115",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dora:2001:HC,
author = "Jean Della Dora and Aude Maignan and Mihaela
Mirica-Ruse and Sergio Yovine",
title = "Hybrid computation",
crossref = "Mourrain:2001:IJU",
pages = "101--108",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Fortuna:2001:CRP,
author = "Elisabetta Fortuna and Patrizia Gianni and Barry
Trager",
title = "Computation of the radical of polynomial ideals over
fields of arbitrary characteristic",
crossref = "Mourrain:2001:IJU",
pages = "116--120",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fortune:2001:PRF,
author = "Steven Fortune",
title = "Polynomial root finding using iterated eigenvalue
computation",
crossref = "Mourrain:2001:IJU",
pages = "121--128",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Foursov:2001:CAC,
author = "Mikhail V. Foursov and Marc Moreno Maza",
title = "On computer-assisted classification of coupled
integrable equations",
crossref = "Mourrain:2001:IJU",
pages = "129--136",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Galligo:2001:SND,
author = "Andr{\'e} Galligo and David Rupprecht",
title = "Semi-numerical determination of irreducible branches
of a reduced space curve",
crossref = "Mourrain:2001:IJU",
pages = "137--142",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gemignani:2001:GGI,
author = "Luca Gemignani",
title = "A generalized {Graeffe}'s iteration for evaluating
polynomials and rational functions",
crossref = "Mourrain:2001:IJU",
pages = "143--149",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Granvilliers:2001:SIC,
author = "Laurent Granvilliers and Eric Monfroy and
Fr{\'e}d{\'e}ric Benhamou",
title = "Symbolic-interval cooperation in constraint
programming",
crossref = "Mourrain:2001:IJU",
pages = "150--166",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Gutierrez:2001:UFT,
author = "Jamie Gutierrez and Rosario Rubio and David Sevilla",
title = "Unirational fields of transcendence degree one and
functional decomposition",
crossref = "Mourrain:2001:IJU",
pages = "167--174",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Hanrot:2001:SRA,
author = "G. Hanrot and F. Morain",
title = "Solvability by radicals from an algorithmic point of
view",
crossref = "Mourrain:2001:IJU",
pages = "175--182",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Hunt:2001:SLR,
author = "Harry B. Hunt and Madhav V. Marathe and Richard E.
Stearns",
title = "Strongly-local reductions and the complexity\slash
efficient approximability of algebra and optimization
on abstract algebraic structures",
crossref = "Mourrain:2001:IJU",
pages = "183--191",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Jinwang:2001:MPI,
author = "Liu Jinwang and Liu Zhuojun and Liu Xiaoqi and Wang
Mingsheng",
title = "The membership problem for ideals of binomial skew
polynomial rings",
crossref = "Mourrain:2001:IJU",
pages = "192--195",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Jurkovic:2001:DCS,
author = "Neven Jurkovic",
title = "Diagnosing and correcting student's misconceptions in
an educational computer algebra system",
crossref = "Mourrain:2001:IJU",
pages = "195--200",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Khanin:2001:DAC,
author = "Raya Khanin",
title = "Dimensional analysis in computer algebra",
crossref = "Mourrain:2001:IJU",
pages = "201--208",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Korelc:2001:HSM,
author = "Joze Korelc",
title = "Hybrid system for multi-language and multi-environment
generation of numerical codes",
crossref = "Mourrain:2001:IJU",
pages = "209--216",
year = "2001",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Mansfield:2001:TAW,
author = "Elizabeth L. Mansfield and Peter E. Hydon",
title = "Towards approximations which preserve integrals",
crossref = "Mourrain:2001:IJU",
pages = "217--222",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{McCallum:2001:PEC,
author = "Scott McCallum",
title = "On propagation of equational constraints in
{CAD}-based quantifier elimination",
crossref = "Mourrain:2001:IJU",
pages = "223--231",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Micciancio:2001:LSA,
author = "Daniele Micciancio and Bogdan Warinschi",
title = "A linear space algorithm for computing the {Hermite}
normal form",
crossref = "Mourrain:2001:IJU",
pages = "231--236",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Mingsheng:2001:RGB,
author = "Wang Mingsheng and Liu Zhuojun",
title = "Remarks on {Gr{\"o}bner} basis for ideals under
composition",
crossref = "Mourrain:2001:IJU",
pages = "237--244",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Mulholland:2001:ATP,
author = "Jamie Mulholland and Michael Monagan",
title = "Algorithms for trigonometric polynomials",
crossref = "Mourrain:2001:IJU",
pages = "245--252",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Pan:2001:UPN,
author = "Victor Y. Pan",
title = "Univariate polynomials: nearly optimal algorithms for
factorization and rootfinding",
crossref = "Mourrain:2001:IJU",
pages = "253--267",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Pericleous:2001:NCB,
author = "Savvas Pericleous and Nicolai Vorobjov",
title = "New complexity bounds for cylindrical decompositions
of sub-{Pfaffian} sets",
crossref = "Mourrain:2001:IJU",
pages = "268--275",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ruatta:2001:MWI,
author = "Olivier Ruatta",
title = "A multivariate {Weierstrass} iterative rootfinder",
crossref = "Mourrain:2001:IJU",
pages = "276--283",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Sasaki:2001:AMP,
author = "Tateaki Sasaki",
title = "Approximate multivariate polynomial factorization
based on zero-sum relations",
crossref = "Mourrain:2001:IJU",
pages = "284--291",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Sato:2001:DCG,
author = "Yosuke Sato and Akira Suzuki",
title = "Discrete comprehensive {Gr{\"o}bner} bases",
crossref = "Mourrain:2001:IJU",
pages = "292--296",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Saunders:2001:BBM,
author = "B. D. Saunders",
title = "Black box methods for least squares problems",
crossref = "Mourrain:2001:IJU",
pages = "297--302",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Sedjelmaci:2001:PLE,
author = "Sidi Mohammed Sedjelmaci",
title = "On a parallel {Lehmer--Euclid GCD} algorithm",
crossref = "Mourrain:2001:IJU",
pages = "303--308",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Sedoglavic:2001:PAT,
author = "Alexandre Sedoglavic",
title = "A probabilistic algorithm to test local algebraic
observability in polynomial time",
crossref = "Mourrain:2001:IJU",
pages = "309--317",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Sendra:2001:CDR,
author = "J. Rafael Sendra and Franz Winkler",
title = "Computation of the degree of rational maps between
curves",
crossref = "Mourrain:2001:IJU",
pages = "317--322",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Thome:2001:FCL,
author = "Emmanuel Thom{\'e}",
title = "Fast computation of linear generators for matrix
sequences and application to the block {Wiedemann}
algorithm",
crossref = "Mourrain:2001:IJU",
pages = "323--331",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:2001:ITF,
author = "Joachim von zur Gathen",
title = "Irreducible trinomials over finite fields",
crossref = "Mourrain:2001:IJU",
pages = "332--336",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Wang:2001:IAP,
author = "P. Wang and S. Gray and N. Kajler and D. Lin and W.
Liao and X. Zou",
title = "{IAMC} architecture and prototyping: a progress
report",
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pages = "337--344",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Zima:2001:CPC,
author = "Eugene V. Zima",
title = "On computational properties of chains of recurrences",
crossref = "Mourrain:2001:IJU",
pages = "345--345",
year = "2001",
bibdate = "Wed May 15 14:28:03 MDT 2002",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Abramov:2002:AZA,
author = "S. A. Abramov",
title = "Applicability of {Zeilberger}'s algorithm to
hypergeometric terms",
crossref = "Mora:2002:IPI",
pages = "1--7",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Beckermann:2002:FFR,
author = "Bernhard Beckermann and Howard Cheng and George
Labahn",
title = "Fraction-free row reduction of matrices of skew
polynomials",
crossref = "Mora:2002:IPI",
pages = "8--15",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bradford:2002:TBS,
author = "Russell Bradford and James H. Davenport",
title = "Towards better simplification of elementary
functions",
crossref = "Mora:2002:IPI",
pages = "16--22",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Bronstein:2002:SLO,
author = "Manuel Bronstein and S{\'e}bastien Lafaille",
title = "Solutions of linear ordinary differential equations in
terms of special functions",
crossref = "Mora:2002:IPI",
pages = "23--28",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chtcherba:2002:EOD,
author = "Arthur D. Chtcherba and Deepak Kapur",
title = "On the efficiency and optimality of {Dixon}-based
resultant methods",
crossref = "Mora:2002:IPI",
pages = "29--36",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Corless:2002:GNA,
author = "Robert M. Corless and Andr{\'e} Galligo and Ilias S.
Kotsireas and Stephen M. Watt",
title = "A geometric-numeric algorithm for absolute
factorization of multivariate polynomials",
crossref = "Mora:2002:IPI",
pages = "37--45",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Dickenstein:2002:MRM,
author = "Alicia Dickenstein and Ioannis Z. Emiris",
title = "Multihomogeneous resultant matrices",
crossref = "Mora:2002:IPI",
pages = "46--54",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dooley:2002:EMC,
author = "Samuel S. Dooley",
title = "Editing mathematical content and presentation markup
in interactive mathematical documents",
crossref = "Mora:2002:IPI",
pages = "55--62",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Dumas:2002:FFL,
author = "Jean Guillaume Dumas and Thierry Gautier and
Cl{\'e}ment Pernet",
title = "Finite field linear algebra subroutines",
crossref = "Mora:2002:IPI",
pages = "63--74",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2002:NEA,
author = "Jean Charles Faug{\`e}re",
title = "A new efficient algorithm for computing {Gr{\"o}bner}
bases without reduction to zero {$(F_5)$}",
crossref = "Mora:2002:IPI",
pages = "75--83",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Fernandez-Ferreiros:2002:PSR,
author = "P. Fernandez-Ferreiros and M. A. Gomez-Molleda and L.
Gonzalez-Vega",
title = "Partial solvability by radicals",
crossref = "Mora:2002:IPI",
pages = "84--91",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Fortuna:2002:CTR,
author = "Elisabetta Fortuna and Patrizia Gianni and Paola
Parenti and Carlo Traverso",
title = "Computing the topology of real algebraic surfaces",
crossref = "Mora:2002:IPI",
pages = "92--100",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:2002:ACS,
author = "Mark Giesbrecht and Erich Kaltofen and Wen-shin Lee",
title = "Algorithms for computing the sparsest shifts of
polynomials via the {Berlekamp\slash Massey}
algorithm",
crossref = "Mora:2002:IPI",
pages = "101--108",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hoeij:2002:MGA,
author = "Mark van Hoeij and Michael Monagan",
title = "A modular {GCD} algorithm over number fields presented
with multiple extensions",
crossref = "Mora:2002:IPI",
pages = "109--116",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hoeven:2002:NZT,
author = "Joris van der Hoeven",
title = "A new zero-test for formal power series",
crossref = "Mora:2002:IPI",
pages = "117--122",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hossain:2002:SIC,
author = "Shahadat Hossain and Trond Steihaug",
title = "Sparsity issues in the computation of {Jacobian}
matrices",
crossref = "Mora:2002:IPI",
pages = "123--130",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeannerod:2002:RFP,
author = "Claude Pierre Jeannerod",
title = "A reduced form for perturbed matrix polynomials",
crossref = "Mora:2002:IPI",
pages = "131--137",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2002:OSV,
author = "Erich Kaltofen",
title = "An output-sensitive variant of the baby steps\slash
giant steps determinant algorithm",
crossref = "Mora:2002:IPI",
pages = "138--144",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Khetan:2002:DFC,
author = "Amit Khetan",
title = "Determinantal formula for the chow form of a toric
surface",
crossref = "Mora:2002:IPI",
pages = "145--150",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kogan:2002:CCF,
author = "Irina A. Kogan and Marc Moreno Maza",
title = "Computation of canonical forms for ternary cubics",
crossref = "Mora:2002:IPI",
pages = "151--160",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Le:2002:SDS,
author = "Ha Le",
title = "Simplification of definite sums of rational functions
by creative symmetrizing method",
crossref = "Mora:2002:IPI",
pages = "161--167",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Li:2002:FZD,
author = "Ziming Li and Fritz Schwarz and Serguei P. Tsarev",
title = "Factoring zero-dimensional ideals of linear partial
differential operators",
crossref = "Mora:2002:IPI",
pages = "168--175",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Luks:2002:PTN,
author = "Eugene M. Luks and Takunari Miyazaki",
title = "Polynomial-time normalizers for permutation groups
with restricted composition factors",
crossref = "Mora:2002:IPI",
pages = "176--183",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Matera:2002:DHF,
author = "Guillermo Matera and Alexandre Sedoglavic",
title = "The differential {Hilbert} function of a differential
rational mapping can be computed in polynomial time",
crossref = "Mora:2002:IPI",
pages = "184--191",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Nagasaka:2002:TCI,
author = "Kosaku Nagasaka",
title = "Towards certified irreducibility testing of bivariate
approximate polynomials",
crossref = "Mora:2002:IPI",
pages = "192--199",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Noro:2002:YAP,
author = "Masayuki Noro and Kazuhiro Yokoyama",
title = "Yet another practical implementation of polynomial
factorization over finite fields",
crossref = "Mora:2002:IPI",
pages = "200--206",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2002:AEA,
author = "Victor Y. Pan and Xinmao Wang",
title = "Acceleration of {Euclidean} algorithm and extensions",
crossref = "Mora:2002:IPI",
pages = "207--213",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Richardson:2002:SOF,
author = "Daniel Richardson and Simon Langley",
title = "Some observations on familiar numbers",
crossref = "Mora:2002:IPI",
pages = "214--220",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rioboo:2002:TFR,
author = "Renaud Rioboo",
title = "Towards faster real algebraic numbers",
crossref = "Mora:2002:IPI",
pages = "221--228",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schicho:2002:SSP,
author = "Josef Schicho",
title = "Simplification of surface parametrizations",
crossref = "Mora:2002:IPI",
pages = "229--237",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schost:2002:DBL,
author = "{\'E}ric Schost",
title = "Degree bounds and lifting techniques for triangular
sets",
crossref = "Mora:2002:IPI",
pages = "238--245",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Storjohann:2002:HOL,
author = "Arne Storjohann",
title = "High-order lifting",
crossref = "Mora:2002:IPI",
pages = "246--254",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Suzuki:2002:AAC,
author = "Akira Suzuki and Yosuke Sato",
title = "An alternative approach to comprehensive {Gr{\"o}bner}
bases",
crossref = "Mora:2002:IPI",
pages = "255--261",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Traverso:2002:NSS,
author = "Carlo Traverso and Alberto Zanoni",
title = "Numerical stability and stabilization of {Gr{\"o}bner}
basis computation",
crossref = "Mora:2002:IPI",
pages = "262--269",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Weispfenning:2002:CCG,
author = "Volker Weispfenning",
title = "Canonical comprehensive {Gr{\"o}bner} bases",
crossref = "Mora:2002:IPI",
pages = "270--276",
year = "2002",
bibdate = "Sat Dec 13 18:13:15 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2003:RCF,
author = "S. A. Abramov and H. Q. Le and M. Petkov{\v{s}}ek",
title = "Rational canonical forms and efficient representations
of hypergeometric terms",
crossref = "Senda:2003:IPI",
pages = "7--14",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Aroca:2003:PSS,
author = "F. Aroca and J. Cano and F. Jung",
title = "Power series solutions for non-linear {PDE}'s",
crossref = "Senda:2003:IPI",
pages = "15--22",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barnett:2003:CCA,
author = "Michael P. Barnett",
title = "Chemistry and computer algebra: past, present,
future",
crossref = "Senda:2003:IPI",
pages = "1--2",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Basiri:2003:COG,
author = "Abdolali Basiri and Jean-Charles Faug{\`e}re",
title = "Changing the ordering of {Gr{\"o}bner} bases with
{LLL}: case of two variables",
crossref = "Senda:2003:IPI",
pages = "23--29",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beaumont:2003:BSE,
author = "James Beaumont and Russell Bradford and James H.
Davenport",
title = "Better simplification of elementary functions through
power series",
crossref = "Senda:2003:IPI",
pages = "30--36",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2003:TPP,
author = "A. Bostan and G. Lecerf and {\'E}. Schost",
title = "{Tellegen}'s principle into practice",
crossref = "Senda:2003:IPI",
pages = "37--44",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Boucher:2003:FOL,
author = "Delphine Boucher and Philippe Gaillard and Felix
Ulmer",
title = "Fourth order linear differential equations with
imprimitive group",
crossref = "Senda:2003:IPI",
pages = "45--49",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
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}
@InProceedings{Chapman:2003:EAA,
author = "Frederick W. Chapman",
title = "An elementary algorithm for the automatic derivation
and proof of tensor product identities via computer
algebra",
crossref = "Senda:2003:IPI",
pages = "50--57",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cluzeau:2003:FDS,
author = "Thomas Cluzeau",
title = "Factorization of differential systems in
characteristic {\em p\/}",
crossref = "Senda:2003:IPI",
pages = "58--65",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cooperman:2003:MBD,
author = "Gene Cooperman and Eric Robinson",
title = "Memory-based and disk-based algorithms for very high
degree permutation groups",
crossref = "Senda:2003:IPI",
pages = "66--73",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Datta:2003:UCA,
author = "Ruchira S. Datta",
title = "Using computer algebra to find {Nash} equilibria",
crossref = "Senda:2003:IPI",
pages = "74--79",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Din:2003:PVC,
author = "Mohab Safey El Din and {\'E}ric Schost",
title = "Polar varieties and computation of one point in each
connected component of a smooth real algebraic set",
crossref = "Senda:2003:IPI",
pages = "224--231",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:2003:ETS,
author = "Wayne Eberly",
title = "Early termination over small fields",
crossref = "Senda:2003:IPI",
pages = "80--87",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fateman:2003:CCR,
author = "Richard J. Fateman and Raymond Toy",
title = "Converting call-by-reference to call-by-value:
{Fortran} and {Lisp} coexisting",
crossref = "Senda:2003:IPI",
pages = "95--102",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fateman:2003:HLP,
author = "Richard Fateman",
title = "High-level proofs of mathematical programs using
automatic differentiation, simplification, and some
common sense",
crossref = "Senda:2003:IPI",
pages = "88--94",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fredet:2003:FLD,
author = "Anne Fredet",
title = "Factorization of linear differential operators in
exponential extensions",
crossref = "Senda:2003:IPI",
pages = "103--110",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Geddes:2003:EFH,
author = "Keith O. Geddes and Wei Wei Zheng",
title = "Exploiting fast hardware floating point in high
precision computation",
crossref = "Senda:2003:IPI",
pages = "111--118",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gerhard:2003:SDP,
author = "J. Gerhard and M. Giesbrecht and A. Storjohann and E.
V. Zima",
title = "Shiftless decomposition and polynomial-time rational
summation",
crossref = "Senda:2003:IPI",
pages = "119--126",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:2003:FDO,
author = "Mark Giesbrecht and Yang Zhang",
title = "Factoring and decomposing {{\O}re} polynomials over
{$\mathcal{F}_q(t)$}",
crossref = "Senda:2003:IPI",
pages = "127--134",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giorgi:2003:CPM,
author = "Pascal Giorgi and Claude-Pierre Jeannerod and Gilles
Villard",
title = "On the complexity of polynomial matrix computations",
crossref = "Senda:2003:IPI",
pages = "135--142",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hoeven:2003:RMU,
author = "Joris van der Hoeven",
title = "Relaxed multiplication using the middle product",
crossref = "Senda:2003:IPI",
pages = "143--147",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hubert:2003:CPS,
author = "E. Hubert and N. Le Roux",
title = "Computing power series solutions of a nonlinear {PDE}
system",
crossref = "Senda:2003:IPI",
pages = "148--155",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hulpke:2003:TOS,
author = "Alexander Hulpke and Steve Linton",
title = "Total ordering on subgroups and cosets",
crossref = "Senda:2003:IPI",
pages = "156--160",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2003:AIP,
author = "Erich Kaltofen and John May",
title = "On approximate irreducibility of polynomials in
several variables",
crossref = "Senda:2003:IPI",
pages = "161--168",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2003:PFS,
author = "Erich Kaltofen",
title = "Polynomial factorization: a success story",
crossref = "Senda:2003:IPI",
pages = "3--4",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Koepf:2003:PSB,
author = "Wolfram Koepf",
title = "Power series, {Bieberbach} conjecture and the {de
Branges} and {Weinstein} functions",
crossref = "Senda:2003:IPI",
pages = "169--175",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Laubenbacher:2003:CAA,
author = "Reinhard Laubenbacher",
title = "A computer algebra approach to biological systems",
crossref = "Senda:2003:IPI",
pages = "5--6",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Levandovskyy:2003:PCA,
author = "Viktor Levandovskyy and Hans Sch{\"o}nemann",
title = "Plural: a computer algebra system for noncommutative
polynomial algebras",
crossref = "Senda:2003:IPI",
pages = "176--183",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mansfield:2003:ETD,
author = "E. L. Mansfield and A. Szanto",
title = "Elimination theory for differential difference
polynomials",
crossref = "Senda:2003:IPI",
pages = "191--198",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{McCallum:2003:OIB,
author = "Scott McCallum",
title = "On order-invariance of a binomial over a nullifying
cell",
crossref = "Senda:2003:IPI",
pages = "184--190",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Meunier:2003:EAG,
author = "Ludovic Meunier and Bruno Salvy",
title = "{ESF}: an automatically generated encyclopedia of
special functions",
crossref = "Senda:2003:IPI",
pages = "199--206",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Minimair:2003:FSR,
author = "Manfred Minimair",
title = "Factoring sparse resultants of linearly combined
polynomials",
crossref = "Senda:2003:IPI",
pages = "207--214",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Reid:2003:CSN,
author = "Greg Reid and Jianliang Tang and Lihong Zhi",
title = "A complete symbolic-numeric linear method for camera
pose determination",
crossref = "Senda:2003:IPI",
pages = "215--223",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sasaki:2003:SCC,
author = "Tateaki Sasaki",
title = "The subresultant and clusters of close roots",
crossref = "Senda:2003:IPI",
pages = "232--239",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Seidl:2003:GPO,
author = "Andreas Seidl and Thomas Sturm",
title = "A generic projection operator for partial cylindrical
algebraic decomposition",
crossref = "Senda:2003:IPI",
pages = "240--247",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shaska:2003:DAG,
author = "Tanush Shaska",
title = "Determining the automorphism group of a hyperelliptic
curve",
crossref = "Senda:2003:IPI",
pages = "248--254",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Vollmer:2003:NHB,
author = "Ulrich Vollmer",
title = "A note on the {Hermite} basis computation of large
integer matrices",
crossref = "Senda:2003:IPI",
pages = "255--257",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2003:WTW,
author = "Paul S. Wang and Norbert Kajler and Yi Zhou and Xiao
Zou",
title = "{WME}: towards a {Web for Mathematics Education}",
crossref = "Senda:2003:IPI",
pages = "258--265",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zeng:2003:MCM,
author = "Zhonggang Zeng",
title = "A method computing multiple roots of inexact
polynomials",
crossref = "Senda:2003:IPI",
pages = "266--272",
year = "2003",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Aruliah:2004:NPA,
author = "D. A. Aruliah and Robert M. Corless",
title = "Numerical parameterization of affine varieties using",
crossref = "Gutierrez:2004:IJU",
pages = "12--18",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bayer:2004:ODO,
author = "Thomas Bayer",
title = "Optimal descriptions of orbit spaces and strata of
finite groups",
crossref = "Gutierrez:2004:IJU",
pages = "19--26",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beaumont:2004:PAA,
author = "James C. Beaumont and Russell J. Bradford and James H.
Davenport and Nalina Phisanbut",
title = "A poly-algorithmic approach to simplifying elementary
functions",
crossref = "Gutierrez:2004:IJU",
pages = "27--34",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bodnar:2004:EDR,
author = "G{\'a}bor Bodn{\'a}r",
title = "Efficient desingularization of reducible algebraic
sets",
crossref = "Gutierrez:2004:IJU",
pages = "35--41",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2004:CIB,
author = "A. Bostan and G. Lecerf and B. Salvy and {\'E}. Schost
and B. Wiebelt",
title = "Complexity issues in bivariate polynomial
factorization",
crossref = "Gutierrez:2004:IJU",
pages = "42--49",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brunat:2004:CIF,
author = "Josep M. Brunat and Antonio Montes",
title = "The characteristic ideal of a finite, connected,
regular graph",
crossref = "Gutierrez:2004:IJU",
pages = "50--57",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Burger:2004:CFS,
author = "Reinhold Burger and George Labahn and Mark van Hoeij",
title = "Closed form solutions of linear {ODEs} having elliptic
function coefficients",
crossref = "Gutierrez:2004:IJU",
pages = "58--64",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Buse:2004:IPH,
author = "Laurent Bus{\'e} and Carlos D'Andrea",
title = "Inversion of parameterized hypersurfaces by means of
subresultants",
crossref = "Gutierrez:2004:IJU",
pages = "65--71",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Carette:2004:UES,
author = "Jacques Carette",
title = "Understanding expression simplification",
crossref = "Gutierrez:2004:IJU",
pages = "72--79",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chan:2004:NLS,
author = "L. Chan and E. S. Cheb-Terrab",
title = "Non-{Liouvillian} solutions for second order linear
{ODEs}",
crossref = "Gutierrez:2004:IJU",
pages = "80--86",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheze:2004:APF,
author = "Guillaume Ch{\`e}ze",
title = "Absolute polynomial factorization in two variables and
the knapsack problem",
crossref = "Gutierrez:2004:IJU",
pages = "87--94",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chtcherba:2004:SHR,
author = "Arthur D. Chtcherba and Deepak Kapur",
title = "Support hull: relating the {Cayley--Dixon} resultant
constructions to the support of a polynomial system",
crossref = "Gutierrez:2004:IJU",
pages = "95--102",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dahan:2004:SET,
author = "Xavier Dahan and {\'E}ric Schost",
title = "Sharp estimates for triangular sets",
crossref = "Gutierrez:2004:IJU",
pages = "103--110",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dolzmann:2004:EPO,
author = "Andreas Dolzmann and Andreas Seidl and Thomas Sturm",
title = "Efficient projection orders for {CAD}",
crossref = "Gutierrez:2004:IJU",
pages = "111--118",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dumas:2004:FFF,
author = "Jean-Guillaume Dumas and Pascal Giorgi and Cl{\'e}ment
Pernet",
title = "{FFPACK}: finite field linear algebra package",
crossref = "Gutierrez:2004:IJU",
pages = "119--126",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:2004:RKB,
author = "Wayne Eberly",
title = "Reliable {Krylov}-based algorithms for matrix null
space and rank",
crossref = "Gutierrez:2004:IJU",
pages = "127--134",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Elkadi:2004:PSH,
author = "Mohamed Elkadi and Andr{\'e} Galligo and Thi Ha
L{\^e}",
title = "Parametrized surfaces in huge {$P^3$} of bidegree
$(1,2)$",
crossref = "Gutierrez:2004:IJU",
pages = "141--148",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eriksson:2004:TIH,
author = "Nicholas Eriksson",
title = "Toric ideals of homogeneous phylogenetic models",
crossref = "Gutierrez:2004:IJU",
pages = "149--154",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Feng:2004:RGS,
author = "Ruyong Feng and Xiao-shan Gao",
title = "Rational general solutions of algebraic ordinary
differential equations",
crossref = "Gutierrez:2004:IJU",
pages = "155--162",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Frandsen:2004:RSE,
author = "Gudmund S. Frandsen and Igor E. Shparlinski",
title = "On reducing a system of equations to a single
equation",
crossref = "Gutierrez:2004:IJU",
pages = "163--166",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gao:2004:AFM,
author = "Shuhong Gao and Erich Kaltofen and John May and
Zhengfeng Yang and Lihong Zhi",
title = "Approximate factorization of multivariate polynomials
via differential equations",
crossref = "Gutierrez:2004:IJU",
pages = "167--174",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gao:2004:DDP,
author = "Xiao-Shan Gao and Mingbo Zhang",
title = "Decomposition of differential polynomials with
constant coefficients",
crossref = "Gutierrez:2004:IJU",
pages = "175--182",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Geddes:2004:DRN,
author = "Keith Geddes and Ha Le and Ziming Li",
title = "Differential rational normal forms and a reduction
algorithm for hyperexponential func",
crossref = "Gutierrez:2004:IJU",
pages = "183--190",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Houari:2004:ARC,
author = "Hassan El Houari and M'hammed El Kahoui",
title = "Algorithms for recognizing coordinates in two
variables over {UFD}'s",
crossref = "Gutierrez:2004:IJU",
pages = "135--140",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hubert:2004:ITD,
author = "Evelyne Hubert",
title = "Improvements to a triangulation-decomposition
algorithm for ordinary differential systems in higher
degree cases",
crossref = "Gutierrez:2004:IJU",
pages = "191--198",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2004:CPP,
author = "Manuel Kauers",
title = "Computer proofs for polynomial identities in arbitrary
many variables",
crossref = "Gutierrez:2004:IJU",
pages = "199--204",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Khetan:2004:SRB,
author = "Amit Khetan and Ning Song and Ron Goldman",
title = "{Sylvester}-resultants for bivariate polynomials with
planar {Newton} polygons",
crossref = "Gutierrez:2004:IJU",
pages = "205--212",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Labahn:2004:HSF,
author = "George Labahn and Ziming Li",
title = "Hyperexponential solutions of finite-rank ideals in
orthogonal {{\O}re} rings",
crossref = "Gutierrez:2004:IJU",
pages = "213--220",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2004:SCH,
author = "Hongbo Li",
title = "Symbolic computation in the homogeneous geometric
model with {Clifford} algebra",
crossref = "Gutierrez:2004:IJU",
pages = "221--228",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Linton:2004:FSI,
author = "Steve Linton",
title = "Finding the smallest image of a set",
crossref = "Gutierrez:2004:IJU",
pages = "229--234",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Milowski:2004:CII,
author = "R. Alexander Milowski",
title = "Computing irredundant irreducible decompositions of
large scale monomial ideals",
crossref = "Gutierrez:2004:IJU",
pages = "235--242",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:2004:MQR,
author = "Michael Monagan",
title = "Maximal quotient rational reconstruction: an almost
optimal algorithm for rational reconstruction",
crossref = "Gutierrez:2004:IJU",
pages = "243--249",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Orden:2004:PNC,
author = "David Orden and Francisco Santos",
title = "The polytope of non-crossing graphs on a planar point
set",
crossref = "Gutierrez:2004:IJU",
pages = "250--257",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Parrilo:2004:SSP,
author = "Pablo A. Parrilo",
title = "Sums of squares of polynomials and their
applications",
crossref = "Gutierrez:2004:IJU",
pages = "1--1",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Recio:2004:HU,
author = "Tomas Recio and J. Rafael Sendra and Carlos
Villarino",
title = "From hypercircles to units",
crossref = "Gutierrez:2004:IJU",
pages = "258--265",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rodriguez-Carbonell:2004:AGP,
author = "Enric Rodr{\'\i}guez-Carbonell and Deepak Kapur",
title = "Automatic Generation of Polynomial Loop Invariants:
Algebraic Foundations",
crossref = "Gutierrez:2004:IJU",
pages = "266--273",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Salem:2004:FPP,
author = "Fatima Abu Salem and Shuhong Gao and Alan G. B.
Lauder",
title = "Factoring polynomials via polytopes",
crossref = "Gutierrez:2004:IJU",
pages = "4--11",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Santos:2004:TPA,
author = "Francisco Santos",
title = "Triangulations of polytopes and algebraic geometry",
crossref = "Gutierrez:2004:IJU",
pages = "2--2",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Saunders:2004:SNF,
author = "David Saunders and Zhendong Wan",
title = "{Smith Normal Form} of dense integer matrices fast
algorithms into practice",
crossref = "Gutierrez:2004:IJU",
pages = "274--281",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schneider:2004:SSS,
author = "Carsten Schneider",
title = "Symbolic summation with single-nested sum extensions",
crossref = "Gutierrez:2004:IJU",
pages = "282--289",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderHoeven:2004:TFT,
author = "Joris van der Hoeven",
title = "The truncated {Fourier} transform and applications",
crossref = "Gutierrez:2004:IJU",
pages = "290--296",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2004:APG,
author = "Mark van Hoeij and Michael Monagan",
title = "Algorithms for polynomial {GCD} computation over
algebraic function fields",
crossref = "Gutierrez:2004:IJU",
pages = "297--304",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Verschelde:2004:NAG,
author = "Jan Verschelde",
title = "Numerical algebraic geometry and symbolic
computation",
crossref = "Gutierrez:2004:IJU",
pages = "3--3",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yang:2004:EME,
author = "Michael Yang and Richard Fateman",
title = "Extracting mathematical expressions from {PostScript}
documents",
crossref = "Gutierrez:2004:IJU",
pages = "305--311",
year = "2004",
DOI = "https://doi.org/10.1145/1005285.1005329",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.ocf.berkeley.edu/~mlyang/papers/MichaelYangPsmath.pdf",
abstract = "Full-text indexing of documents containing mathematics
cannot be considered a complete success unless the
mathematics symbolism is extracted and represented in a
standardized form permitting both searching for
formulas, and re-use of this information in (for
example) computer algebra systems. Most documents
produced in the past and subsequently digitally
encoded, and even most of those potentially ``born
digital'' in current journal production are---at
best---encoded in a printer form such as Adobe
Postscript [1], in which mathematics is not explicitly
marked or easily identifiable. While one might look
forward in the future to other document encodings such
as MathML, the common journal or textbook product is
essentially without semantic content: a jumble of odd
characters. Sometimes it is just a jumble of black and
white dots! In this paper we demonstrate an approach to
decoding, to recognizing and extracting mathematical
expressions, from a Postscript document. We can produce
a syntactic representation of the extracted expressions
which can then be used to generate various forms. For
example, if we extract TeX or Presentation MathML, we
can re-typeset the expression, but perhaps in a
different size or font family. More significantly, if
we start from this presentation information, we can
hope to combine it with additional contextual
processing of the surrounding text and meta-data
associated with the document, to assign semantics,(e.g.
content MathML), or provide versions in computer
algebra system languages such as Maple or Mathematica.
Finally, it is possible to use this material to present
audio or braille versions of mathematics for the
visually disabled. We have previously addressed some
aspects of the higher level of processing (parsing TeX
for example). In this paper we address the only first
stage and concentrate on what may seem to be overly
simple, but is in fact difficult to do precisely:
extracting the mathematics parts from text.",
acknowledgement = ack-nhfb,
}
@InProceedings{Yokoyama:2004:SAE,
author = "Kazuhiro Yokoyama",
title = "On systems of algebraic equations with parametric
exponents",
crossref = "Gutierrez:2004:IJU",
pages = "312--319",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zeng:2004:AGI,
author = "Zhonggang Zeng and Barry H. Dayton",
title = "The approximate {GCD} of inexact polynomials",
crossref = "Gutierrez:2004:IJU",
pages = "320--327",
year = "2004",
bibdate = "Fri Oct 21 06:52:53 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2005:GAA,
author = "S. A. Abramov and M. Petkov{\v{s}}sek",
title = "{Gosper}'s algorithm, accurate summation, and the
discrete {Newton--Leibniz} formula",
crossref = "Kauers:2005:IJB",
pages = "5--12",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Adams:2005:SSR,
author = "Jeffrey Adams and B. David Saunders and Zhendong Wan",
title = "Signature of symmetric rational matrices and the
unitary dual of {Lie} groups",
crossref = "Kauers:2005:IJB",
pages = "13--20",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Anai:2005:SRP,
author = "Hirokazu Anai and Shinji Hara and Kazuhiro Yokoyama",
title = "Sum of roots with positive real parts",
crossref = "Kauers:2005:IJB",
pages = "21--28",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Aroca:2005:AGS,
author = "J. M. Aroca and J. Cano and R. Feng and X. S. Gao",
title = "Algebraic general solutions of algebraic ordinary
differential equations",
crossref = "Kauers:2005:IJB",
pages = "29--36",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beaumont:2005:ABT,
author = "James C. Beaumont and Russell J. Bradford and James H.
Davenport and Nalina Phisanbut",
title = "Adherence is better than adjacency: computing the
{Riemann} index using {CAD}",
crossref = "Kauers:2005:IJB",
pages = "37--44",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2005:FAP,
author = "Alin Bostan and Thomas Cluzeau and Bruno Salvy",
title = "Fast algorithms for polynomial solutions of linear
differential equations",
crossref = "Kauers:2005:IJB",
pages = "45--52",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Boucher:2005:NCI,
author = "Delphine Boucher",
title = "Non complete integrability of a magnetic satellite in
circular orbit",
crossref = "Kauers:2005:IJB",
pages = "53--60",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bretto:2005:SSG,
author = "Alain Bretto and Luc Gillibert and Bernard Laget",
title = "Symmetric and semisymmetric graphs construction using
{G}-graphs",
crossref = "Kauers:2005:IJB",
pages = "61--67",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bronstein:2005:PVE,
author = "Manuel Bronstein and Ziming Li and Min Wu",
title = "Picard--Vessiot extensions for linear functional
systems",
crossref = "Kauers:2005:IJB",
pages = "68--75",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brown:2005:UBE,
author = "Christopher W. Brown and Scott McCallum",
title = "On using bi-equational constraints in {CAD}
construction",
crossref = "Kauers:2005:IJB",
pages = "76--83",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Buchberger:2005:VFS,
author = "Bruno Buchberger",
title = "A view on the future of symbolic computation",
crossref = "Kauers:2005:IJB",
pages = "1--1",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Carvajal:2005:HSN,
author = "Orlando A. Carvajal and Frederick W. Chapman and Keith
O. Geddes",
title = "Hybrid symbolic-numeric integration in multiple
dimensions via tensor-product series",
crossref = "Kauers:2005:IJB",
pages = "84--91",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2005:BBC,
author = "Zhuliang Chen and Arne Storjohann",
title = "A {BLAS} based {C} library for exact linear algebra on
integer matrices",
crossref = "Kauers:2005:IJB",
pages = "92--99",
year = "2005",
DOI = "https://doi.org/10.1145/1073884.1073899",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algorithms for solving linear systems of equations
over the integers are designed and implemented. The
implementations are based on the highly optimized and
portable ATLAS/BLAS library for numerical linear
algebra and the GNU Multiple Precision library (GMP)
for large integer arithmetic.",
acknowledgement = ack-nhfb,
}
@InProceedings{Costermans:2005:SAE,
author = "C. Costermans and J. Y. Enjalbert and Hoang Ngoc Minh
and M. Petitot",
title = "Structure and asymptotic expansion of multiple
harmonic sums",
crossref = "Kauers:2005:IJB",
pages = "100--107",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dahan:2005:LTT,
author = "Xavier Dahan and Marc Moreno Maza and Eric Schost and
Wenyuan Wu and Yuzhen Xie",
title = "Lifting techniques for triangular decompositions",
crossref = "Kauers:2005:IJB",
pages = "108--115",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dayton:2005:CMS,
author = "Barry H. Dayton and Zhonggang Zeng",
title = "Computing the multiplicity structure in solving
polynomial systems",
crossref = "Kauers:2005:IJB",
pages = "116--123",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{deKleine:2005:ANM,
author = "Jennifer de Kleine and Michael Monagan and Allan
Wittkopf",
title = "Algorithms for the non-monic case of the sparse
modular {GCD} algorithm",
crossref = "Kauers:2005:IJB",
pages = "124--131",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Deng:2005:CBR,
author = "Jiansong Deng and Falai Chen and Liyong Shen",
title = "Computing {$\mu$}-bases of rational curves and
surfaces using polynomial matrix factorization",
crossref = "Kauers:2005:IJB",
pages = "132--139",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dumas:2005:ECC,
author = "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and
Zhendong Wan",
title = "Efficient computation of the characteristic
polynomial",
crossref = "Kauers:2005:IJB",
pages = "140--147",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Galligo:2005:SBB,
author = "Andr{\'e} Galligo and Jean Pascal Pavone",
title = "Selfintersections of a {B{\'e}zier} bicubic surface",
crossref = "Kauers:2005:IJB",
pages = "148--155",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gerhold:2005:PPS,
author = "Stefan Gerhold and Manuel Kauers",
title = "A procedure for proving special function inequalities
involving a discrete parameter",
crossref = "Kauers:2005:IJB",
pages = "156--162",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Grigoriev:2005:GLD,
author = "Dima Grigoriev and Fritz Schwarz",
title = "Generalized {Loewy}-decomposition of $d$-modules",
crossref = "Kauers:2005:IJB",
pages = "163--170",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hitz:2005:CNS,
author = "Markus A. Hitz",
title = "On computing nearest singular {Hankel} matrices",
crossref = "Kauers:2005:IJB",
pages = "171--176",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hovinen:2005:RBL,
author = "Bradford Hovinen and Wayne Eberly",
title = "A reliable block {Lanczos} algorithm over small finite
fields",
crossref = "Kauers:2005:IJB",
pages = "177--184",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Huang:2005:SPS,
author = "Fangjian Huang and Shengli Chen",
title = "{Schur} partition for symmetric ternary forms and
readable proof to inequalities",
crossref = "Kauers:2005:IJB",
pages = "185--192",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeffrey:2005:ATA,
author = "D. J. Jeffrey and Pratibha and K. B. Roach",
title = "Affine transformations of algebraic numbers",
crossref = "Kauers:2005:IJB",
pages = "193--199",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Johnson:2005:AAC,
author = "Jeremy R. Johnson and Werner Krandick and Anatole D.
Ruslanov",
title = "Architecture-aware classical {Taylor} shift by $1$",
crossref = "Kauers:2005:IJB",
pages = "200--207",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2005:CFB,
author = "Erich Kaltofen and Pascal Koiran",
title = "On the complexity of factoring bivariate supersparse
(Lacunary) polynomials",
crossref = "Kauers:2005:IJB",
pages = "208--215",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2005:GMM,
author = "Erich Kaltofen and Dmitriy Morozov and George Yuhasz",
title = "Generic matrix multiplication and memory management in
{linBox}",
crossref = "Kauers:2005:IJB",
pages = "216--223",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2005:EAS,
author = "Biao Li and Yong Chen and Qi Wang",
title = "Exact analytical solutions to the nonlinear
{Schr{\"o}dinger} equation model",
crossref = "Kauers:2005:IJB",
pages = "224--230",
year = "2005",
DOI = "https://doi.org/10.1145/1073884.1073916",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A method is developed for constructing a series of
exact analytical solutions of the nonlinear
Schr{\"o}dinger equation model (NLSE) with varying
dispersion, nonlinearity, and gain or absorption. With
the help of symbolic computation, a broad class of
analytical solutions of NLSE are obtained. From our
results, many previous known results of NLSE obtained
by some authors can be recovered by means of some
suitable selections of the arbitrary functions and
arbitrary constants. Further, the formation,
interaction and stability of solitons have been
investigated.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lichtblau:2005:HGF,
author = "Daniel Lichtblau",
title = "Half-{GCD} and fast rational recovery",
crossref = "Kauers:2005:IJB",
pages = "231--236",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mao:2005:AWM,
author = "Weibo Mao and Jinzhao Wu",
title = "Application of {Wu}'s method to symbolic model
checking",
crossref = "Kauers:2005:IJB",
pages = "237--244",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:2005:PAC,
author = "Michael Monagan",
title = "Probabilistic algorithms for computing resultants",
crossref = "Kauers:2005:IJB",
pages = "245--252",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mourrain:2005:GNF,
author = "Bernard Mourrain",
title = "Generalized normal forms and polynomial system
solving",
crossref = "Kauers:2005:IJB",
pages = "253--260",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Oancea:2005:DEI,
author = "Cosmin E. Oancea and Stephen M. Watt",
title = "Domains and expressions: an interface between two
approaches to computer algebra",
crossref = "Kauers:2005:IJB",
pages = "261--268",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Perez-Diaz:2005:PDF,
author = "Sonia P{\'e}rez-D{\'\i}az and J. Rafael Sendra",
title = "Partial degree formulae for rational algebraic
surfaces",
crossref = "Kauers:2005:IJB",
pages = "301--308",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Reid:2005:SNC,
author = "Greg Reid and Jan Verschelde and Allan Wittkopf and
Wenyuan Wu",
title = "Symbolic-numeric completion of differential systems by
homotopy continuation",
crossref = "Kauers:2005:IJB",
pages = "269--276",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rondepierre:2005:ASN,
author = "Aude Rondepierre and Jean-Guillaume Dumas",
title = "Algorithms for symbolic\slash numeric control of
affine dynamical systems",
crossref = "Kauers:2005:IJB",
pages = "277--284",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Salvy:2005:FAA,
author = "Bruno Salvy",
title = "{$D$}-finiteness: algorithms and applications",
crossref = "Kauers:2005:IJB",
pages = "2--3",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schneider:2005:FTM,
author = "Carsten Schneider",
title = "Finding telescopers with minimal depth for indefinite
nested sum and product expressions",
crossref = "Kauers:2005:IJB",
pages = "285--292",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schost:2005:MPS,
author = "{\'E}ric Schost",
title = "Multivariate power series multiplication",
crossref = "Kauers:2005:IJB",
pages = "293--300",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Storjohann:2005:CRS,
author = "Arne Storjohann and Gilles Villard",
title = "Computing the rank and a small nullspace basis of a
polynomial matrix",
crossref = "Kauers:2005:IJB",
pages = "309--316",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tournier:2005:ADS,
author = "Laurent Tournier",
title = "Approximation of dynamical systems using s-systems
theory: application to biological systems",
crossref = "Kauers:2005:IJB",
pages = "317--324",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tsarev:2005:GLT,
author = "Sergey P. Tsarev",
title = "Generalized {Laplace} transformations and integration
of hyperbolic systems of linear partial differential
equations",
crossref = "Kauers:2005:IJB",
pages = "325--331",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Turner:2005:PSB,
author = "William J. Turner",
title = "Preconditioners for singular black box matrices",
crossref = "Kauers:2005:IJB",
pages = "332--339",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vandeWoestijne:2005:DES,
author = "Christiaan van de Woestijne",
title = "Deterministic equation solving over finite fields",
crossref = "Kauers:2005:IJB",
pages = "348--353",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2005:SSO,
author = "M. van Hoeij and J.-A. Weil",
title = "Solving second order linear differential equations
with {Klein}'s theorem",
crossref = "Kauers:2005:IJB",
pages = "340--347",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2005:SAB,
author = "Dongming Wang and Bican Xia",
title = "Stability analysis of biological systems with real
solution classification",
crossref = "Kauers:2005:IJB",
pages = "354--361",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wu:2005:FKT,
author = "Wen-tsun Wu",
title = "On a finite kernel theorem for polynomial-type
optimization problems and some of its applications",
crossref = "Kauers:2005:IJB",
pages = "4--4",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yang:2005:OPM,
author = "Lu Yang and Zhenbing Zeng",
title = "An open problem on metric invariants of tetrahedra",
crossref = "Kauers:2005:IJB",
pages = "362--364",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zobnin:2005:AOF,
author = "Aleksey Zobnin",
title = "Admissible orderings and finiteness criteria for
differential standard bases",
crossref = "Kauers:2005:IJB",
pages = "365--372",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abo:2006:IKC,
author = "Hirotachi Abo and Chris Peterson",
title = "Implementation of {Kumar}'s correspondence",
crossref = "Trager:2006:PIS",
pages = "9--16",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2006:SRS,
author = "S. A. Abramov",
title = "On the summation of {$P$}-recursive sequences",
crossref = "Trager:2006:PIS",
pages = "17--22",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bigatti:2006:CSC,
author = "Anna Bigatti and Lorenzo Robbiano",
title = "CoCo{A}: a system for computations in commutative
algebra",
crossref = "Trager:2006:PIS",
pages = "6--6",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Borwein:2006:SCM,
author = "Jonathan M. Borwein and Chris H. Hamiltony",
title = "Symbolic computation of multidimensional {Fenchel}
conjugates",
crossref = "Trager:2006:PIS",
pages = "23--30",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2006:LCA,
author = "A. Bostan and F. Chyzak and B. Salvy and T. Cluzeau",
title = "Low complexity algorithms for linear recurrences",
crossref = "Trager:2006:PIS",
pages = "31--38",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Boyle:2006:AHP,
author = "Phelim Boyle and Alex Potapchik",
title = "Application of high-precision computing for pricing
arithmetic {Asian} options",
crossref = "Trager:2006:PIS",
pages = "39--46",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheng:2006:CPG,
author = "Howard Cheng and George Labahn",
title = "On computing polynomial {GCD}s in alternate bases",
crossref = "Trager:2006:PIS",
pages = "47--54",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chtcherba:2006:CDF,
author = "Arthur D. Chtcherba and Deepak Kapur",
title = "Conditions for determinantal formula for resultant of
a polynomial system",
crossref = "Trager:2006:PIS",
pages = "55--62",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:2006:SSR,
author = "Wayne Eberly and Mark Giesbrecht and Pascal Giorgi and
Arne Storjohann and Gilles Villard",
title = "Solving sparse rational linear systems",
crossref = "Trager:2006:PIS",
pages = "63--70",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eigenwillig:2006:ATR,
author = "Arno Eigenwillig and Vikram Sharma and Chee K. Yap",
title = "Almost tight recursion tree bounds for the {Descartes}
method",
crossref = "Trager:2006:PIS",
pages = "71--78",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Farcot:2006:SNA,
author = "Etienne Farcot",
title = "Symbolic numeric analysis of attractors in randomly
generated piecewise affine models of gene networks",
crossref = "Trager:2006:PIS",
pages = "79--86",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Farzan:2006:SRF,
author = "Arash Farzan and J. Ian Munro",
title = "Succinct representation of finite abelian groups",
crossref = "Trager:2006:PIS",
pages = "87--92",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Filatei:2006:ITF,
author = "Akpodigha Filatei and Xin Li and Marc Moreno Maza and
{\'E}ric Schost",
title = "Implementation techniques for fast polynomial
arithmetic in a high-level programming environment",
crossref = "Trager:2006:PIS",
pages = "93--100",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gao:2006:RSD,
author = "Xiao-Shan Gao and Chun-Ming Yuan",
title = "Resolvent systems of difference polynomial ideals",
crossref = "Trager:2006:PIS",
pages = "101--108",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gaudry:2006:FAC,
author = "P. Gaudry and F. Morain",
title = "Fast algorithms for computing the eigenvalue in the
{Schoof--Elkies--Atkin} algorithm",
crossref = "Trager:2006:PIS",
pages = "109--115",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:2006:SNS,
author = "Mark Giesbrecht and George Labahn and Wen-shin Lee",
title = "Symbolic-numeric sparse interpolation of multivariate
polynomials",
crossref = "Trager:2006:PIS",
pages = "116--123",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2006:ERB,
author = "Li Guo and William Y. Sit",
title = "Enumeration of {Rota--Baxter} words",
crossref = "Trager:2006:PIS",
pages = "124--131",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Harrison:2006:RPD,
author = "Michael Harrison and Josef Schicho",
title = "Rational parametrisation for degree $6$ {Del Pezzo}
surfaces using {Lie} algebras",
crossref = "Trager:2006:PIS",
pages = "132--137",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Janovitz-Freireich:2006:ARI,
author = "Itnuit Janovitz-Freireich and Lajos R{\'o}nyai and
{\'A}gnes Sz{\'a}nt{\'o}",
title = "Approximate radical of ideals with clusters of roots",
crossref = "Trager:2006:PIS",
pages = "146--153",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Johnson:2006:HPI,
author = "Jeremy R. Johnson and Werner Krandick and Kevin Lynch
and David G. Richardson and Anatole D. Ruslanov",
title = "High-performance implementations of the {Descartes}
method",
crossref = "Trager:2006:PIS",
pages = "154--161",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2006:AGC,
author = "Erich Kaltofen and Zhengfeng Yang and Lihong Zhi",
title = "Approximate greatest common divisors of several
polynomials with linearly constrained coefficients and
singular polynomials",
crossref = "Trager:2006:PIS",
pages = "169--176",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2006:FSD,
author = "Erich Kaltofen and Pascal Koiran",
title = "Finding small degree factors of multivariate
supersparse (lacunary) polynomials over algebraic
number fields",
crossref = "Trager:2006:PIS",
pages = "162--168",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2006:HSN,
author = "Erich Kaltofen and Lihong Zhi",
title = "Hybrid symbolic-numeric computation",
crossref = "Trager:2006:PIS",
pages = "7--7",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2006:AUS,
author = "Manuel Kauers and Carsten Schneider",
title = "Application of unspecified sequences in symbolic
summation",
crossref = "Trager:2006:PIS",
pages = "177--183",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Khodadad:2006:FRF,
author = "Sara Khodadad and Michael Monagan",
title = "Fast rational function reconstruction",
crossref = "Trager:2006:PIS",
pages = "184--190",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Laplagne:2006:ACR,
author = "Santiago Laplagne",
title = "An algorithm for the computation of the radical of an
ideal",
crossref = "Trager:2006:PIS",
pages = "191--195",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lazard:2006:SKC,
author = "Daniel Lazard",
title = "Solving {Kaltofen}'s challenge on {Zolotarev}'s
approximation problem",
crossref = "Trager:2006:PIS",
pages = "196--203",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Levandovskyy:2006:IIN,
author = "Viktor Levandovskyy",
title = "Intersection of ideals with non-commutative
subalgebras",
crossref = "Trager:2006:PIS",
pages = "212--219",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2006:RMD,
author = "Ziming Li and Michael F. Singer and Min Wu and Dabin
Zheng",
title = "A recursive method for determining the one-dimensional
submodules of {Laurent--{\O}re} modules",
crossref = "Trager:2006:PIS",
pages = "220--227",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Maza:2006:TDP,
author = "Marc Moreno Maza",
title = "Triangular decompositions of polynomial systems: from
theory to practice",
crossref = "Trager:2006:PIS",
pages = "8--8",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Minimair:2006:RSC,
author = "Manfred Minimair",
title = "Resultants of skewly composed polynomials",
crossref = "Trager:2006:PIS",
pages = "228--233",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Miyamoto:2006:IGN,
author = "Izumi Miyamoto",
title = "An improvement of {GAP} normalizer function for
permutation groups",
crossref = "Trager:2006:PIS",
pages = "234--238",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:2006:RSM,
author = "Michael Monagan and Roman Pearce",
title = "Rational simplification modulo a polynomial ideal",
crossref = "Trager:2006:PIS",
pages = "239--245",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Moroz:2006:CRP,
author = "Guillaume Moroz",
title = "Complexity of the resolution of parametric systems of
polynomial equations and inequations",
crossref = "Trager:2006:PIS",
pages = "246--253",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Neunhoffer:2006:DSU,
author = "Max Neunh{\"o}ffer and {\'A}kos Seress",
title = "A data structure for a uniform approach to
computations with finite groups",
crossref = "Trager:2006:PIS",
pages = "254--261",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Noro:2006:MDE,
author = "Masayuki Noro",
title = "Modular dynamic evaluation",
crossref = "Trager:2006:PIS",
pages = "262--268",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2006:UGA,
author = "Wei Pan and Dongming Wang",
title = "Uniform {Gr{\"o}bner} bases for ideals generated by
polynomials with parametric exponents",
crossref = "Trager:2006:PIS",
pages = "269--276",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pascal:2006:COB,
author = "Cyril Pascal and {\'E}ric Schost",
title = "Change of order for bivariate triangular sets",
crossref = "Trager:2006:PIS",
pages = "277--284",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Poulisse:2006:CCA,
author = "Hennie Poulisse",
title = "Computational communicative algebra",
crossref = "Trager:2006:PIS",
pages = "3--4",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Powers:2006:QPT,
author = "Victoria Powers and Bruce Reznick",
title = "A quantitative {P{\'o}lya's Theorem} with corner
zeros",
crossref = "Trager:2006:PIS",
pages = "285--289",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Renault:2006:CSF,
author = "Gu{\'e}na{\"e}l Renault",
title = "Computation of the splitting field of a dihedral
polynomial",
crossref = "Trager:2006:PIS",
pages = "290--297",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Robinson:2006:PAD,
author = "Eric Robinson and Gene Cooperman",
title = "A parallel architecture for disk-based computing over
the {Baby Monster} and other large finite simple
groups",
crossref = "Trager:2006:PIS",
pages = "298--305",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Roux:2006:RRC,
author = "Nicolas Le Roux and Moulay Barkatou",
title = "Rank reduction of a class of {Pfaffian} systems in two
variables",
crossref = "Trager:2006:PIS",
pages = "204--211",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rubio:2006:NIN,
author = "Rosario Rubio and J. Miguel Serradilla and M. Pilar
V{\'e}lez",
title = "A note on implicitization and normal parametrization
of rational curves",
crossref = "Trager:2006:PIS",
pages = "306--309",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sekigawa:2006:LRM,
author = "Hiroshi Sekigawa and Kiyoshi Shirayanagi",
title = "Locating real multiple zeros of a real interval
polynomial",
crossref = "Trager:2006:PIS",
pages = "310--317",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sexton:2006:AMS,
author = "Alan Sexton and Volker Sorge",
title = "Abstract matrices in symbolic computation",
crossref = "Trager:2006:PIS",
pages = "318--325",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Suzuki:2006:SAC,
author = "Akira Suzuki and Yosuke Sato",
title = "A simple algorithm to compute comprehensive
{Gr{\"o}bner} bases using {Gr{\"o}bner} bases",
crossref = "Trager:2006:PIS",
pages = "326--331",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Turner:2006:BWR,
author = "William J. Turner",
title = "A block {Wiedemann} rank algorithm",
crossref = "Trager:2006:PIS",
pages = "332--339",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Umans:2006:GTA,
author = "Christopher Umans",
title = "Group-theoretic algorithms for matrix multiplication",
crossref = "Trager:2006:PIS",
pages = "5--5",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderHoeven:2006:ERN,
author = "Joris van der Hoeven",
title = "Effective real numbers in {Mmxlib}",
crossref = "Trager:2006:PIS",
pages = "138--145",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vandeWoestijne:2006:SPD,
author = "Christiaan van de Woestijne",
title = "Surface parametrisation without diagonalisation",
crossref = "Trager:2006:PIS",
pages = "340--344",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:2006:WWW,
author = "Joachim von zur Gathen",
title = "Who was who in polynomial factorization: 1",
crossref = "Trager:2006:PIS",
pages = "2--2",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wu:2006:ANA,
author = "Wenyuan Wu and Greg Reid",
title = "Application of numerical algebraic geometry and
numerical linear algebra to {PDE}",
crossref = "Trager:2006:PIS",
pages = "345--352",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhou:2006:GAB,
author = "Meng Zhou and Franz Winkler",
title = "{Gr{\"o}bner} bases in difference-differential
modules",
crossref = "Trager:2006:PIS",
pages = "353--360",
year = "2006",
bibdate = "Wed Aug 23 09:43:45 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2007:CSI,
author = "Moulay A. Barkatou and Eckhard Pfl{\"u}gel",
title = "Computing super-irreducible forms of systems of linear
differential equations via {Moser}-reduction: a new
approach",
crossref = "Brown:2007:PIS",
pages = "1--8",
year = "2007",
DOI = "https://doi.org/10.1145/983065.983067",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bini:2007:SMB,
author = "Dario A. Bini and Paola Boito",
title = "Structured matrix-based methods for polynomial
$\in$-gcd: analysis and comparisons",
crossref = "Brown:2007:PIS",
pages = "9--16",
year = "2007",
DOI = "https://doi.org/10.1145/983065.983068",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bodrato:2007:IPM,
author = "Marco Bodrato and Alberto Zanoni",
title = "Integer and polynomial multiplication: towards optimal
{Toom--Cook} matrices",
crossref = "Brown:2007:PIS",
pages = "17--24",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277552",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Karatsuba and Toom--Cook are well-known methods used
to multiply efficiently long integers. There have been
different proposal about the interpolating values used
to determine the matrix to be inverted and the sequence
of operations to invert it. A definitive word about
which is the optimal matrix (values) and the (number
of) basic operations to invert it seems still not to
have been said. In this paper we present some
particular examples of useful matrices and a method to
generate automatically, by means of optimised
exhaustive searches on a graph, the best sequence of
basic operations to invert them.",
acknowledgement = ack-nhfb,
keywords = "integer and polynomial multiplication; interpolation;
Karatsuba; matrix inversion; squaring; Toom--Cook",
}
@InProceedings{Bostan:2007:DEA,
author = "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Bruno
Salvy and Gr{\'e}goire Lecerf and {\'E}ric Schost",
title = "Differential equations for algebraic functions",
crossref = "Brown:2007:PIS",
pages = "25--32",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277553",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "It is classical that univariate algebraic functions
satisfy linear differential equations with polynomial
coefficients. Linear recurrences follow for the
coefficients of their power series expansions. We show
that the linear differential equation of minimal order
has coefficients whose degree is cubic in the degree of
the function. We also show that there exists a linear
differential equation of order linear in the degree
whose coefficients are only of quadratic degree.
Furthermore, we prove the existence of recurrences of
order and degree close to optimal. We study the
complexity of computing these differential equations
and recurrences. We deduce a fast algorithm for the
expansion of algebraic series.",
acknowledgement = ack-nhfb,
keywords = "algebraic series; complexity; computer algebra;
creative telescoping; differential resolvents",
}
@InProceedings{Bostan:2007:STV,
author = "Alin Bostan and Claude-Pierre Jeannerod and {\'E}ric
Schost",
title = "Solving {Toeplitz}- and {Vandermonde}-like linear
systems with large displacement rank",
crossref = "Brown:2007:PIS",
pages = "33--40",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277554",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Linear systems with structures such as Toeplitz-,
Vandermonde-or Cauchy-likeness can be solved in
$O\tilde$ operations, where $n$ is the matrix size,
$\alpha$ is its displacement rank, and $O\tilde$
denotes the omission of logarithmic factors. We show
that for Toeplitz-like and Vandermonde-like matrices,
this cost can be reduced to $O(\alpha^{\omega-1} n)$,
where $\omega$ is a feasible exponent for matrix
multiplication over the base field. The best known
estimate for $\omega$ is $\omega O(\alpha^{1.38} n)$.
We also present consequences for Hermite--Pad{\'e}
approximation and bivariate interpolation.",
acknowledgement = ack-nhfb,
keywords = "dense linear algebra; structured linear algebra",
}
@InProceedings{Bremner:2007:NSP,
author = "Murray R. Bremner and Michael J. Hancock and Yunfeng
Piao",
title = "Nonassociative structures on polynomial algebras
arising from bio-operations on formal languages: an
application of computer algebra to nonassociative
systems",
crossref = "Brown:2007:PIS",
pages = "41--48",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277555",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider sequential insertion and deletion, and
contextual insertion and deletion, on the free monoid
$\Sigma$ where $\Sigma = \{ x \}$; in each case the
result can be regarded as either a set or a multiset.
Over any coefficient field $F$ the vector space with
basis $\Sigma*$ is linearly isomorphic to the
polynomial algebra $F[x]$; each operation on $\Sigma*$
extends bilinearly to give a new algebra structure (not
necessarily commutative or associative) on $F[x]$. We
determine the polynomial identities of degree $\leq 5$
satisfied by these structures.",
acknowledgement = ack-nhfb,
keywords = "bio-operations; computer algebra; DNA computing;
finite fields; formal languages; linear systems;
nonassociative algebra; polynomial identities",
}
@InProceedings{Bretto:2007:GGC,
author = "Alain Bretto and Luc Gillibert",
title = "{G}-graphs for the cage problem: a new upper bound",
crossref = "Brown:2007:PIS",
pages = "49--53",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277556",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Constructing some regular graph with a given girth,a
given degree and the fewest possible vertices is a hard
problem. This problem is called the cage graph problem
and has some links with the error codes theory. In this
paper we presents some new graphs, constructed from a
group, with a girth of 6 and regular of degree $p$, for
any prime number $p$. This graphs are of order $2
\times p^2$ when the best upper bound known for the
$(p,6)$-cage problem was the Sauer bound, equal to
$4(p-1)^3$.",
acknowledgement = ack-nhfb,
keywords = "cage graphs; G-graphs; graphs from group",
}
@InProceedings{Brown:2007:CQE,
author = "Christopher W. Brown and James H. Davenport",
title = "The complexity of quantifier elimination and
cylindrical algebraic decomposition",
crossref = "Brown:2007:PIS",
pages = "54--60",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277557",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper has two parts. In the first part we give a
simple and constructive proof that quantifier
elimination in real algebra is doubly exponential, even
when there is only one free variable and all
polynomials in the quantified input are linear. The
general result is not new, but we hope the simple and
explicit nature of the proof makes it interesting. The
second part of the paper uses the construction of the
first part to prove some results on the effects of
projection order on CAD construction -- roughly that
there are CAD construction problems for which one order
produces a constant number of cells and another
produces a doubly exponential number of cells, and that
there are problems for which all orders produce a
doubly exponential number of cells. The second of these
results implies that there is a true singly vs. doubly
exponential gap between the worst-case running times of
several modern quantifier elimination algorithms and
CAD-based quantifier elimination when the number of
quantifier alternations is constant.",
acknowledgement = ack-nhfb,
keywords = "cylindrical algebraic decomposition; quantifier
elimination",
}
@InProceedings{Burgisser:2007:DFC,
author = "Peter B{\"u}rgisser and Peter Scheiblechner",
title = "Differential forms in computational algebraic
geometry",
crossref = "Brown:2007:PIS",
pages = "61--68",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277558",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We give a uniform method for the two problems \#CC$_C$
and \#IC$_C$ of counting connected and irreducible
components of complex algebraic varieties,
respectively. Our algorithms are purely algebraic,
i.e., they use only the field structure of C. They work
efficiently in parallel and can be implemented by
algebraic circuits of polynomial depth, i.e., in
parallel polynomial time. The design of our algorithms
relies on the concept of algebraic differential forms.
A further important building block is an algorithm of
S{\'a}nt{\'o} [40] computing a variant of
characteristic sets. The crucial complexity parameter
for \#IC$_C$ turns out to be the number of equations.
We describe a randomised algorithm solving \#IC$_C$ for
a fixed number of rational equations given by
straight-line programs (slps), which runs in parallel
polylogarithmic time in the length and the degree of
the slps.",
acknowledgement = ack-nhfb,
keywords = "complexity; connected components; differential forms;
irreducible components",
}
@InProceedings{Buse:2007:IBP,
author = "Laurent Bus{\'e} and Marc Dohm",
title = "Implicitization of bihomogeneous parametrizations of
algebraic surfaces via linear syzygies",
crossref = "Brown:2007:PIS",
pages = "69--76",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277559",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We show that the implicit equation of a surface in
3-dimensional projective space parametrized by
bi-homogeneous polynomials of bi-degree $(d,d)$ for a
given integer $d \geq $1 can be represented and
computed from the linear syzygies of its
parametrization if the base points are isolated and
form locally a complete intersection.",
acknowledgement = ack-nhfb,
keywords = "approximation complexes; implicitization; linear
syzygies",
}
@InProceedings{Carette:2007:CFP,
author = "Jacques Carette",
title = "A canonical form for piecewise defined functions",
crossref = "Brown:2007:PIS",
pages = "77--84",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277560",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We define a canonical form for piecewise defined
functions. We show that the domains and ranges for
which these functions are defined is larger than in
previous work. Also, our canonical form algorithm is
linear in the number of breakpoints instead of
exponential. These results rely on the linear structure
of the underlying domain of definition.",
acknowledgement = ack-nhfb,
keywords = "canonical form; normal form; piecewise",
}
@InProceedings{Cheng:2007:CNI,
author = "Jin-San Cheng and Xiao-Shan Gao and Chee-Keng Yap",
title = "Complete numerical isolation of real zeros in
zero-dimensional triangular systems",
crossref = "Brown:2007:PIS",
pages = "92--99",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277562",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a complete numerical algorithm of isolating
all the real zeros of a zero-dimensional triangular
polynomial system $F_n Z[x_1 \ldots, x_n]$. Our system
$F_n$ is general, with no further assumptions. In
particular, our algorithm successfully treat multiple
zeros directly in such systems. A key idea is to
introduce evaluation bounds and sleeve bounds. We
implemented our algorithm and promising experimental
results are shown.",
acknowledgement = ack-nhfb,
keywords = "evaluation bound; real zero isolation; sleeve bound;
triangular system",
}
@InProceedings{Cheng:2007:TSE,
author = "Howard Cheng and Guillaume Hanrot and Emmanuel
Thom{\'e} and Paul Zimmermann and Eugene Zima",
title = "Time-and space-efficient evaluation of some
hypergeometric constants",
crossref = "Brown:2007:PIS",
pages = "85--91",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277561",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The currently best known algorithms for the numerical
evaluation of hypergeometric constants such as
$\zeta(3)$ to $d$ decimal digits have time complexity
$O(M(d) \log^2 d)$ and space complexity of $O(d \log
d)$ or $O(d)$. Following work from Cheng, Gergel, Kim
and Zima, we present a new algorithm with the same
asymptotic complexity, but more efficient in practice.
Our implementation of this algorithm improves over
existing programs for the computation of $\Pi$, and we
announce a new record of 2 billion digits for
\zeta(3).",
acknowledgement = ack-nhfb,
keywords = "high-precision evaluation; hypergeometric constants",
}
@InProceedings{Cicalo:2007:NAG,
author = "Serena Cical{\`o} and Willem de Graaf",
title = "Non-associative {Gr{\"o}bner} bases,
finitely-presented {Lie} rings and the {Engel}
condition",
crossref = "Brown:2007:PIS",
pages = "100--107",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277563",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We give an algorithm for constructing a basis and a
multiplication table of a finite-dimensional
finitely-presented Lie ring. We apply this to construct
the biggest $t$ generator Lie rings that satisfy the
$n$-Engel condition, for $(t,n) = (t,2), (2,3), (3,3),
(2,4)$.",
acknowledgement = ack-nhfb,
keywords = "Engel condition; Gr{\"o}bner basis; Lie ring",
}
@InProceedings{Corless:2007:JHF,
author = "Robert M. Corless and Dawit Assefa",
title = "{Jeffery--Hamel} flow with {Maple}: a case study of
integration of elliptic functions in a {CAS}",
crossref = "Brown:2007:PIS",
pages = "108--115",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277564",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper takes a classical problem in
two-dimensional fluid flow-namely, flow into or out of
a wedge-shaped channel with a sink or source at the
vertex, which flow is known as Jeffery--Hamel flow and
has `well-known' solutions containing elliptic
functions-and tries to duplicate, or even extend, the
classical solutions by using a CAS, in this instance
Maple. The purposes of this case study include
examining just how good CAS can be at elliptic
functions; and, more importantly, identifying needs for
improvement. Another purpose is to compare the
analytical solution with modern numerical solutions.
Finally, we believe that this work will motivate
improvements to CAS facilities for automatic case
analysis. As an aside, we present some simple methods
for integration of elliptic functions that seem not to
be widely known.",
acknowledgement = ack-nhfb,
keywords = "elliptic functions; integration",
}
@InProceedings{Corless:2007:SEA,
author = "Robert M. Corless and Hui Ding and Nicholas J. Higham
and David J. Jeffrey",
title = "The solution of $s \exp(s) = a$ is not always the
{Lambert} ${W}$ function of $a$",
crossref = "Brown:2007:PIS",
pages = "116--121",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277565",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study the solutions of the matrix equation $S
\exp(S) = A$. Our motivation comes from the study of
systems of delay differential equations $y'(t) = Ay(t -
1)$, which occur in some models of practical interest,
especially in mathematical biology. This paper
concentrates on the distinction between evaluating a
matrix function and solving a matrix equation. In
particular, it shows that the matrix Lambert $W$
function evaluated at the matrix $A$ does not represent
all possible solutions of $S \exp(S) = A$. These
results can easily be extended to more general matrix
equations.",
acknowledgement = ack-nhfb,
keywords = "Lambert $W$ function; matrix function; nonlinear
matrix equation",
}
@InProceedings{Cox:2007:GBS,
author = "David A. Cox",
title = "{Gr{\"o}bner} bases: a sampler of recent
developments",
crossref = "Brown:2007:PIS",
pages = "387--388",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277601",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This tutorial will explore the theory of Gr{\"o}bner
bases. The first part will review classic material on
monomial orders, the Buchberger Algorithm, and
elimination theory. This will be followed by a
discussion of the geometry of elimination, where
resultants can be replaced with Gr{\"o}bner bases using
ideas of Schauenberg [15]. The tutorial will conclude
with a sampler of topics about Gr{\"o}bner bases,
including graph theory [11], geometric theorem proving
via comprehensive Gr{\"o}bner systems [13, 14], the
generic Gr{\"o}bner walk [12], alternatives to the
Buchberger algorithm and applications [8, 9, 10], and
moduli of quiver representations via Gr{\"o}bner bases
[5]. (This list of topics is tentative--the tutorial
may cover slightly different topics.)",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner bases; elimination theory",
}
@InProceedings{Dimitrova:2007:GFM,
author = "Elena S. Dimitrova and Abdul Salam Jarrah and Reinhard
Laubenbacher and Brandilyn Stigler",
title = "A {Gr{\"o}bner} fan method for biochemical network
modeling",
crossref = "Brown:2007:PIS",
pages = "122--126",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277566",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Polynomial dynamical systems (PDSs) have been used
successfully as a framework for the reconstruction, or
reverse engineering of biochemical networks from
experimental data. Within this modeling space, a
particular PDS is chosen by way of a Gr{\"o}bner basis,
and using different monomial orders may result in
different polynomial models. In this paper, we present
a systematic method for selecting most likely
polynomial models for a given data set, using the
Gr{\"o}bner fan of the ideal of the input data. We
apply the method to reverse engineer two biochemical
networks, a Boolean model of lactose metabolism in {\em
E. coli} and a protein signal transduction network in
{\em S. cerevisiae} and compare our results to those
from two published network-reconstruction methods.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner bases; Gr{\"o}bner fan; computational
algebra; model selection; monomial orderings; network
inference; polynomial dynamical systems; reverse
engineering",
}
@InProceedings{Diochnos:2007:CRS,
author = "Dimitrios I. Diochnos and Ioannis Z. Emiris and Elias
P. Tsigaridas",
title = "On the complexity of real solving bivariate systems",
crossref = "Brown:2007:PIS",
pages = "127--134",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277567",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider exact real solving of well-constrained,
bivariate systems of relatively prime polynomials. The
main problem is to compute all common real roots in
isolating interval representation, and to determine
their intersection multiplicities. We present three
algorithms and analyze their asymptotic bit complexity,
obtaining a bound of $\tilde{O}_B(N^{14})$ for the
purely projection-based method, and
$\tilde{O}_B(N^{12})$ for two subresultants-based
methods: these ignore polylogarithmic factors, and $N$
bounds the degree and the bitsize of the polynomials.
The previous record bound was
$\tilde{O}_B(N^{14})$.\par
Our main tool is signed subresultant sequences,
extended to several variables by binary segmentation.
We exploit advances on the complexity of univariate
root isolation, and extend them to multipoint sign
evaluation, sign evaluation of bivariate polynomials
over two algebraic numbers, and real root counting over
an extension field. Our algorithms apply to the problem
of simultaneous inequalities; they also compute the
topology of real plane algebraic curves in.\par
All algorithms have been implemented in Maple, in
conjunction with numeric filtering. We compare them
against {\sc FGB\slash RS} and {\sc SYNAPS}; we also
consider Maple libraries {\sc INSULATE} and {\sc TOP},
which compute curve topology. Our software is among the
most robust, and its runtimes are within a small
constant factor, with respect to the C/C++ libraries.",
acknowledgement = ack-nhfb,
keywords = "Maple; polynomial system; real algebraic number; real
solving; topology of real algebraic curve",
}
@InProceedings{Dridi:2007:TNO,
author = "Raouf Dridi and Michel Petitot",
title = "Towards a new {ODE} solver based on {Cartan}'s
equivalence method",
crossref = "Brown:2007:PIS",
pages = "135--142",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277568",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The aim of the present paper is to propose an
algorithm for a new ODE-solver which should improve the
abilities of current solvers to handle second order
differential equations. The paper provides also a
theoretical result revealing the relationship between
the change of coordinates, that maps the generic
equation to a given target equation, and the symmetry
$D$-groupoid of this target.",
acknowledgement = ack-nhfb,
keywords = "Cartan's equivalence method; differential algebra;
equivalence problems; ODE-solver",
}
@InProceedings{Eberly:2007:FIO,
author = "Wayne Eberly and Mark Giesbrecht and Pascal Giorgi and
Arne Storjohann and Gilles Villard",
title = "Faster inversion and other black box matrix
computations using efficient block projections",
crossref = "Brown:2007:PIS",
pages = "143--150",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277569",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Efficient block projections of non-singular matrices
have recently been used by the authors in [10] to
obtain an efficient algorithm to find rational
solutions for sparse systems of linear equations. In
particular a bound of $O^~(n^{2.5})$ machine operations
is presented for this computation assuming that the
input matrix can be multiplied by a vector with
constant-sized entries using $O^~(n)$ machine
operations. Somewhat more general bounds for black-box
matrix computations are also derived. Unfortunately,
the correctness of this algorithm depends on the
existence of efficient block projections of
non-singular matrices, and this was only
conjectured.\par
In this paper we establish the correctness of the
algorithm from [10] by proving the existence of
efficient block projections for arbitrary non-singular
matrices over sufficiently large fields. We further
demonstrate the usefulness of these projections by
incorporating them into existing black-box matrix
algorithms to derive improved bounds for the cost of
several matrix problems. We consider, in particular,
matrices that can be multiplied by a vector using
$O^~(n)$ field operations: We show how to compute the
inverse of any such non-singular matrix over any field
using an expected number of $O^~(n^{2.27})$ operations
in that field. A basis for the null space of such a
matrix, and a certification of its rank, are obtained
at the same cost. An application of this technique to
Kaltofen and Villard's Baby-Steps\slash Giant-Steps
algorithms for the determinant and Smith Form of an
integer matrix is also sketched, yielding algorithms
requiring $O^~(n^{2.66})$ machine operations. More
general bounds involving the number of black-box matrix
operations to be used are also obtained.\par
The derived algorithms are all probabilistic of the Las
Vegas type. They are assumed to be able to generate
random elements --- bits or field elements --- at unit
cost, and always output the correct answer in the
expected time given.",
acknowledgement = ack-nhfb,
keywords = "black box linear algebra; linear system solving;
sparse integer matrix; structured integer matrix",
}
@InProceedings{Eigenwillig:2007:FEG,
author = "Arno Eigenwillig and Michael Kerber and Nicola
Wolpert",
title = "Fast and exact geometric analysis of real algebraic
plane curves",
crossref = "Brown:2007:PIS",
pages = "151--158",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277570",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An algorithm is presented for the geometric analysis
of an algebraic curve $f(x,y) = 0$ in the real affine
plane. It computes a cylindrical algebraic
decomposition (CAD) of the plane, augmented with
adjacency information. The adjacency information
describes the curve's topology by a topologically
equivalent planar graph. The numerical data in the CAD
gives an embedding of the graph.\par
The algorithm is designed to provide the exact result
for all inputs but to perform only few symbolic
operations for the sake of efficiency. In particular,
the roots of $f(\propto,y)$ at a critical
$x$-coordinate.\par
The algorithm is implemented as C++ library AlciX in
the EXACUS project. Running time comparisons with top
by Gonzalez-Vega and Necula (2002), and with cad2d by
Brown demonstrate its efficiency.",
acknowledgement = ack-nhfb,
keywords = "algebraic curves; cylindrical algebraic decomposition;
Descartes method; exact geometric computation;
Sturm--Habicht sequence; topology computation",
}
@InProceedings{Elkadi:2007:STP,
author = "Mohamed Elkadi and Andr{\'e} Galligo",
title = "Systems of three polynomials with two separated
variables",
crossref = "Brown:2007:PIS",
pages = "159--166",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277571",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Motivated by the computation of intersection loci in
Computer Aided Geometric Design (CAGD), we introduce
and study the elimination problem for systems of three
bivariate polynomial equations with separated
variables. Such systems are simple sparse bivariate
ones but resemble to univariate systems of two
equations both geometrically and algebraically.
Interesting structures for generalized Sylvester and
bezoutian matrices can be explicited. Then one can take
advantage of these structures to represent the objects
and speed up the computations. A corresponding notion
of subresultant is presented and related to a
Gr{\"o}bner basis of the polynomial system.",
acknowledgement = ack-nhfb,
keywords = "algorithms; bezoutian; bivariate resultants; bivariate
subresultant; CAGD; intersection problem; structured
matrix; Sylvester matrix; system with separated
variables",
}
@InProceedings{Gaudry:2007:GBI,
author = "Pierrick Gaudry and Alexander Kruppa and Paul
Zimmermann",
title = "A {\tt gmp}-based implementation of
{Sch{\"o}nhage--Strassen}'s large integer
multiplication algorithm",
crossref = "Brown:2007:PIS",
pages = "167--174",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277572",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Sch{\"o}nhage--Strassen's algorithm is one of the best
known algorithms for multiplying large integers.
Implementing it efficiently is of utmost importance,
since many other algorithms rely on it as a subroutine.
We present here an improved implementation, based on
the one distributed within the GMP library. The
following ideas and techniques were used or tried:
faster arithmetic modulo $2^n + 1$, improved cache
locality, Mersenne transforms, Chinese Remainder
Reconstruction, the $\sqrt 2$ trick, Harley's and
Granlund's tricks, improved tuning.",
acknowledgement = ack-nhfb,
keywords = "integer multiplication; multiprecision arithmetic",
}
@InProceedings{Gemignani:2007:SMM,
author = "Luca Gemignani",
title = "Structured matrix methods for polynomial
root-finding",
crossref = "Brown:2007:PIS",
pages = "175--180",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277573",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we discuss the use of structured matrix
methods for the numerical approximation of the zeros of
a univariate polynomial. In particular, it is shown
that root-finding algorithms based on floating-point
eigenvalue computation can benefit from the structure
of the matrix problem to reduce their complexity and
memory requirements by an order of magnitude.",
acknowledgement = ack-nhfb,
keywords = "complexity; eigenvalue computation; polynomial
root-finding; rank-structured matrices",
}
@InProceedings{Hanke:2007:IPC,
author = "Timo Hanke",
title = "The isomorphism problem for cyclic algebras and an
application",
crossref = "Brown:2007:PIS",
pages = "181--186",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277574",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The isomorphism problem means to decide if two given
finite-dimensional simple algebras with center $K$ are
$K$-isomorphic and, if so, to construct a
$K$-isomorphism between them. Applications lie in
computational aspects of representation theory,
algebraic geometry and Brauer group theory. The paper
presents an algorithm for cyclic algebras that reduces
the isomorphism problem to field theory and thus
provides a solution if certain field theoretic problems
including norm equations can be solved (this is
satisfied over number fields). As an application, we
can compute all automorphisms of any given cyclic
algebra over a number field. A detailed example is
provided which leads to the construction of an explicit
noncrossed product division algebra.",
acknowledgement = ack-nhfb,
keywords = "abelian crossed product; bicyclic crossed product;
cyclic algebra; extension of automorphism;
finite-dimensional central-simple algebra; isomorphism
problem; noncrossed product; norm equation",
}
@InProceedings{Javadi:2007:SMG,
author = "Seyed Mohammad Mahdi Javadi and Michael Monagan",
title = "A sparse modular {GCD} algorithm for polynomials over
algebraic function fields",
crossref = "Brown:2007:PIS",
pages = "187--194",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277575",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a first sparse modular algorithm for
computing a greatest common divisor of two polynomials
$f_1, f_2 \epsilon L [ x ]$ where $L$ is an algebraic
function field in $k \geq 0$ parameters with $r \geq 0$
field extensions. Our algorithm extends the dense
algorithm of Monagan and van Hoeij from 2004 to support
multiple field extensions and to be efficient when the
gcd is sparse. Our algorithm is an output sensitive Las
Vegas algorithm.\par
We have implemented our algorithm in Maple. We provide
timings demonstrating the efficiency of our algorithm
compared to that of Monagan and van Hoeij and with a
primitive fraction-free Euclidean algorithm for both
dense and sparse GCD problems.",
acknowledgement = ack-nhfb,
keywords = "algebraic function fields; GCD algorithms; sparse
interpolation",
}
@InProceedings{Johnson:2007:GSD,
author = "Jeremy Johnson and Xu Xu",
title = "Generating symmetric {DFTs} and equivariant {FFT}
algorithms",
crossref = "Brown:2007:PIS",
pages = "195--202",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277576",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper presents a code generator which produces
efficient implementations of multi-dimensional fast
Fourier transform (FFT) algorithms which utilize
symmetries in the input data to reduce memory usage and
the number of arithmetic operations. The FFT algorithms
are constructed using a group theoretic version of the
divide and conquer step in the FFT that is compatible
with the group of symmetries. The GAP compute algebra
system is used to perform the necessary group
computations and the generated algorithm is represented
as a symbolic matrix factorization, which is translated
into efficient code using the SPIRAL system.
Performance data is given that shows that the resulting
code is significantly faster than state-of-the-art FFT
implementations that do not utilize the symmetries.",
acknowledgement = ack-nhfb,
keywords = "code generation; fast Fourier transform; group
symmetries; matrix factorization; multi-dimensional
discrete Fourier transform",
}
@InProceedings{Kaltofen:2007:EAI,
author = "Erich Kaltofen and Zhengfeng Yang",
title = "On exact and approximate interpolation of sparse
rational functions",
crossref = "Brown:2007:PIS",
pages = "203--210",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277577",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The black box algorithm for separating the numerator
from the denominator of a multivariate rational
function can be combined with sparse multivariate
polynomial interpolation algorithms to interpolate a
sparse rational function. Randomization and early
termination strategies are exploited to minimize the
number of black box evaluations. In addition, rational
number coefficients are recovered from modular images
by rational vector recovery. The need for separate
numerator and denominator size bounds is avoided via
correction, and the modulus is minimized by use of
lattice basis reduction, a process that can be applied
to sparse rational function vector recovery itself.
Finally, one can deploy sparse rational function
interpolation algorithm in the hybrid symbolic-numeric
setting when the black box for the function returns
real and complex values with noise. We present and
analyze five new algorithms for the above problems and
demonstrate their effectiveness on a mark
implementation.",
acknowledgement = ack-nhfb,
keywords = "early termination; hybrid symbolic-numeric
computation; lattice basis reduction; rational vector
recovery; sparse rational function interpolation",
}
@InProceedings{Kanno:2007:POC,
author = "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
and Shinji Hara",
title = "Parametric optimization in control using the sum of
roots for parametric polynomial spectral
factorization",
crossref = "Brown:2007:PIS",
pages = "211--218",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277578",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper proposes an algebraic approach for
parametric optimization which can be utilized for
various problems in signal processing and control. The
approach exploits the relationship between the sum of
roots and polynomial spectral factorization and solves
parametric polynomial spectral factorization by means
of the sum of roots and the theory of Gr{\"o}bner
basis. This enables us to express quantities such as
the optimal cost in terms of parameters and the sum of
roots. Furthermore an optimization method over
parameters is suggested that makes use of the results
from parametric polynomial spectral factorization and
also employs quantifier elimination. The proposed
approach is demonstrated on a numerical example of a
particular control problem.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner basis; H_2 control; parametric
optimization; polynomial spectral factorization;
quantifier elimination; sum of roots",
}
@InProceedings{Kauers:2007:SSR,
author = "Manuel Kauers and Carsten Schneider",
title = "Symbolic summation with radical expressions",
crossref = "Brown:2007:PIS",
pages = "219--226",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277579",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An extension of Karr's summation algorithm is
presented by which symbolic sums involving radical
expressions can be simplified. We discuss the
construction of appropriate difference fields as well
as algorithms for solving difference equations in these
fields. The paper is concluded by a list of identities
found with an implementation of our techniques.",
acknowledgement = ack-nhfb,
keywords = "algebraic functions; difference fields; square roots;
symbolic summation",
}
@InProceedings{Khungurn:2007:MCP,
author = "Pramook Khungurn and Hiroshi Sekigawa and Kiyoshi
Shirayanagi",
title = "Minimum converging precision of the {QR}-factorization
algorithm for real polynomial {GCD}",
crossref = "Brown:2007:PIS",
pages = "227--234",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277580",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Shirayanagi and Sweedler proved that a large class of
algorithms over the reals can be modified slightly so
that they also work correctly on fixed-precision
floating-point numbers. Their main theorem states that,
for each input, there exists a precision, called the
minimum converging precision (MCP), at and beyond which
the modified `stabilized' algorithm follows the same
sequence of instructions as that of the original
`exact' algorithm. Bounding the MCP of any non-trivial
and useful algorithm has remained an open
problem.\par
This paper studies the MCP of an algorithm for finding
the GCD of two univariate polynomials based on the
QR-factorization. We show that the MCP is generally
incomputable. Additionally, we derive a bound on the
minimal precision at and beyond which the stabilized
algorithm gives a polynomial with the same degree as
that of the exact GCD, and another bound on the minimal
precision at and beyond which the algorithm gives a
polynomial with the same support as that of the exact
GCD.",
acknowledgement = ack-nhfb,
keywords = "algebraic algorithm stabilization; polynomial greatest
common divisor",
}
@InProceedings{Kunkle:2007:TSM,
author = "Daniel Kunkle and Gene Cooperman",
title = "Twenty-six moves suffice for {Rubik}'s cube",
crossref = "Brown:2007:PIS",
pages = "235--242",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277581",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The number of moves required to solve any state of
Rubik's cube has been a matter of long-standing
conjecture for over 25 years -- since Rubik's cube
appeared. This number is sometimes called `God's
number'. An upper bound of 29 (in the face-turn metric)
was produced in the early 1990's, followed by an upper
bound of 27 in 2006.\par
An improved upper bound of 26 is produced using 8000
CPU hours. One key to this result is a new, fast
multiplication in the mathematical group of Rubik's
cube. Another key is efficient out-of-core (disk-based)
parallel computation using terabytes of disk storage.
One can use the precomputed data structures to produce
such solutions for a specific Rubik's cube position in
a fraction of a second. Work in progress will use the
new `brute-forcing' technique to further reduce the
bound.",
acknowledgement = ack-nhfb,
keywords = "disk-based methods; fast multiplication; permutation
groups; Rubik's cube; upper bound",
}
@InProceedings{Kurata:2007:CDC,
author = "Yosuke Kurata and Masayuki Noro",
title = "Computation of discrete comprehensive {Gr{\"o}bner}
bases using modular dynamic evaluation",
crossref = "Brown:2007:PIS",
pages = "243--250",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277582",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we propose a new algorithm to compute a
discrete comprehensive Gr{\"o}bner basis (DCGB) [9, 11]
which is a special case of a comprehensive Gr{\"o}bner
system. Our new algorithm enables us to compute the
quasi-inverse and the idempotent in von Neumann regular
rings without computing the prime decomposition of the
defining ideal of the parameter space, by using the
Modular Dynamic Evaluation [7]. The computation of DCGB
is frequently executed in Suzuki-Sato's algorithm for
computing CGS and CGB [13], and our new algorithm can
improve its practical efficiency.",
acknowledgement = ack-nhfb,
keywords = "comprehensive Gr{\"o}bner bases; comprehensive
discrete Gr{\"o}bner bases; comprehensive Gr{\"o}bner
systems; dynamic evaluation; modular dynamic
evaluation; von Neumann regular rings",
}
@InProceedings{Levin:2007:GBR,
author = "Alexander B. Levin",
title = "{Gr{\"o}bner} bases with respect to several term
orderings and multivariate dimension polynomials",
crossref = "Brown:2007:PIS",
pages = "251--260",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277583",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let {$D$} be a ring of {\O}re polynomials in $m$
variables $ x_1, \ldots {}, x_m $ over a field {$K$}
and let a partition of the set $ \{ x_1, \ldots {}, x_m
\} $ into $p$ disjoint subsets be fixed, so that {$D$}
can be treated as a filtered ring with the natural
$p$-dimensional filtration associated with the
partition. We introduce a special type of reduction in
a finitely generated free {$D$}-module and develop the
corresponding Gr{\"o}bner basis technique that allows
one to prove the existence and find invariants of a
dimension polynomial in $p$ variables associated with a
finitely generated {$D$}-module. We also outline a
method of computation of such a polynomial and obtain
an essential generalization of the Kolchin theorem on
the dimension polynomial of a differential field
extension.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner basis; differential field extension;
dimension polynomial; {\O}re polynomials;
$p$-dimensional filtration",
}
@InProceedings{Li:2007:FAT,
author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
title = "Fast arithmetic for triangular sets: from theory to
practice",
crossref = "Brown:2007:PIS",
pages = "269--276",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277585",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study arithmetic operations for triangular families
of polynomials, concentrating on multiplication in
dimension zero. By a suitable extension of fast
univariate Euclidean division, we obtain theoretical
and practical improvements over a direct recursive
approach; for a family of special cases, we reach
quasi-linear complexity. The main outcome we have in
mind is the acceleration of higher-level algorithms, by
interfacing our low-level implementation with languages
such as AXIOM or Maple We show the potential for huge
speed-ups, by comparing two AXIOM implementations of
van Hoeij and Monagan's modular GCD algorithm.",
acknowledgement = ack-nhfb,
keywords = "high-performance; multiplication; triangular set",
}
@InProceedings{Li:2007:RSG,
author = "Hongbo Li",
title = "A recipe for symbolic geometric computing: long
geometric product, {BREEFS} and {Clifford}
factorization",
crossref = "Brown:2007:PIS",
pages = "261--268",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277584",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In symbolic computing, a major bottleneck is middle
expression swell. Symbolic geometric computing based on
invariant algebras can alleviate this difficulty. For
example, the size of projective geometric computing
based on bracket algebra can often be restrained to two
terms, using final polynomials, area method, Cayley
expansion,etc. This is the `binomial' feature of
projective geometric computing in the language of
bracket algebra.\par
In this paper we report a stunning discovery in
Euclidean geometric computing: the term preservation
phenomenon. Input an expression in the language of Null
Bracket Algebra (NBA), by the recipe we are to propose
in this paper, the computing procedure can often be
controlled to within the same number of terms as the
input, through to the end. In particular, the
conclusions of most Euclidean geometric theorems can be
expressed by monomials in NBA, and the expression size
in the proving procedure can often be controlled to
within one term! Euclidean geometric computing can now
be announced as having a `monomial' feature in the
language of NBA.\par
The recipe is composed of three parts: use long
geometric product to represent and compute
multiplicatively, use `BREEFS' to control the
expression size locally, and use Clifford factorization
for term reduction and transition from algebra to
geometry.\par
By the time this paper is being written, the recipe has
been tested by 70+ examples from [1], among which 30+
have monomial proofs. Among those outside the scope,
the famous Miquel's five circle theorem [2 ], whose
analytic proof is straightforward but very difficult
for symbolic computing, is discovered to have a
3-termed elegant proof with the recipe.",
acknowledgement = ack-nhfb,
keywords = "conformal geometric algebra; geometric invariance;
geometric theorem proving; null bracket algebra;
symbolic geometric computing",
}
@InProceedings{May:2007:EMR,
author = "John P. May and David Saunders and Zhendong Wan",
title = "Efficient matrix rank computation with application to
the study of strongly regular graphs",
crossref = "Brown:2007:PIS",
pages = "277--284",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277586",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present algorithms for computing the $p$-rank of
integer matrices. They are designed to be particularly
effective when $p$ is a small prime, the rank is
relatively low, and the matrix itself is large and
dense and may exceed virtual memory space. Our
motivation comes from the study of difference sets and
partial difference sets in algebraic design theory. The
$p$-rank of the adjacency matrix of an associated
strongly regular graph is a key tool for distinguishing
difference set constructions and thus answering various
existence questions and conjectures. For the $p$-rank
computation, we review several memory efficient
methods, and present refinements suitable to the small
prime, small rank case. We give a new heuristic
approach that is notably effective in practice as
applied to the strongly regular graph adjacency
matrices. It involves projection to a matrix of order
slightly above the rank. The projection is extremely
sparse, is chosen according to one of several
heuristics, and is combined with a small dense
certifying component. Our algorithms and heuristics are
implemented in the LinBox library. We also briefly
discuss some of the software design issues and we
present results of experiments for the Paley and
Dickson sequences of strongly regular graphs.",
acknowledgement = ack-nhfb,
keywords = "matrix $p$-rank; out of core methods",
}
@InProceedings{Mihailescu:2007:CES,
author = "P. Mihailescu and F. Morain and {\'E}. Schost",
title = "Computing the eigenvalue in the
{Schoof--Elkies--Atkin} algorithm using {Abelian}
lifts",
crossref = "Brown:2007:PIS",
pages = "285--292",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277587",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Schoof--Elkies=-Atkin algorithm is the best known
method for counting the number of points of an elliptic
curve defined over a finite field of large
characteristic. We use Abelian properties of division
polynomials to design a fast theoretical and practical
algorithm for finding the eigenvalue.",
acknowledgement = ack-nhfb,
keywords = "elliptic curves; finite fields; SEA algorithm",
}
@InProceedings{Miyamoto:2007:CSM,
author = "Izumi Miyamoto",
title = "A computation of some multiply homogeneous
superschemes from transitive permutation groups",
crossref = "Brown:2007:PIS",
pages = "293--298",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277588",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $G$ be a doubly transitive permutation group on a
set $X$. A doubly homogeneous superscheme is formed by
the orbits on the set of triples of $X$ of $G$. Let
$\alpha$ be a point of a set $X$ and let $H$ be a
transitive group on $X\{\alpha\}$. Then from the
combinatorial structure of the superscheme formed by
the orbits of $H$ on $X^3$ ,we may construct some
doubly homogeneous superschemes on $X$. We will give a
general algorithm to compute such superschemes and show
how to implement it practically. In particular if $H =
G_\alpha$, the stabilizer of $\alpha$ in $G$, then we
can construct a superscheme of which automorphism group
is $G$ in the cases of moderate size. Furthermore, even
if $H$ is not a stabilizer of a doubly transitive
group, we can consider some orbit-like sets of a doubly
homogeneous superscheme. We see whether such sets form
a design in some cases. As a related combinatorial
algorithm we have developed a program to compute the
automorphism group of a superscheme which is a kind of
a labeled hyper graph.",
acknowledgement = ack-nhfb,
}
@InProceedings{Nabeshima:2007:SAC,
author = "Katsusuke Nabeshima",
title = "A speed-up of the algorithm for computing
comprehensive {Gr{\"o}bner} systems",
crossref = "Brown:2007:PIS",
pages = "299--306",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277589",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We introduce a new algorithm for computing
comprehensive Gr{\"o}bner systems. There exists the
Suzuki--Sato algorithm for computing comprehensive
Gr{\"o}bner systems. The Suzuki--Sato algorithm often
creates overmuch cells of the parameter space for
comprehensive Gr{\"o}bner systems. Therefore the
computation becomes heavy. However, by using
inequations (`not equal zero'), we can obtain different
cells. In many cases, this number of cells of parameter
space is smaller than that of Suzuki--Sato's.
Therefore, our new algorithm is more efficient than
Suzuki--Sato's one, and outputs a nice comprehensive
Gr{\"o}bner system. Our new algorithm has been
implemented in the computer algebra system Risa\slash
Asir We compare the runtime of our implementation with
the Suzuki--Sato algorithm and find our algorithm
superior in many cases.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner bases; comprehensive Gr{\"o}bner bases",
}
@InProceedings{Pernet:2007:FAC,
author = "Cl{\'e}ment Pernet and Arne Storjohann",
title = "Faster algorithms for the characteristic polynomial",
crossref = "Brown:2007:PIS",
pages = "307--314",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277590",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A new randomized algorithm is presented for computing
the characteristic polynomial of an $n \times n$ matrix
over a field. Over a sufficiently large field the
asymptotic expected complexity of the algorithm is
$O(n^\theta)$ field operations, improving by a factor
of $\log n$ on the worst case complexity of
Keller--Gehrig's algorithm [11].",
acknowledgement = ack-nhfb,
keywords = "characteristic polynomial; complexity; Frobenius
normal form",
}
@InProceedings{Robinson:2007:DBP,
author = "Eric Robinson and J{\"u}rgen M{\"u}ller and Gene
Cooperman",
title = "A disk-based parallel implementation for direct
condensation of large permutation modules",
crossref = "Brown:2007:PIS",
pages = "315--322",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277591",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Through the use of a new disk-based method for
enumerating very large orbits, condensation for orbits
with tens of billions of elements can be performed. The
algorithm is novel in that it offers efficient access
to data using distributed disk-based data structures.
This provides fast access to hundreds of gigabytes of
data,which allows for computing without worrying about
memory limitations.\par
The new algorithm is demonstrated on one of the
long-standing open problems in the Modular Atlas
Project [11]: the Brauer tree of the principal 17-block
the sporadic simple Fischer group $Fi_{23}$. The tree
is completed by computing three orbit counting matrices
for the $Fi_{23}$ orbit of size 11,739,046,176 acting
on vectors of dimension 728 over GF(2). The
construction of these matrices requires 3-1/2 days on a
cluster of 56 computers, and uses 8 GB of disk storage
and 800 MB of memory per machine.",
acknowledgement = ack-nhfb,
keywords = "Brauer trees; condensation; disk-based computation;
matrix groups; parallel computation; permutation
groups; sporadic Fischer group",
}
@InProceedings{Ruffo:2007:SLD,
author = "James Ruffo",
title = "A straightening law for the {Drinfel'd Lagrangian
Grassmannian}",
crossref = "Brown:2007:PIS",
pages = "323--330",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277592",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Drinfel'd Lagrangian Grassmannian compacts the
space of algebraic maps of fixed degree from the
projective line into the Lagrangian Grassmannian. It
has a natural projective embedding arising from the
highest weight embedding of the ordinary Lagrangian
Grassmannian. We show that the defining ideal of any
Schubert subvariety is generated by polynomials which
give a straightening law on an ordered set.
Consequentially, any such subvariety is Cohen--Macaulay
and Koszul.",
acknowledgement = ack-nhfb,
keywords = "algebras with straightening law; Drinfel'd ag
varieties quasimaps",
}
@InProceedings{Schwarz:2007:LDL,
author = "F. Schwarz",
title = "{Loewy} decomposition of linear differential
equations",
crossref = "Brown:2007:PIS",
pages = "389--390",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277602",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "D-module; Janet basis; Loewy decomposition",
}
@InProceedings{Sekigawa:2007:RFR,
author = "Hiroshi Sekigawa",
title = "On real factors of real interval polynomials",
crossref = "Brown:2007:PIS",
pages = "331--338",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277593",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For a real multivariate interval polynomial $P$ and a
real multivariate polynomial $f$, we provide a rigorous
method for deciding whether there exists a polynomial
$p$ in $P$ such that $p$ is divisible by $f$. When $P$
is univariate, there is a well-known criterion for
whether there exists a polynomial $p(\chi)$ in $P$ such
that $p(\alpha) = 0$ for a given real number $\alpha$.
Since $p(\alpha) = 0$ if and only if $p(\chi)$ is
divisible by $\chi - \alpha$, our result is a
generalization of the criterion to multivariate
polynomials and higher degree factors.",
acknowledgement = ack-nhfb,
keywords = "divisibility; factor; interval polynomial; polytope",
}
@InProceedings{Sharma:2007:CRR,
author = "Vikram Sharma",
title = "Complexity of real root isolation using continued
fractions",
crossref = "Brown:2007:PIS",
pages = "339--346",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277594",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The efficiency of the continued fraction algorithm for
isolating the real roots of a univariate polynomial
depends upon computing tight lower bounds on the
smallest positive root of a polynomial. The known
complexity bounds for the algorithm rely on the
impractical assumption that it is possible to
efficiently compute the floor of the smallest positive
root of a polynomial; without this assumption, the
worst case bounds are exponential. In this paper, we
derive the first polynomial worst case bound on the
algorithm: for a square-free integer polynomial of
degree $n$ and coefficients of bit-length $L$, the
bit-complexity of the continued fraction algorithm is
$\tilde{O}(n^7 L^2)$, using a bound by Hong to compute
the floor of the smallest positive root of a
polynomial; here $\tilde{O}$ indicates that we are
omitting logarithmic factors.",
acknowledgement = ack-nhfb,
keywords = "continued fractions; Davenport-Mahler bound; Descartes
rule of signs; polynomial real root isolation",
}
@InProceedings{Smith:2007:ADA,
author = "Jacob Smith and Gabriel {Dos Reis} and Jaakko
J{\"a}rvi",
title = "Algorithmic differentiation in {Axiom}",
crossref = "Brown:2007:PIS",
pages = "347--354",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277595",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper describes the design and implementation of
an algorithmic differentiation framework in the Axiom
computer algebra system. Our implementation works by
transformations on Spad programs at the level of the
typed abstract syntax tree -- Spad is the language for
extending Axiom with libraries. The framework
illustrates an algebraic theory of algorithmic
differentiation, here only for Spad programs, but we
suggest that the theory is general. In particular, if
it is possible to define a compositional semantics for
programs, we define the exact requirements for when a
program can be algorithmically differentiated. This
leads to a general algorithmic differentiation system,
and is not confined to functions which compute with
basic data types, such as floating point numbers.",
acknowledgement = ack-nhfb,
keywords = "algorithmic differentiation; axiom; program
transformation; symbolic-numeric computation",
}
@InProceedings{vanHoeij:2007:STO,
author = "Mark van Hoeij",
title = "Solving third order linear differential equations in
terms of second order equations",
crossref = "Brown:2007:PIS",
pages = "355--360",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277596",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper presents a simplified version of a method
by Michael Singer for reducing a third order linear ODE
to a second order linear ode whenever possible. An
implementation is available as well.",
acknowledgement = ack-nhfb,
keywords = "linear differential equations; reduction of order",
}
@InProceedings{Villard:2007:CFL,
author = "Gilles Villard",
title = "Certification of the {$QR$} factor {$R$} and of
lattice basis reducedness",
crossref = "Brown:2007:PIS",
pages = "361--368",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277597",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a lattice basis of $n$ vectors in $Z_n$, we
propose an algorithm using $12 n^3 + O(n^2)$ floating
point operations for checking whether the basis is
$LLL$-reduced. If the basis is reduced then the
algorithm will hopefully answer `yes'. If the basis is
not reduced, or if the precision used is not sufficient
with respect to $n$, and to the numerical properties of
the basis, the algorithm will answer `failed'. Hence a
positive answer is a rigorous certificate. For
implementing the certificate itself, we propose a
floating point algorithm for computing (certified)
error bounds for the $R$ factor of the $QR$
factorization. This algorithm takes into account all
possible approximation and rounding errors. The
certificate may be implemented using matrix library
routines only. We report experiments that show that for
a reduced basis of adequate dimension and quality the
certificate succeeds, and establish the effectiveness
of the certificate. This effectiveness is applied for
certifying the output of fastest existing floating
point heuristics of $LLL$ reduction, without slowing
down the whole process.",
acknowledgement = ack-nhfb,
keywords = "lattice basis reducedness; linear algebra; QR
factorization; verification algorithm",
}
@InProceedings{Villard:2007:SRP,
author = "Gilles Villard",
title = "Some recent progress in exact linear algebra and
related questions",
crossref = "Brown:2007:PIS",
pages = "391--392",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277603",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We describe some major recent progress in exact and
symbolic linear algebra. These advances concern the
improvement of complexity estimates for fundamental
problems such as linear system solution, determinant,
inversion and computation of canonical forms. The
matrices are over a finite field, the integers, or
univariate polynomials. We show how selected techniques
are key ingredients for the new solutions:
randomization and algebraic conditioning, lifting,
subspace approach, divide-double and conquer, minimum
matrix polynomial, matrix approximants. These
algorithmic progress allow the design of new generation
high performance libraries such as LinBox, and open
various research directions.\par
We refer to [3] for an overview of methods in exact
linear algebra, see also [37], [1] (in French), and [7,
x2.3]. For fundamentals of computer algebra we refer to
[16, 7].",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:2007:CRS,
author = "Joachim von zur Gathen",
title = "Counting reducible and singular bivariate
polynomials",
crossref = "Brown:2007:PIS",
pages = "369--376",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277598",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Among the bivariate polynomials over a finite field,
most are irreducible. We count some classes of special
polynomials, namely the reducible ones, those with a
square factor, the `relatively irreducible' ones which
are irreducible but factor over an extension field, and
the singular ones, which have a root at which both
partial derivatives vanish.",
acknowledgement = ack-nhfb,
keywords = "bivariate polynomials; combinatorics on polynomials;
counting problems; finite fields; reducible
polynomials; singular polynomials",
}
@InProceedings{Wu:2007:SNC,
author = "Wenyuan Wu and Greg Reid",
title = "Symbolic-numeric computation of implicit {Riquier
Bases} for {PDE}",
crossref = "Brown:2007:PIS",
pages = "377--386",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277599",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Riquier Bases for systems of analytic pde are, loosely
speaking, a differential analogue of Gr{\"o}bner Bases
for polynomial equations. They are determined in the
exact case by applying a sequence of prolongations
(differentiations) and eliminations to an input system
of pde.\par
We present a symbolic-numeric method to determine
Riquier Bases in implicit form for systems which are
dominated by pure derivatives in one of the independent
variables and have the same number of pde and
unknowns.\par
The method is successful provided the prolongations
with respect to the dominant independent variable have
a block structure which is uncovered by Linear
Programming and certain Jacobians are non-singular when
evaluated at points on the zero sets defined by the
functions of the pde. For polynomially nonlinear pde,
homotopy continuation methods from Numerical Algebraic
Geometry can be used to compute approximations of the
points.\par
We give a differential algebraic interpretation of
Pryce's method for ode, which generalizes to the pde
case. A major aspect of the method's efficiency is that
only prolongations with respect to a single (dominant)
independent variable are made, possibly after a random
change of coordinates. Potentially expensive and
numerically unstable eliminations are not made.
Examples are given to illustrate theoretical features
of the method, including a curtain of Pendula and the
control of a crane.",
acknowledgement = ack-nhfb,
keywords = "implicit function theorem; jet spaces; linear
programming; numerical algebraic geometry; partial
differential equation; ranking; Riquier Bases",
}
@InProceedings{Abramov:2008:PSL,
author = "Sergei A. Abramov",
title = "Power series and linear difference equations",
crossref = "Jeffrey:2008:PAM",
pages = "1--2",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390769",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "linear difference equation with polynomial
coefficients; power series; sequential solution;
subanalytic solution",
}
@InProceedings{Achatz:2008:DPE,
author = "Melanie Achatz and Scott McCallum and Volker
Weispfenning",
title = "Deciding polynomial-exponential problems",
crossref = "Jeffrey:2008:PAM",
pages = "215--222",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390799",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper presents a decision procedure for a certain
class of sentences of first order logic involving
integral polynomials and the exponential function in
which the variables range over the real numbers. The
inputs to the decision procedure are prenex sentences
in which only the outermost quantified variable can
occur in the exponential function. The decision
procedure has been implemented in the computer logic
system REDLOG. Closely related work is reported in [2,
7, 16, 20, 24].",
acknowledgement = ack-nhfb,
keywords = "decision procedure; exponential polynomials",
}
@InProceedings{Antritter:2008:TCA,
author = "Felix Antritter and Jean L{\'e}vine",
title = "Towards a computer algebraic algorithm for flat output
determination",
crossref = "Jeffrey:2008:PAM",
pages = "7--14",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390773",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This contribution deals with nonlinear control
systems. More precisely, we are interested in the
formal computation of a so-called flat output, a
particular generalized output whose property is,
roughly speaking, that all the integral curves of the
system may be expressed as smooth functions of the
components of this flat output and their successive
time derivatives up to a finite order (to be
determined). Recently, a characterization of such flat
output has been obtained in the framework of manifolds
of jets of infinite order that yields an abstract
algorithm for its computation. In this paper it is
discussed how these conditions can be checked using
computer algebra. All steps of the algorithm are
discussed for the simple (but rich enough) example of a
non holonomic car.",
acknowledgement = ack-nhfb,
keywords = "control systems; differential flatness",
}
@InProceedings{Aschenbrenner:2008:AFS,
author = "Matthias Aschenbrenner and Christopher J. Hillar",
title = "An algorithm for finding symmetric {Gr{\"o}bner} bases
in infinite dimensional rings",
crossref = "Jeffrey:2008:PAM",
pages = "117--124",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390787",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A {\em symmetric ideal\/} $I \subset R = K[x_1,
x_2,\ldots{}]$ is an ideal that is invariant under the
natural action of the infinite symmetric group. We give
an explicit algorithm to find Gr{\"o}bner bases for
symmetric ideals in the infinite dimensional polynomial
ring $R$. This allows for symbolic computation in a new
class of rings. In particular, we solve the ideal
membership problem for symmetric ideals of $R$.",
acknowledgement = ack-nhfb,
keywords = "algorithm; Gr{\"o}bner basis; invariant ideal; partial
ordering; polynomial reduction; symmetric group",
}
@InProceedings{Barkatou:2008:RSL,
author = "Moulay A. Barkatou and Gary Broughton and Eckhard
Pfl{\"u}gel",
title = "Regular systems of linear functional equations and
applications",
crossref = "Jeffrey:2008:PAM",
pages = "15--22",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390774",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The algorithmic classification of singularities of
linear differential systems via the computation of
Moser- and super-irreducible forms as introduced in
[21] and [16] respectively has been widely studied in
Computer Algebra ([8, 12, 22, 6, 10]). Algorithms have
subsequently been given for other forms of systems such
as linear difference systems [4, 3] and the perturbed
algebraic eigenvalue problem [18]. In this paper, we
extend these concepts to the general class of systems
of linear functional equations. We derive a definition
of regularity for these type of equations, and an
algorithm for recognizing regular systems. When
specialised to $q$-difference systems, our results lead
to new algorithms for computing polynomial solutions
and regular formal solutions.",
acknowledgement = ack-nhfb,
keywords = "computer algebra; Moser-reduction; singularities;
super-reduction; systems of linear functional
equations",
}
@InProceedings{Bostan:2008:POD,
author = "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Nicolas Le
Roux",
title = "Products of ordinary differential operators by
evaluation and interpolation",
crossref = "Jeffrey:2008:PAM",
pages = "23--30",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390775",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "It is known that multiplication of linear differential
operators over ground fields of characteristic zero can
be reduced to a constant number of matrix products. We
give a new algorithm by evaluation and interpolation
which is faster than the previously-known one by a
constant factor, and prove that in characteristic zero,
multiplication of differential operators and of
matrices are computationally equivalent problems. In
positive characteristic, we show that differential
operators can be multiplied in nearly optimal time.
Theoretical results are validated by intensive
experiments.",
acknowledgement = ack-nhfb,
keywords = "differential operators; fast algorithms",
}
@InProceedings{Bostan:2008:PSC,
author = "Alin Bostan and Bruno Salvy and {\'E}ric Schost",
title = "Power series composition and change of basis",
crossref = "Jeffrey:2008:PAM",
pages = "269--276",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390806",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Efficient algorithms are known for many operations on
truncated power series (multiplication, powering,
exponential, \ldots{}). Composition is a more complex
task. We isolate a large class of power series for
which composition can be performed efficiently. We
deduce fast algorithms for converting polynomials
between various bases, including Euler, Bernoulli,
Fibonacci, and the orthogonal Laguerre, Hermite,
Jacobi, Krawtchouk, Meixner and Meixner--Pollaczek.",
acknowledgement = ack-nhfb,
keywords = "basis conversion; fast algorithms; orthogonal
polynomials; transposed algorithms",
}
@InProceedings{Brickenstein:2008:GFN,
author = "Michael Brickenstein and Alexander Dreyer",
title = "{Gr{\"o}bner}-free normal forms for {Boolean}
polynomials",
crossref = "Jeffrey:2008:PAM",
pages = "55--62",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390779",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper introduces a new method for interpolation
of Boolean functions using Boolean polynomials. It was
motivated by some problems arising from computational
biology, for reverse engineering the structure of
mechanisms in gene regulatory networks. For this
purpose polynomial expressions have to be generated,
which match known state combinations observed during
experiments. Earlier approaches using Gr{\"o}bner
techniques have not been powerful enough to treat
real-world applications. The proposed method avoids
expensive Gr{\"o}bner basis computations completely by
directly calculating reduced normal forms. The problem
statement can be described by Boolean polynomials,
i.e., polynomials with coefficients in $\{0,1\}$ and a
degree bound of one. Therefore, the reference
implementations mentioned in this work are built on the
top of the PolyBoRi framework, which has been designed
exclusively for the treatment of this special class of
polynomials. A series of randomly generated examples is
used to demonstrate the performance of the direct
method. It is also compared with other approaches,
which incorporate Gr{\"o}bner basis computations.",
acknowledgement = ack-nhfb,
keywords = "Boolean polynomials; Gr{\"o}bner interpolation; normal
forms",
}
@InProceedings{Burr:2008:CSA,
author = "Michael Burr and Sung Woo Choi and Benjamin Galehouse
and Chee K. Yap",
title = "Complete subdivision algorithms, {II}: isotopic
meshing of singular algebraic curves",
crossref = "Jeffrey:2008:PAM",
pages = "87--94",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390783",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a real function $f(X,Y)$, a box region $B$ and
$\epsilon > 0$, we want to compute an
$\epsilon$-isotopic polygonal approximation to the
curve $C : f(X,Y) = 0$ within $B$. We focus on
subdivision algorithms because of their adaptive
complexity. Plantinga \& Vegter (2004) gave a numerical
subdivision algorithm that is exact when the curve $C$
is non-singular. They used a computational model that
relies only on function evaluation and interval
arithmetic.\par
We generalize their algorithm to any (possibly
non-simply connected) region $B$ that does not contain
singularities of $C$. With this generalization as
subroutine, we provide a method to detect isolated
algebraic singularities and their branching degree.
This appears to be the first complete {\em numerical\/}
method to treat implicit algebraic curves with isolated
singularities.",
acknowledgement = ack-nhfb,
keywords = "complete numerical algorithm; evaluation bound;
implicit algebraic curve; meshing; root bound;
singularity; subdivision algorithm",
}
@InProceedings{Caboara:2008:GBP,
author = "Massimo Caboara and Fabrizio Caruso and Carlo
Traverso",
title = "{Gr{\"o}bner} bases for public key cryptography",
crossref = "Jeffrey:2008:PAM",
pages = "315--324",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390811",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Up to now, any attempt to use Gr{\"o}bner bases in the
design of public key cryptosystems has failed, as
anticipated by a classical paper of B. Barkee et al.;
we show why, and show that the only residual hope is to
use binomial ideals, i.e., lattices. We propose two
lattice-based cryptosystems that will show the
usefulness of multivariate polynomial algebra and
Gr{\"o}bner bases in the construction of public key
cryptosystems. The first one tries to revive two
cryptosystems Polly Cracker and GGH, that have been
considered broken, through a hybrid; the second one
improves a cryptosystem (NTRU) that only has heuristic
and challenged evidence of security, providing evidence
that the extension cannot be broken with some of the
standard lattice tools that can be used to break some
reduced form of NTRU. Because of the bounds on length,
we only sketch the construction of these two
cryptosystems, and leave many details of the
construction of private and public keys, of the proofs
and of the security considerations to forthcoming
technical papers.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner basis; Gr{\"o}bner Hermite normal form;
lattice; public key cryptosystem",
}
@InProceedings{Daouda:2008:CTN,
author = "Diatta Niang Daouda and Bernard Mourrain and Olivier
Ruatta",
title = "On the computation of the topology of a non-reduced
implicit space curve",
crossref = "Jeffrey:2008:PAM",
pages = "47--54",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390778",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An algorithm is presented for the computation of the
topology of a non-reduced space curve defined as the
intersection of two implicit algebraic surfaces.\par
It computes a Piecewise Linear Structure (PLS) isotopic
to the original space curve.\par
The algorithm is designed to provide the exact result
for all inputs. It's a symbolic-numeric algorithm based
on subresultant computation. Simple algebraic criteria
are given to certify the output of the
algorithm.\par
The algorithm uses only one projection of the
non-reduced space curve augmented with adjacency
information around some 'particular points' of the
space curve.\par
The algorithm is implemented with the Mathemagix
Computer Algebra System (CAS) using the SYNAPS library
as a backend.",
acknowledgement = ack-nhfb,
keywords = "algebraic curves; exact geometric computation; generic
conditions; Sturm--Habicht sequence; subresultants
sequence; topology computation",
}
@InProceedings{Debeerst:2008:SDE,
author = "Ruben Debeerst and Mark van Hoeij and Wolfram Koepf",
title = "Solving differential equations in terms of {Bessel}
functions",
crossref = "Jeffrey:2008:PAM",
pages = "39--46",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390777",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For differential operators of order 2, this paper
presents a new method that combines generalized
exponents to find those solutions that can be
represented in terms of Bessel functions.",
acknowledgement = ack-nhfb,
keywords = "Bessel functions; differential equations; generalized
exponents",
}
@InProceedings{Din:2008:CGO,
author = "Mohab Safey El Din",
title = "Computing the global optimum of a multivariate
polynomial over the reals",
crossref = "Jeffrey:2008:PAM",
pages = "71--78",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390781",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $f$ be a polynomial in $Q[X_1, \ldots{}, X_n]$ of
degree $D$. We provide an efficient algorithm in
practice to compute the global supremum $\sup_{x \in
R^n} f(x)$ of $f$ (or its infimum $\inf_{x \in R^n}
f(x)$). The complexity of our method is bounded by
$D^{O(n)}$. In a probabilistic model, a more precise
result yields a complexity bounded by $O(n^7 D^{4n})$
arithmetic operations in $Q$. Our implementation is
more efficient by several orders of magnitude than
previous ones based on quantifier elimination.
Sometimes, it can tackle problems that numerical
techniques do not reach. Our algorithm is based on the
computation of generalized critical values of the
mapping $x \rightarrow f(x)$, i.e., the set of points
\{$c \in C \mid \exists (x_\ell)_{\ell \in N} \subset
C^n f(x_\ell) \rightarrow c$, $||x_\ell ||
||d_{x_\ell}f|| \rightarrow 0$ when $\ell \rightarrow
\infty$\}. We prove that the global optimum of $f$ lies
in its set of generalized critical values and provide
an efficient way of deciding which value is the global
optimum.",
acknowledgement = ack-nhfb,
keywords = "complexity; global optimization; polynomial system
solving; real solutions",
}
@InProceedings{Dumas:2008:QAT,
author = "Jean-Guillaume Dumas",
title = "{Q}-adic transform revisited",
crossref = "Jeffrey:2008:PAM",
pages = "63--70",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390780",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present an algorithm to perform a simultaneous
modular reduction of several residues. This enables to
compress polynomials into integers and perform several
modular operations with machine integer arithmetic. The
idea is to convert the $X$-adic representation of
modular polynomials, with $X$ an indeterminate, to a
$q$-adic representation where $q$ is an integer larger
than the field characteristic. With some control on the
different involved sizes it is then possible to perform
some of the $q$-adic arithmetic directly with machine
integers or floating points. Depending also on the
number of performed numerical operations one can then
convert back to the $q$-adic or X-adic representation
and eventually mod out high residues. In this note we
present a new version of both conversions: more
tabulations and a way to reduce the number of divisions
involved in the process are presented. The polynomial
multiplication is then applied to arithmetic and linear
algebra in small finite field extensions.",
acknowledgement = ack-nhfb,
keywords = "DQT (discrete $q$-adic transform); finite field; FQT
(fast $q$-adic transform); Kronecker substitution;
modular polynomial multiplication; REDQ (simultaneous
modular reduction); small extension field",
}
@InProceedings{Faugere:2008:CPT,
author = "Jean-Charles Faug{\`e}re and Guillaume Moroz and
Fabrice Rouillier and Mohab Safey El Din",
title = "Classification of the perspective-three-point problem,
discriminant variety and real solving polynomial
systems of inequalities",
crossref = "Jeffrey:2008:PAM",
pages = "79--86",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390782",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Classifying the Perspective-Three-Point problem
(abbreviated by P3P in the sequel) consists in
determining the number of possible positions of a
camera with respect to the apparent position of three
points. In the case where the three points form an
isosceles triangle, we give a full classification of
the P3P. This leads to consider a polynomial system of
polynomial equations and inequalities with 4 parameters
which is generically zero-dimensional. In the present
situation, the parameters represent the apparent
position of the three points so that solving the
problem means determining all the possible numbers of
real solutions with respect to the parameters' values
and give a sample point for each of these possible
numbers. One way for solving such systems consists
first in computing a {\em discriminant variety}. Then,
one has to compute at least one point in each connected
component of its real complementary in the parameter's
space. The last step consists in specializing the
parameters appearing in the initial system by these
sample points. Many computational tools may be used for
implementing such a general method, starting with the
well known Cylindrical Algebraic Decomposition (CAD in
short), which provides more information than required.
In a first stage, we propose a full algorithm based on
the straightforward use of some sophisticated software
such as FGb (Gr{\"o}bner bases computations) RS (real
roots of zero-dimensional systems), DV (Discriminant
varieties) and RAGlib (Critical point methods for
semi-algebraic systems). We then improve the global
algorithm by refining the required computable
mathematical objects and related algorithms and finally
provide the classification. Three full days of
computation were necessary to get this classification
which is obtained from more than 40000 points in the
parameter's space.",
acknowledgement = ack-nhfb,
keywords = "complexity; computer vision; perspective-three-point
problem; polynomial system solving; real solutions",
}
@InProceedings{Fukuda:2008:EAS,
author = "Komei Fukuda",
title = "Exact algorithms and software in optimization and
polyhedral computation",
crossref = "Jeffrey:2008:PAM",
pages = "333--334",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390814",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this tutorial, we present a new field of research
on implementing exact algorithms in optimization and
polyhedral computation in exact (arbitrary precision)
arithmetic. Such algorithms including those to solve
linear programming and convex hull problems have been
implemented mostly with floating-point arithmetic. This
new field of developing 'exact software' in
optimization and polyhedral computation is now at the
second stage where new mathematical tools relying on
optimization and polyhedral codes are being developed
that have not been implemented before. This tutorial is
not meant to cover all important developments but to
look at some interesting facets.",
acknowledgement = ack-nhfb,
keywords = "algorithms; convex geometry; exact implementation;
optimization; polytopes",
}
@InProceedings{Gerdt:2008:PDA,
author = "Vladimir P. Gerdt and Mikhail V. Zinin",
title = "A {Pommaret} division algorithm for computing
{Gr{\"o}bner} bases in {Boolean} rings",
crossref = "Jeffrey:2008:PAM",
pages = "95--102",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390784",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper an involutive algorithm for construction
of Gr{\"o}bner bases in Boolean rings is presented. The
algorithm exploits the Pommaret monomial division as an
involutive division. In distinction to other approaches
and due to special properties of Pommaret division the
algorithm allows to perform the Gr{\"o}bner basis
computation directly in a Boolean ring which can be
defined as the quotient ring $F_2 [x_1 ,\ldots{},x_n ],
1^2 + x_1 ,\ldots{}, x_n^2 + x_n$. Some related
cardinality bounds for Pommaret and Gr{\"o}bner bases
are derived. Efficiency of our first implementation of
the algorithm is illustrated by a number of serial
benchmarks.",
acknowledgement = ack-nhfb,
keywords = "Boolean ring; Gr{\"o}bner basis; involutive algorithm;
Pommaret division",
}
@InProceedings{Giesbrecht:2008:LPP,
author = "Mark Giesbrecht and Daniel S. Roche",
title = "On lacunary polynomial perfect powers",
crossref = "Jeffrey:2008:PAM",
pages = "103--110",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390785",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider the problem of determining whether a
$t$-sparse or lacunary polynomial $f$ is a perfect
power, that is, $f = h^r$ for some other polynomial $h$
and positive integer $r$, and of finding $h$ and $r$
should they exist. We show how to determine if $f$ is a
perfect power in time polynomial in the size of the
lacunary representation. The algorithm works over
GF(q)[x] (at least for large characteristic) and over
Z[x], where the cost is also polynomial in the log of
the infinity norm of $f$. Subject to a conjecture, we
show how to find $h$ if it exists via a kind of sparse
Newton iteration, again in time polynomial in the size
of the sparse representation. Finally, we demonstrate
an implementation using the C++ library NTL.",
acknowledgement = ack-nhfb,
keywords = "black box polynomial; lacunary polynomial; perfect
power; sparse polynomial",
}
@InProceedings{Grigoriev:2008:LDT,
author = "Dima Grigoriev and Fritz Schwarz",
title = "{Loewy} decomposition of third-order linear {PDE}'s in
the plane",
crossref = "Jeffrey:2008:PAM",
pages = "277--286",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390807",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Loewy's decomposition of a linear ordinary
differential operator as the product of largest
completely reducible components is generalized to
partial differential operators of order three in two
variables. This is made possible by considering the
problem in the ring of partial differential operators
where both left intersections and right divisors of
left ideals are not necessarily principal. Listings of
possible decomposition types are given. Many of them
are illustrated by worked out examples. Algorithmic
questions and questions of uniqueness are discussed in
the Summary.",
acknowledgement = ack-nhfb,
keywords = "factorization; linear partial differential equations;
Loewy decomposition",
}
@InProceedings{Henrion:2008:PGC,
author = "Didier Henrion and Michael Sebek",
title = "Plane geometry and convexity of polynomial stability
regions",
crossref = "Jeffrey:2008:PAM",
pages = "111--116",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390786",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The set of controllers stabilizing a linear system is
generally non-convex in the parameter space. In the
case of two-parameter controller design (e.g. PI
control or static output feedback with one input and
two outputs), we observe however that quite often for
benchmark problem instances, the set of stabilizing
controllers seems to be convex. In this note we use
elementary techniques from real algebraic geometry
(resultants and Bezoutian matrices) to explain this
phenomenon. As a byproduct, we derive a convex linear
matrix inequality (LMI) formulation of two-parameter
fixed-order controller design problem, when possible.",
acknowledgement = ack-nhfb,
keywords = "control theory; convexity; resultants",
}
@InProceedings{Janovitz-Freireich:2008:MMT,
author = "Itnuit Janovitz-Freireich and Agnes Sz{\'a}nt{\'o} and
Bernard Mourrain and Lajos Ronyai",
title = "Moment matrices, trace matrices and the radical of
ideals",
crossref = "Jeffrey:2008:PAM",
pages = "125--132",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390788",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $f_1, \ldots{}, f_s$ be a system of polynomials in
$K[x_1,\ldots{}, x_m]$ generating a zero-dimensional
ideal $I$ , where $K$ is an arbitrary algebraically
closed field. Assume that the factor algebra $A = K[x_
, \ldots{}, x_m] / I$ is Gorenstein and that we have a
bound $\delta > 0$ such that a basis for $A$ can be
computed from multiples of $f_1,\ldots{}, f_s$ of
degrees at most $\delta$. We propose a method using
Sylvester or Macaulay type resultant matrices of
$f_1,\ldots{}, f_s$ and $J$, where $J$ is a polynomial
of degree $\delta$ generalizing the Jacobian, to
compute moment matrices, and in particular matrices of
traces for $A$. These matrices of traces in turn allow
us to compute a system of multiplication matrices
$\{Mx_i|i = 1,\ldots{}, m\}$ of the radical of $I$,
following the approach in the previous work by
Janovitz-Freireich, Ronyai and Szanto. Additionally, we
give bounds for delta for the case when $I$ has
finitely many projective roots.",
acknowledgement = ack-nhfb,
keywords = "matrices of traces; moment matrices; radical ideal;
solving polynomial systems",
}
@InProceedings{Kadyrsizova:2008:LRS,
author = "Zhibek Kadyrsizova and Valery G. Romanovski",
title = "Linearizablity of $1$:$-3$ resonant system with
homogeneous cubic nonlinearities",
crossref = "Jeffrey:2008:PAM",
pages = "255--260",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390804",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study the systems of differential equations of the
form $\dot{x} = x + p(x,y)$, $\dot{y} = -3y + q(x,y)$,
where $p$ and $q$ are homogeneous polynomials of degree
three (either of which may be zero). The necessary and
sufficient coefficient conditions for linearization of
such systems are obtained.",
acknowledgement = ack-nhfb,
keywords = "normal forms; ordinary differential equations;
polynomial ideals; the center and linearizability
problems",
}
@InProceedings{Kaltofen:2008:ECG,
author = "Erich Kaltofen and Bin Li and Zhengfeng Yang and
Lihong Zhi",
title = "Exact certification of global optimality of
approximate factorizations via rationalizing
sums-of-squares with floating point scalars",
crossref = "Jeffrey:2008:PAM",
pages = "155--164",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390792",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We generalize the technique by Peyrl and Parillo
[Proc. SNC 2007] to computing lower bound certificates
for several well-known factorization problems in hybrid
symbolic-numeric computation. The idea is to transform
a numerical sum-of-squares (SOS) representation of a
positive polynomial into an exact rational identity.
Our algorithms successfully certify accurate rational
lower bounds near the irrational global optima for
benchmark approximate polynomial greatest common
divisors and multivariate polynomial irreducibility
radii from the literature, and factor coefficient
bounds in the setting of a model problem by Rump (up to
$n = 14$, factor degree $= 13$).\par
The numeric SOSes produced by the current fixed
precision semi-definite programming (SDP) packages
(SeDuMi, SOSTOOLS, YALMIP) are usually too coarse to
allow successful projection to exact SOSes via Maple
11's exact linear algebra. Therefore, before projection
we refine the SOSes by rank-preserving Newton
iteration. For smaller problems the starting SOSes for
Newton can be guessed without SDP (`SDP-free SOS'), but
for larger inputs we additionally appeal to sparsity
techniques in our SDP formulation.",
acknowledgement = ack-nhfb,
keywords = "approximate factorization; hybrid method; semidefinite
programming; sum-of-squares; validated output",
}
@InProceedings{Kaltofen:2008:EFT,
author = "Erich Kaltofen and Pascal Koiran",
title = "Expressing a fraction of two determinants as a
determinant",
crossref = "Jeffrey:2008:PAM",
pages = "141--146",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390790",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Suppose the polynomials $f$ and $g$ in $K[x_1,
\ldots{}, x_r]$ over the field $K$ are determinants of
non-singular $m \times m$ and $n \times n$ matrices,
respectively, whose entries are in $K \cup x_1,
\ldots{}, x_r$. Furthermore, suppose $h = f/g$ is a
polynomial in $K[x_1, \ldots{}, x_r]$. We construct an
$s \times s$ matrix $C$ whose entries are in $K \cup
x_1,\ldots{}, x_r$, such that $h = \det(C)$ and $s =
\gamma(m+n)^6$, where $\gamma = O(1)$ if $K$ is an
infinite field or if for the finite field $K = F\{q\}$
with $q$ elements we have $m = O(q)$, and where $\gamma
= (\log_q m)^{1 + o(1)}$ if $q = o(m)$. Our
construction utilizes the notion of skew circuits by
Toda and WSK circuits by Malod and Portier. Our problem
was motivated by resultant formulas derived from Chow
forms.\par
Additionally, we show that divisions can be removed
from formulas that compute polynomials in the input
variables over a sufficiently large field within
polynomial formula size growth.",
acknowledgement = ack-nhfb,
keywords = "algebraic complexity theory; formula complexity;
Strassen's removal of divisions; Toda's skew circuits;
Valiant's universality of determinants",
}
@InProceedings{Kanno:2008:SOA,
author = "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
and Shinji Hara",
title = "Symbolic optimization of algebraic functions",
crossref = "Jeffrey:2008:PAM",
pages = "147--154",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390791",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper attempts to establish a new framework of
symbolic optimization of algebraic functions that is
relevant to possibly a wide variety of practical
application areas. The crucial aspects of the framework
are (i) the suitable use of algebraic methods coupled
with the discovery and exploitation of structural
properties of the problem in the conversion process
into the framework, and (ii) the feasibility of
algebraic methods when performing the optimization. As
an example an algebraic approach is developed for the
discrete-time polynomial spectral factorization problem
that illustrates the significance and relevance of the
proposed framework. A numerical example of a particular
control problem is also included to demonstrate the
development.",
acknowledgement = ack-nhfb,
keywords = "Gr{\"o}bner basis; parametric optimization; polynomial
spectral factorization; quantifier elimination",
}
@InProceedings{Kauers:2008:IAF,
author = "Manuel Kauers",
title = "Integration of algebraic functions: a simple heuristic
for finding the logarithmic part",
crossref = "Jeffrey:2008:PAM",
pages = "133--140",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390789",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A new method is proposed for finding the logarithmic
part of an integral over an algebraic function. The
method uses Groebner bases and is easy to implement. It
does not have the feature of finding a closed form of
an integral whenever there is one. But it very often
does, as we will show by a comparison with the built-in
integrators of some computer algebra systems.",
acknowledgement = ack-nhfb,
keywords = "algebraic functions; symbolic integration",
}
@InProceedings{Kemper:2008:AIT,
author = "Gregor Kemper",
title = "Algorithmic invariant theory",
crossref = "Jeffrey:2008:PAM",
pages = "335--336",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390815",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "computational commutative algebra; invariant theory",
}
@InProceedings{Lemaire:2008:WDE,
author = "Francois Lemaire and Marc Moreno Maza and Wei Pan and
Yuzhen Xie",
title = "When does $({T})$ equal {${\rm Sat}(T)$}?",
crossref = "Jeffrey:2008:PAM",
pages = "207--214",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390798",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a regular chain $T$, we aim at finding an
efficient way for computing a system of generators of
${\rm Sat}(T)$, the saturated ideal of $T$. A natural
idea is to test whether the equality $(T) = {\rm
Sat}(T)$ holds, that is, whether $T$ generates its
saturated ideal. By generalizing the notion of
primitivity from univariate polynomials to regular
chains, we establish a necessary and sufficient
condition, together with a Gr{\"o}bner basis free
algorithm, for testing this equality. Our experimental
results illustrate the efficiency of this approach in
practice.",
acknowledgement = ack-nhfb,
keywords = "megasquid; primitivity of polynomials; regular chain;
saturated ideal",
}
@InProceedings{Levandovskyy:2008:CMT,
author = "Viktor Levandovskyy and Jorge Martin Morales",
title = "Computational {$D$}-module theory with singular,
comparison with other systems and two new algorithms",
crossref = "Jeffrey:2008:PAM",
pages = "173--180",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390794",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present the new implementation of core functions
for the computational $D$-module theory. It is realized
as a library {\tt dmod.lib} in the computer algebra
system Singular. We show both theoretical advances,
such as the LOT and checkRoot algorithms as well as the
comparison of our implementation with other packages
for $D$-modules in computer algebra systems kan/sm1,
Asir and Macaulay. The comparison indicates, that our
implementation is among the fastest ones. With our
package we are able to solve several challenges in
D-module theory and we demonstrate the answers to these
problems.",
acknowledgement = ack-nhfb,
keywords = "annihilator; Bernstein--Sato polynomial; D-modules;
Gr{\"o}bner bases; intersection with subalgebra;
non-commutative Gr{\"o}bner bases; preimage of ideal",
}
@InProceedings{Leykin:2008:NPD,
author = "Anton Leykin",
title = "Numerical primary decomposition",
crossref = "Jeffrey:2008:PAM",
pages = "165--172",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390793",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Consider an ideal $I \subset R = C[x_1, \ldots{},
x_n]$ defining a complex affine variety $X \subset
C^n$. We describe the components associated to $I$ by
means of {\em numerical primary decomposition\/} (NPD).
The method is based on the construction of {\em
deflation ideal\/} $I^{(d)}$ that defines the {\em
deflated variety\/} $X^{(d)}$ in a complex space of
higher dimension. For every embedded component there
exists $d$ and an isolated component $Y^{(d)}$ of
$I^{(d)}$ projecting onto $Y$. In turn, $Y^{(d)}$ can
be discovered by existing methods for prime
decomposition, in particular, the {\em numerical
irreducible decomposition}, applied to $X^{(d)}$. The
concept of NPD gives a full description of the scheme
Spec(R/I) by representing each component with a {\em
witness set}. We propose an algorithm to produce a
collection of witness sets that contains a NPD and that
can be used to solve the {\em ideal membership
problem\/} for $I$.",
acknowledgement = ack-nhfb,
keywords = "deflation; numerical algebraic geometry; polynomial
homotopy continuation; primary decomposition",
}
@InProceedings{Li:2008:CBB,
author = "Hongbo Li and Lei Huang",
title = "Complex brackets, balanced complex differences, and
applications in symbolic geometric computing",
crossref = "Jeffrey:2008:PAM",
pages = "181--188",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390795",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In advanced invariant algebras such as null bracket
algebra (NBA), symmetries of algebraic operators are
the most important devices of encoding and employing
syzygies of advanced geometric invariants. The larger
the symmetry group, the more powerful the computing
devices. In this paper, the largest symmetry group of
the two kinds of bracket operators in the NBA of plane
geometry is found. An algorithm of complexity $O(N \log
N)$ is proposed to reduce a bracket of length $N$ to
its normal form, and then decide the congruence of two
brackets of length $N$. By writing the two bracket
operators as the real and pure imaginary parts of a
complex bracket operator, their normal forms can be
translated into a class of complex polynomials whose
variables are first-order differences, called balanced
complex difference (BCD) polynomials. BCD polynomials
provide a complex-numbers-based invariant language for
advanced algebraic manipulations of geometric problems.
A simplification algorithm is proposed for making
symbolic geometric computing with NBA and BCD
polynomials, with the unique feature of controlling the
expression size by avoiding multilinear expansions of
the first-order difference variables of complex
polynomials.",
acknowledgement = ack-nhfb,
keywords = "bracket algebra; complex numbers method; geometric
algebra; graph theory; theorem proving",
}
@InProceedings{Liang:2008:CRC,
author = "Songxin Liang and David J. Jeffrey and Marc Moreno
Maza",
title = "The complete root classification of a parametric
polynomial on an interval",
crossref = "Jeffrey:2008:PAM",
pages = "189--196",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390796",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a real parametric polynomial $p(x)$ and an
interval $(a,b) \subset R$, the Complete Root
Classification (CRC) of $p(x)$ on $(a,b)$ is a
collection of all possible cases of its root
classification on $(a,b)$, together with the conditions
its coefficients must satisfy for each case. In this
paper, a new algorithm is proposed for the automatic
computation of the complete root classification of a
parametric polynomial on an interval. As a direct
application, the new algorithm is applied to some real
quantifier elimination problems.",
acknowledgement = ack-nhfb,
keywords = "complete root classification; interval; parametric
polynomial; real quantifier elimination; real root",
}
@InProceedings{Loera:2008:HNA,
author = "J. A. De Loera and J. Lee and P. N. Malkin and S.
Margulies",
title = "{Hilbert}'s {Nullstellensatz} and an algorithm for
proving combinatorial infeasibility",
crossref = "Jeffrey:2008:PAM",
pages = "197--206",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390797",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Systems of polynomial equations over an
algebraically-closed field $K$ can be used to concisely
model many combinatorial problems. In this way, a
combinatorial problem is feasible (e.g., a graph is
3-colorable, Hamiltonian, etc.) if and only if a
related system of polynomial equations has a solution
over $K$. In this paper, we investigate an algorithm
aimed at proving combinatorial infeasibility based on
the observed low degree of Hilbert's Nullstellensatz
certificates for polynomial systems arising in
combinatorics and on large-scale linear-algebra
computations over $K$. We report on experiments based
on the problem of proving the non-3-colorability of
graphs. We successfully solved graph problem instances
having thousands of nodes and tens of thousands of
edges.",
acknowledgement = ack-nhfb,
keywords = "Nullstellensatz",
}
@InProceedings{Mansfield:2008:DAD,
author = "Elizabeth L. Mansfield",
title = "Digital atlases and difference forms",
crossref = "Jeffrey:2008:PAM",
pages = "3--4",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390770",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "When integrating a differential equation numerically,
it can be important for the solution method to reflect
the geometric properties of the original model. These
include conservation laws and first integrals,
symmetries, and symplectic or variational structures.
Thus there is an increasingly sophisticated subject of
'geometric integration' concentrating mostly on local
properties of the equation.\par
This talk is concerned with ways of ensuring that
finite difference schemes accurately mirror {\em
global\/} properties. To this end, lattice varieties
are introduced on which finite difference schemes
amongst others may be defined. There is no assumption
of continuity, or that either the lattice variety or
the difference systems have a continuum limit; our
theory is more general than that of cubical complexes,
and the proofs require a different foundation.\par
We show that the global structure of a lattice variety
can be determined from its digital atlas. This is
important for two reasons. First, if the digital atlas
has the same 'system of intersections' as that of the
smooth model it approximates, you are guaranteed the
same global information. Secondly, since our proofs are
independent of any continuum limit, global information
for inherently discrete models may be obtained. The
techniques used are algebraic, specifically homological
algebra, which amounts to linear algebra.\par
This talk has two meta-messages: (1) Continuity is an
illusion. (2) If you want to capture analytic
structures in discrete models successfully, cherchez
l'alg{\`e}bre.\par
No particular expertise is assumed for this talk, which
is based on the paper, Difference Forms by Elizabeth L.
Mansfield and Peter E. Hydon, to appear in Foundations
of Computational Mathematics.",
acknowledgement = ack-nhfb,
keywords = "cohomology; difference chains; difference forms;
lattice variety; local difference potentials; local
exactness; symbolic numeric methods",
}
@InProceedings{Peternell:2008:GSS,
author = "Martin Peternell and Boris Odehnal",
title = "On generalized $\ln$-surfaces in $4$-space",
crossref = "Jeffrey:2008:PAM",
pages = "223--230",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390800",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The present paper investigates a class of
two-dimensional rational surfaces &\#966; in {\em
R\/}$^4$ whose tangent planes satisfy the following
property: For any three-space {\em E\/} in {\em
R\/}$^4$ there exists a unique tangent plane {\em T\/}
of &\#966; which is parallel to {\em E}. The most
interesting families of surfaces are constructed
explicitly and geometric properties of these surfaces
are derived. Quadratically parameterized surfaces in
{\em R\/}$^4$ occur as special cases. This construction
generalizes the concept of LN-surfaces in {\em R\/}$^3$
to two-dimensional surfaces in {\em R\/}$^4$.",
acknowledgement = ack-nhfb,
keywords = "chordal variety; linear congruence of lines;
ln-surface; quadratically parameterized surface;
rational parameterization.",
}
@InProceedings{Pfluegel:2008:RDL,
author = "Eckhard Pfl{\"u}egel",
title = "A rational decomposition-lemma for systems of linear
differential-algebraic equations",
crossref = "Jeffrey:2008:PAM",
pages = "231--238",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390801",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We give a new decomposition lemma for linear
differential-algebraic equations (DAEs). This
generalises a result which we have given in [12] for
singular linear systems of ordinary differential
equations to the class of linear DAEs with formal power
series coefficients. The results of this paper are a
first step towards a formal reduction algorithm for
this type of equations.",
acknowledgement = ack-nhfb,
keywords = "computer algebra; linear daes; local reduction;
splitting lemma",
}
@InProceedings{Poteaux:2008:GRP,
author = "Adrien Poteaux and Marc Rybowicz",
title = "Good reduction of {Puiseux} series and complexity of
the {Newton--Puiseux} algorithm over finite fields",
crossref = "Jeffrey:2008:PAM",
pages = "239--246",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390802",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In [12], we sketched a numeric-symbolic method to
compute Puiseux series with floating point
coefficients. In this paper, we address the symbolic
part of our algorithm. We study the reduction of
Puiseux series coefficients modulo a prime ideal and
prove a good reduction criterion sufficient to preserve
the required information, namely Newton polygon trees.
We introduce a convenient modification of Newton
polygons that greatly simplifies proofs and statements
of our results. Finally, we improve complexity bounds
for Puiseux series calculations over finite fields, and
estimate the bit-complexity of polygon tree
computation.",
acknowledgement = ack-nhfb,
keywords = "algebraic functions; complexity; finite fields;
modular methods; Puiseux series; symbolic-numeric
algorithms",
}
@InProceedings{Renault:2008:MMA,
author = "Gu{\'e}na{\"e}l Renault and Kazuhiro Yokoyama",
title = "Multi-modular algorithm for computing the splitting
field of a polynomial",
crossref = "Jeffrey:2008:PAM",
pages = "247--254",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390803",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $f$ be a univariate monic integral polynomial of
degree $n$ and let $(\alpha_1, \ldots{}, \alpha_n)$ be
an $n$-tuple of its roots in an algebraic closure $Q$
of $Q$. Obtaining an algebraic representation of the
splitting field $Q(\alpha_1, \ldots{}, \alpha_n)$ of
$f$ is a question of first importance in effective
Galois theory. For instance, it allows us to manipulate
symbolically the roots of $f$. In this paper, we
propose a new method based on multi-modular strategy.
Actually, we provide algorithms for this task which
return a triangular set encoding the {\em splitting
ideal\/} of $f$. We examine the ability\slash
practicality of the method by experiments on a real
computer and study its complexity.",
acknowledgement = ack-nhfb,
keywords = "Galois theory; splitting field",
}
@InProceedings{Rosenkranz:2008:IDP,
author = "Markus Rosenkranz and Georg Regensburger",
title = "Integro-differential polynomials and operators",
crossref = "Jeffrey:2008:PAM",
pages = "261--268",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390805",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We propose two algebraic structures for treating
integral operators in conjunction with derivations: The
algebra of integro-differential polynomials describes
nonlinear integral and differential operators together
with initial values. The algebra of
integro-differential operators can be used to solve
boundary problems for linear ordinary differential
equations. In both cases, we describe canonical/normal
forms with algorithmic simplifiers.",
acknowledgement = ack-nhfb,
keywords = "Green's operators; integral operators;
integro-differential algebras; linear boundary value
problems; noncommutative Gr{\"o}bner bases",
}
@InProceedings{Sekigawa:2008:NPZ,
author = "Hiroshi Sekigawa",
title = "The nearest polynomial with a zero in a given domain
from a geometrical viewpoint",
crossref = "Jeffrey:2008:PAM",
pages = "287--294",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390808",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For a real univariate polynomial $f$ and a closed
complex domain $D$, whose boundary $C$ is a simple
curve parameterized by a univariate piecewise rational
function, a rigorous method is given for finding a real
univariate polynomial $f$ such that $f$ has a zero in
$D$ and $||f - \tilde{f}||\infty$ is minimal. First, it
is proved that the minimum distance between $f$ and
polynomials having a zero at $\alpha \in C$ is a
piecewise rational function of the real and imaginary
parts of $\alpha$. Thus, on $C$, the minimum distance
is a piecewise rational function of a parameter
obtained through the parameterization of $C$.
Therefore, by using the property that $\tilde{f}$ has a
zero on $C$ and computing the minimum distance on $C$,
$\tilde{f}$ can be constructed.",
acknowledgement = ack-nhfb,
keywords = "$l\infty$-norm; Davenport--Schinzel sequence;
perturbation; polynomial; zero",
}
@InProceedings{Shemyakova:2008:MFL,
author = "Ekaterina Shemyakova and Elizabeth L. Mansfield",
title = "Moving frames for {Laplace} invariants",
crossref = "Jeffrey:2008:PAM",
pages = "295--302",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390809",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The development of symbolic methods for the
factorization and integration of linear PDEs, many of
the methods being generalizations of the Laplace
transformations method, requires the finding of
complete generating sets of invariants for the
corresponding linear operators and their systems with
respect to the gauge transformations $L -> g(x,y)^{-1}
O L O g(x,y)$. Within the theory of Laplace-like
methods, there is no uniform approach to this problem,
though some individual invariants for hyperbolic
bivariate operators, and complete generating sets of
invariants for second- and third-order hyperbolic
bivariate ones have been obtained. Here we demonstrate
a systematic and much more efficient approach to the
same problem by application of moving-frame methods. We
give explicit formulae for complete generating sets of
invariants for second- and third-order bivariate linear
operators, hyperbolic and non-hyperbolic, and also
demonstrate the approach for pairs of operators
appearing in Darboux transformations.",
acknowledgement = ack-nhfb,
keywords = "gauge transformations; invariants; moving frames;
partial differential operators",
}
@InProceedings{Stein:2008:CWC,
author = "William A. Stein",
title = "Can we create a viable free open source alternative to
{Magma}, {Maple}, {Mathematica} and {Matlab}?",
crossref = "Jeffrey:2008:PAM",
pages = "5--6",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390771",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The goal of the Sage project ({\tt
http://sagemath.org}) is to create a truly viable free
open source alternative to Magma, Maple, Mathematica
and Matlab. Is this possible?",
acknowledgement = ack-nhfb,
keywords = "free; Magma; Maple; Mathematica; Matlab; open source",
}
@InProceedings{Strzebonski:2008:RRI,
author = "Adam Strzebonski",
title = "Real root isolation for $\exp$-$\log$ functions",
crossref = "Jeffrey:2008:PAM",
pages = "303--314",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390810",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a real root isolation procedure for
univariate functions obtained by composition and
rational operations from exp, log, and real constants.
We discuss implementation of the procedure and give
empirical results. The procedure requires the ability
to determine signs of $\exp$-$\log$ functions at simple
roots of other $\exp$-$\log$ functions. The currently
known method to do this depends on Schanuel's
conjecture [6].",
acknowledgement = ack-nhfb,
keywords = "$\exp$-$\log$ functions; real root isolation; solving
equations",
}
@InProceedings{Sudan:2008:AAC,
author = "Madhu Sudan",
title = "Algebraic algorithms and coding theory",
crossref = "Jeffrey:2008:PAM",
pages = "337--337",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390816",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The associated talk surveys some recent developments
in algorithmic coding theory that answer some
fundamental questions with algebraic techniques.",
acknowledgement = ack-nhfb,
keywords = "algebraic algorithms; error correcting codes",
}
@InProceedings{Wang:2008:IPQ,
author = "Xuhui Wang and Falai Chen and Jiansong Deng",
title = "Implicitization and parametrization of quadratic
surfaces with one simple base point",
crossref = "Jeffrey:2008:PAM",
pages = "31--38",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390776",
bibdate = "Tue Aug 5 18:10:09 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper discusses implicitization and
parametrization of quadratic surfaces with one simple
base point. The key point to fulfill the conversion
between the implicit and the parametric form is to
compute three linearly independent moving planes which
we call the weak u-basis of the quadratic surface.
Beginning with the parametric form, it is easy to
compute the weak u-basis, and then to find its implicit
equation. Inversion formulas can also be obtained
easily from the weak u-basis. For conversion from the
implicit into the parametric form, we present a method
based on the observation that there exists one
self-intersection line on a quadratic surface with one
base point. After computing the self-intersection line,
we are able to derive the weak u-basis, from which the
parametric equation can be easily obtained. A method is
also presented to compute the self-intersection line of
a quadratic surface with one base point.",
acknowledgement = ack-nhfb,
keywords = "implicitization; moving plane; parametrization; weak
u-basis",
}
@InProceedings{Wu:2008:CMS,
author = "Xiaoli Wu and Lihong Zhi",
title = "Computing the multiplicity structure from geometric
involutive form",
crossref = "Jeffrey:2008:PAM",
pages = "325--332",
year = "2008",
DOI = "https://doi.org/10.1145/1390768.1390812",
bibdate = "Wed Aug 6 09:11:59 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a method based on symbolic-numeric
reduction to geometric involutive form to compute the
primary component and the differential operators $f$
solution of a polynomial ideal. The singular solution
can be exact or approximate. If the singular solution
is known with limited accuracy, then we propose a new
method to refine it to high accuracy.",
acknowledgement = ack-nhfb,
keywords = "involutive system; numerical linear algebra",
}
@InProceedings{Andres:2009:PIB,
author = "Daniel Andres and Viktor Levandovskyy and Jorge
Mart{\`\i}n Morales",
title = "Principal intersection and {Bernstein--Sato}
polynomial of an affine variety",
crossref = "May:2009:PIS",
pages = "231--238",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2009:ARS,
author = "Moulay A. Barkatou and Thomas Cluzeau and Carole El
Bacha",
title = "Algorithms for regular solutions of higher-order
linear differential systems",
crossref = "May:2009:PIS",
pages = "7--14",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beckermann:2009:FFC,
author = "Bernhard Beckermann and George Labahn",
title = "Fraction-free computation of simultaneous {Pad{\'e}}
approximants",
crossref = "May:2009:PIS",
pages = "15--22",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Benoit:2009:CES,
author = "Alexandre Benoit and Bruno Salvy",
title = "{Chebyshev} expansions for solutions of linear
differential equations",
crossref = "May:2009:PIS",
pages = "23--30",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bigatti:2009:CSK,
author = "Anna M. Bigatti and Eduardo S{\'a}enz-de-Cabez{\'o}n",
title = "Computation of the $(n-1)$-st {Koszul Homology} of
monomial ideals and related algorithms",
crossref = "May:2009:PIS",
pages = "31--38",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bihan:2009:FRF,
author = "Fr{\'e}d{\'e}ric Bihan and J. Maurice Rojas and Casey
E. Stella",
title = "Faster real feasibility via circuit discriminants",
crossref = "May:2009:PIS",
pages = "39--46",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2009:FAD,
author = "Alin Bostan and {\'E}ric Schost",
title = "Fast algorithms for differential equations in positive
characteristic",
crossref = "May:2009:PIS",
pages = "47--54",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Boyer:2009:MES,
author = "Brice Boyer and Jean-Guillaume Dumas and Cl{\'e}ment
Pernet and Wei Zhou",
title = "Memory efficient scheduling of {Strassen--Winograd}'s
matrix multiplication algorithm",
crossref = "May:2009:PIS",
pages = "55--62",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brown:2009:FST,
author = "Christopher W. Brown",
title = "Fast simplifications for {Tarski} formulas",
crossref = "May:2009:PIS",
pages = "63--70",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brownawell:2009:LBZ,
author = "W. Dale Brownawell and Chee K. Yap",
title = "Lower bounds for zero-dimensional projections",
crossref = "May:2009:PIS",
pages = "79--86",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cha:2009:LSI,
author = "Yongjae Cha and Mark van Hoeij",
title = "{Liouvillian} solutions of irreducible linear
difference equations",
crossref = "May:2009:PIS",
pages = "87--94",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2009:CCA,
author = "Changbo Chen and Marc Moreno Maza and Bican Xia and Lu
Yang",
title = "Computing cylindrical algebraic decomposition via
triangular decomposition",
crossref = "May:2009:PIS",
pages = "95--102",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheng:2009:RIB,
author = "Jin-San Cheng and Xiao-Shan Gao and Jia Li",
title = "Root isolation for bivariate polynomial systems with
local generic position method",
crossref = "May:2009:PIS",
pages = "103--110",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chyzak:2009:NHS,
author = "Fr{\'e}d{\'e}ric Chyzak and Manuel Kauers and Bruno
Salvy",
title = "A non-holonomic systems approach to special function
identities",
crossref = "May:2009:PIS",
pages = "111--118",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dahan:2009:SCL,
author = "Xavier Dahan",
title = "Size of coefficients of lexicographical {Gr{\"o}bner}
bases: the zero-dimensional, radical and bivariate
case",
crossref = "May:2009:PIS",
pages = "119--126",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dumas:2009:FMC,
author = "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and B.
David Saunders",
title = "On finding multiplicities of characteristic polynomial
factors of black-box matrices",
crossref = "May:2009:PIS",
pages = "135--142",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Emiris:2009:MRF,
author = "Ioannis Z. Emiris and Angelos A. Mantzaflaris",
title = "Multihomogeneous resultant formulae for systems with
scaled support",
crossref = "May:2009:PIS",
pages = "143--150",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{FaugAre:2009:HOD,
author = "Jean-Charles Faug{\`e}re and Ludovic Perret",
title = "High order derivatives and decomposition of
multivariate polynomials",
crossref = "May:2009:PIS",
pages = "207--214",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{FaugAre:2009:SSP,
author = "Jean-Charles Faug{\`e}re and Sajjad Rahmany",
title = "Solving systems of polynomial equations with
symmetries using {SAGBI-Gr{\"o}bner} bases",
crossref = "May:2009:PIS",
pages = "151--158",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2009:IBC,
author = "Jean-Charles Faug{\`e}re",
title = "Interactions between computer algebra ({Gr{\"o}bner}
bases) and cryptology",
crossref = "May:2009:PIS",
pages = "383--384",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Feo:2009:FAA,
author = "Luca De Feo and {\'E}ric Schost",
title = "Fast arithmetics in {Artin--Schreier} towers over
finite fields",
crossref = "May:2009:PIS",
pages = "127--134",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giusti:2009:GAF,
author = "Marc Giusti",
title = "A {Gr{\"o}bner} free alternative to solving and a
geometric analogue to {Cook}'s thesis",
crossref = "May:2009:PIS",
pages = "1--2",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gonzalez-Sanchez:2009:AGB,
author = "Jon Gonzalez-Sanchez and Laureano Gonzalez-Vega and
Alejandro Pi{\~n}era-Nicolas and Irene Polo-Blanco and
Jorge Caravantes and Ignacio F. Rua",
title = "Analyzing group based matrix multiplication
algorithms",
crossref = "May:2009:PIS",
pages = "159--166",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Graillat:2009:NAC,
author = "Stef Graillat and Philippe Tr{\'e}buchet",
title = "A new algorithm for computing certified numerical
approximations of the roots of a zero-dimensional
system",
crossref = "May:2009:PIS",
pages = "167--174",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{HalAs:2009:SRD,
author = "Miroslav Hal{\'a}s and {\"U}lle Kotta and Ziming Li
and Huaifu Wang and Chunming Yuan",
title = "Submersive rational difference systems and their
accessibility",
crossref = "May:2009:PIS",
pages = "175--182",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hong:2009:VRQ,
author = "Hoon Hong and Mohab Safey El Din",
title = "Variant real quantifier elimination: algorithm and
application",
crossref = "May:2009:PIS",
pages = "183--190",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ida:2009:SAM,
author = "Tetsuo Ida",
title = "Symbolic and algebraic methods in computational
origami: invited talk",
crossref = "May:2009:PIS",
pages = "3--4",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ivanyos:2009:SDP,
author = "G{\'a}bor Ivanyos and Marek Karpinski and Nitin
Saxena",
title = "Schemes for deterministic polynomial factoring",
crossref = "May:2009:PIS",
pages = "191--198",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Javadi:2009:FMP,
author = "Seyed Mohammad Mahdi Javadi and Michael B. Monagan",
title = "On factorization of multivariate polynomials over
algebraic number and function fields",
crossref = "May:2009:PIS",
pages = "199--206",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kanno:2009:SAR,
author = "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
and Shinji Hara",
title = "Solution of algebraic {Riccati} equations using the
sum of roots",
crossref = "May:2009:PIS",
pages = "215--222",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kunkle:2009:BTF,
author = "Daniel Kunkle and Gene Cooperman",
title = "Biased tadpoles: a fast algorithm for centralizers in
large matrix groups",
crossref = "May:2009:PIS",
pages = "223--230",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2009:CMR,
author = "Xin Li and Marc Moreno Maza and Wei Pan",
title = "Computations modulo regular chains",
crossref = "May:2009:PIS",
pages = "239--246",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{McCallum:2009:DVC,
author = "Scott McCallum and Christopher W. Brown",
title = "On delineability of varieties in {CAD}-based
quantifier elimination with two equational
constraints",
crossref = "May:2009:PIS",
pages = "71--78",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mehlhorn:2009:IRR,
author = "Kurt Mehlhorn and Michael Sagraloff",
title = "Isolating real roots of real polynomials",
crossref = "May:2009:PIS",
pages = "247--254",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mevissen:2009:SPS,
author = "Martin Mevissen and Kosuke Yokoyama and Nobuki
Takayama",
title = "Solutions of polynomial systems derived from the
steady cavity flow problem",
crossref = "May:2009:PIS",
pages = "255--262",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Monagan:2009:PSP,
author = "Michael Monagan and Roman Pearce",
title = "Parallel sparse polynomial multiplication using
heaps",
crossref = "May:2009:PIS",
pages = "263--270",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Morel:2009:HLU,
author = "Ivan Morel and Damien Stehl{\'e} and Gilles Villard",
title = "{H-LLL}: using {Householder} inside {LLL}",
crossref = "May:2009:PIS",
pages = "271--278",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Orange:2009:CSS,
author = "S{\'e}bastien Orange and Gu{\'e}na{\"e}l Renault and
Kazuhiro Yokoyama",
title = "Computation schemes for splitting fields of
polynomials",
crossref = "May:2009:PIS",
pages = "279--286",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Paschel:2009:ASH,
author = "Markus P{\"a}schel",
title = "Automatic synthesis of high performance mathematical
programs",
crossref = "May:2009:PIS",
pages = "5--6",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Regensburger:2009:SPA,
author = "Georg Regensburger and Markus Rosenkranz and Johannes
Middeke",
title = "A skew polynomial approach to integro-differential
operators",
crossref = "May:2009:PIS",
pages = "287--294",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Roche:2009:STE,
author = "Daniel S. Roche",
title = "Space- and time-efficient polynomial multiplication",
crossref = "May:2009:PIS",
pages = "295--302",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Romero:2009:IBC,
author = "Ana Romero and Graham Ellis and Julio Rubio",
title = "Interoperating between computer algebra systems:
computing homology of groups with {\tt kenzo} and
{GAP}",
crossref = "May:2009:PIS",
pages = "303--310",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sato:2009:CIR,
author = "Yosuke Sato and Akira Suzuki",
title = "Computation of inverses in residue class rings of
parametric polynomial ideals",
crossref = "May:2009:PIS",
pages = "311--316",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Saunders:2009:LMS,
author = "B. David Saunders and Bryan S. Youse",
title = "Large matrix, small rank",
crossref = "May:2009:PIS",
pages = "317--324",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schweighofer:2009:DCS,
author = "Markus Schweighofer",
title = "Describing convex semialgebraic sets by linear matrix
inequalities",
crossref = "May:2009:PIS",
pages = "385--386",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sexton:2009:CAM,
author = "Alan P. Sexton and Volker Sorge and Stephen M. Watt",
title = "Computing with abstract matrix structures",
crossref = "May:2009:PIS",
pages = "325--332",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Storjohann:2009:IMR,
author = "Arne Storjohann",
title = "Integer matrix rank certification",
crossref = "May:2009:PIS",
pages = "333--340",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Strzebonski:2009:RRI,
author = "Adam Strzebonski",
title = "Real root isolation for tame elementary functions",
crossref = "May:2009:PIS",
pages = "341--350",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Terui:2009:IMC,
author = "Akira Terui",
title = "An iterative method for calculating approximate {GCD}
of univariate polynomials",
crossref = "May:2009:PIS",
pages = "351--358",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:2009:NDU,
author = "Joachim von zur Gathen",
title = "The number of decomposable univariate polynomials.
extended abstract",
crossref = "May:2009:PIS",
pages = "359--366",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yap:2009:ENC,
author = "Chee K. Yap",
title = "Exact numerical computation in algebra and geometry",
crossref = "May:2009:PIS",
pages = "387--388",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zeng:2009:AIF,
author = "Zhonggang Zeng",
title = "The approximate irreducible factorization of a
univariate polynomial: revisited",
crossref = "May:2009:PIS",
pages = "367--374",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhou:2009:ECO,
author = "Wei Zhou and George Labahn",
title = "Efficient computation of order bases",
crossref = "May:2009:PIS",
pages = "375--382",
year = "2009",
bibdate = "Tue Aug 11 18:45:25 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2010:SDU,
author = "S. A. Abramov",
title = "On some decidable and undecidable problems related to
$q$-difference equations with parameters",
crossref = "Watt:2010:IPI",
pages = "311--317",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837993",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Avendano:2010:RNC,
author = "Mart{\'\i}n Avenda{\~n}o and Ashraf Ibrahim and J.
Maurice Rojas and Korben Rusek",
title = "Randomized {NP}-completeness for $p$-adic rational
roots of sparse polynomials in one variable",
crossref = "Watt:2010:IPI",
pages = "331--338",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837997",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2010:SMS,
author = "Moulay A. Barkatou",
title = "Symbolic methods for solving systems of linear
ordinary differential equations",
crossref = "Watt:2010:IPI",
pages = "7--8",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837940",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2010:SRC,
author = "Moulay A. Barkatou and Carole El Bacha and Eckhard
Pfl{\"u}gel",
title = "Simultaneously row- and column-reduced higher-order
linear differential systems",
crossref = "Watt:2010:IPI",
pages = "45--52",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837949",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Berkesch:2010:ABS,
author = "Christine Berkesch and Anton Leykin",
title = "Algorithms for {Bernstein--Sato} polynomials and
multiplier ideals",
crossref = "Watt:2010:IPI",
pages = "99--106",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837958",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bodrato:2010:SLM,
author = "Marco Bodrato",
title = "A {Strassen}-like matrix multiplication suited for
squaring and higher power computation",
crossref = "Watt:2010:IPI",
pages = "273--280",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837987",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Strassen's method is not the asymptotically fastest
known matrix multiplication algorithm, but it is the
most widely used for large matrices. Since his
manuscript was published, a number of variants have
been proposed with different addition complexities.
Here we describe a new one. The new variant is at least
as good as those already known for simple matrix
multiplication, but can save operations either for
chain products or for squaring. Moreover it can be
proved optimal for these tasks. The largest saving is
shown for nth-power computation, in this scenario the
additive complexity can be halved, with respect to
original Strassen's.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2010:CCT,
author = "Alin Bostan and Shaoshi Chen and Fr{\'e}d{\'e}ric
Chyzak and Ziming Li",
title = "Complexity of creative telescoping for bivariate
rational functions",
crossref = "Watt:2010:IPI",
pages = "203--210",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837975",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brisebarre:2010:CIP,
author = "Nicolas Brisebarre and Mioara Jolde{\c{s}}",
title = "{Chebyshev} interpolation polynomial-based tools for
rigorous computing",
crossref = "Watt:2010:IPI",
pages = "147--154",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837966",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Performing numerical computations, yet being able to
provide rigorous mathematical statements about the
obtained result, is required in many domains like
global optimization, ODE solving or integration. Taylor
models, which associate to a function a pair made of a
Taylor approximation polynomial and a rigorous
remainder bound, are a widely used rigorous computation
tool. This approach benefits from the advantages of
numerical methods, but also gives the ability to make
reliable statements about the approximated function.
Despite the fact that approximation polynomials based
on interpolation at Chebyshev nodes offer a
quasi-optimal approximation to a function, together
with several other useful features, an analogous to
Taylor models, based on such polynomials, has not been
yet well-established in the field of validated
numerics.\par
This paper presents a preliminary work for obtaining
such interpolation polynomials together with validated
interval bounds for approximating univariate functions.
We propose two methods that make practical the use of
this: one is based on a representation in Newton basis
and the other uses Chebyshev polynomial basis. We
compare the quality of the obtained remainders and the
performance of the approaches to the ones provided by
Taylor models.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brown:2010:BBW,
author = "Christopher W. Brown and Adam Strzebo{\'n}ski",
title = "Black-box\slash white-box simplification and
applications to quantifier elimination",
crossref = "Watt:2010:IPI",
pages = "69--76",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837953",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cha:2010:SRR,
author = "Yongjae Cha and Mark van Hoeij and Giles Levy",
title = "Solving recurrence relations using local invariants",
crossref = "Watt:2010:IPI",
pages = "303--309",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837992",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2010:TDS,
author = "Changbo Chen and James H. Davenport and John P. May
and Marc Moreno Maza and Bican Xia and Rong Xiao",
title = "Triangular decomposition of semi-algebraic systems",
crossref = "Watt:2010:IPI",
pages = "187--194",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837972",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Conti:2010:SBL,
author = "C. Conti and L. Gemignani and L. Romani",
title = "Solving {Bezout}-like polynomial equations for the
design of interpolatory subdivision schemes",
crossref = "Watt:2010:IPI",
pages = "251--256",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837983",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eberly:2010:YAB,
author = "Wayne Eberly",
title = "Yet another block {Lanczos} algorithm: how to simplify
the computation and reduce reliance on preconditioners
in the small field case",
crossref = "Watt:2010:IPI",
pages = "289--296",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837989",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Emiris:2010:DBM,
author = "Ioannis Z. Emiris and Bernard Mourrain and Elias P.
Tsigaridas",
title = "The {DMM} bound: multivariate (aggregate) separation
bounds",
crossref = "Watt:2010:IPI",
pages = "243--250",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837981",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Emiris:2010:RPE,
author = "Ioannis Z. Emiris and Andr{\'e} Galligo and Elias P.
Tsigaridas",
title = "Random polynomials and expected complexity of
bisection methods for real solving",
crossref = "Watt:2010:IPI",
pages = "235--242",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837980",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2010:CLR,
author = "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
Pierre-Jean Spaenlehauer",
title = "Computing loci of rank defects of linear matrices
using {Gr{\"o}bner} bases and applications to
cryptology",
crossref = "Watt:2010:IPI",
pages = "257--264",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837984",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2010:DGM,
author = "Jean-Charles Faug{\`e}re and Joachim von zur Gathen
and Ludovic Perret",
title = "Decomposition of generic multivariate polynomials",
crossref = "Watt:2010:IPI",
pages = "131--137",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837963",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gao:2010:NIA,
author = "Shuhong Gao and Yinhua Guan and Frank {Volny IV}",
title = "A new incremental algorithm for computing
{Gr{\"o}bner} bases",
crossref = "Watt:2010:IPI",
pages = "13--19",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837944",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gerdt:2010:CFD,
author = "Vladimir P. Gerdt and Daniel Robertz",
title = "Consistency of finite difference approximations for
linear {PDE} systems and its algorithmic verification",
crossref = "Watt:2010:IPI",
pages = "53--59",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837950",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gerhard:2010:AFA,
author = "J{\"u}rgen Gerhard",
title = "Asymptotically fast algorithms for modern computer
algebra",
crossref = "Watt:2010:IPI",
pages = "9--10",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837941",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The solution of computational tasks from the `real
world' requires high performance computations. Not
limited to mathematical computing, asymptotically fast
algorithms have become one of the major contributing
factors in this area. Based on [4], the tutorial will
give an introduction to the beauty and elegance of
modern computer algebra.",
acknowledgement = ack-nhfb,
}
@InProceedings{Grigoriev:2010:AFN,
author = "D. Grigoriev and F. Schwarz",
title = "Absolute factoring of non-holonomic ideals in the
plane",
crossref = "Watt:2010:IPI",
pages = "93--97",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837957",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2010:GOP,
author = "Feng Guo and Mohab Safey {El Din} and Lihong Zhi",
title = "Global optimization of polynomials using generalized
critical values and sums of squares",
crossref = "Watt:2010:IPI",
pages = "107--114",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837960",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Harvey:2010:PTF,
author = "David Harvey and Daniel S. Roche",
title = "An in-place truncated {Fourier} transform and
applications to polynomial multiplication",
crossref = "Watt:2010:IPI",
pages = "325--329",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837996",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The truncated Fourier transform (TFT) was introduced
by van der Hoeven in 2004 as a means of smoothing the
`jumps' in running time of the ordinary FFT algorithm
that occur at power-of-two input sizes. However, the
TFT still introduces these jumps in memory usage. We
describe in-place variants of the forward and inverse
TFT algorithms, achieving time complexity $O(n \log n)$
with only $O(1)$ auxiliary space. As an application, we
extend the second author's results on space-restricted
FFT-based polynomial multiplication to polynomials of
arbitrary degree.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hubert:2010:AIT,
author = "Evelyne Hubert",
title = "Algebraic invariants and their differential algebras",
crossref = "Watt:2010:IPI",
pages = "1--2",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837936",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hutton:2010:CRP,
author = "Sharon Hutton and Erich L. Kaltofen and Lihong Zhi",
title = "Computing the radius of positive semidefiniteness of a
multivariate real polynomial via a dual of
{Seidenberg}'s method",
crossref = "Watt:2010:IPI",
pages = "227--234",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837979",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeannerod:2010:CSG,
author = "Claude-Pierre Jeannerod and Christophe Mouilleron",
title = "Computing specified generators of structured matrix
inverses",
crossref = "Watt:2010:IPI",
pages = "281--288",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837988",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kapur:2010:NAC,
author = "Deepak Kapur and Yao Sun and Dingkang Wang",
title = "A new algorithm for computing comprehensive
{Gr{\"o}bner} systems",
crossref = "Watt:2010:IPI",
pages = "29--36",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837946",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2010:PDB,
author = "Manuel Kauers and Carsten Schneider",
title = "Partial denominator bounds for partial linear
difference equations",
crossref = "Watt:2010:IPI",
pages = "211--218",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837976",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2010:WCW,
author = "Manuel Kauers and Veronika Pillwein",
title = "When can we detect that a {$P$}-finite sequence is
positive?",
crossref = "Watt:2010:IPI",
pages = "195--201",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837974",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Khonji:2010:OSD,
author = "Majid Khonji and Cl{\'e}ment Pernet and Jean-Louis
Roch and Thomas Roche and Thomas Stalinski",
title = "Output-sensitive decoding for redundant residue
systems",
crossref = "Watt:2010:IPI",
pages = "265--272",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837985",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lemaire:2010:MSR,
author = "Fran{\c{c}}ois Lemaire and Asli {\"U}rg{\"u}pl{\"u}",
title = "A method for semi-rectifying algebraic and
differential systems using scaling type {Lie} point
symmetries with linear algebra",
crossref = "Watt:2010:IPI",
pages = "85--92",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837956",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2010:BID,
author = "Zijia Li and Zhengfeng Yang and Lihong Zhi",
title = "Blind image deconvolution via fast approximate {GCD}",
crossref = "Watt:2010:IPI",
pages = "155--162",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837967",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Linton:2010:ECS,
author = "S. Linton and K. Hammond and A. Konovalov and A. D. Al
Zain and P. Trinder and P. Horn and D. Roozemond",
title = "Easy composition of symbolic computation software: a
new lingua franca for symbolic computation",
crossref = "Watt:2010:IPI",
pages = "339--346",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837999",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present the results of the first four years of the
European research project SCIEnce
(www.symbolic-computation.org), which aims to provide
key infrastructure for symbolic computation research. A
primary outcome of the project is that we have
developed a new way of combining computer algebra
systems using the Symbolic Computation Software
Composability Protocol (SCSCP), in which both protocol
messages and data are encoded in the OpenMath format.
We describe SCSCP middleware and APIs, outline some
implementations for various Computer Algebra Systems
(CAS), and show how SCSCP-compliant components may be
combined to solve scientific problems that can not be
solved within a single CAS, or may be organised into a
system for distributed parallel computations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mayr:2010:DBG,
author = "Ernst W. Mayr and Stephan Ritscher",
title = "Degree bounds for {Gr{\"o}bner} bases of
low-dimensional polynomial ideals",
crossref = "Watt:2010:IPI",
pages = "21--27",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837945",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mezzarobba:2010:NPN,
author = "Marc Mezzarobba",
title = "{NumGfun}: a package for numerical and analytic
computation with {D}-finite functions",
crossref = "Watt:2010:IPI",
pages = "139--145",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837965",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2010:RCP,
author = "Victor Y. Pan and Ai-Long Zheng",
title = "Real and complex polynomial root-finding with
eigen-solving and preprocessing",
crossref = "Watt:2010:IPI",
pages = "219--226",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837978",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Roune:2010:SAC,
author = "Bjarke Hammersholt Roune",
title = "A {Slice} algorithm for corners and
{Hilbert--Poincar{\'e}} series of monomial ideals",
crossref = "Watt:2010:IPI",
pages = "115--122",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837961",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rump:2010:VMR,
author = "Siegfried M. Rump",
title = "Verification methods: rigorous results using
floating-point arithmetic",
crossref = "Watt:2010:IPI",
pages = "3--4",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837937",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The classical mathematical proof is performed by
pencil and paper. However, there are many ways in which
computers may be used in a mathematical proof. But
`proofs by computers' or even the use of computers in
the course of a proof are not so readily accepted (the
December 2008 issue of the Notices of the American
Mathematical Society is devoted to formal proofs by
computers).\par
In this talk we discuss how verification methods may
assist in achieving a mathematically rigorous result.
In particular we emphasize how floating-point
arithmetic is used.\par
The goal of verification methods is ambitious: For a
given problem it is proved, with the aid of a computer,
that there exists a (unique) solution within computed
bounds. The methods are constructive, and the results
are rigorous in every respect. Verification methods
apply to data with tolerances as well.\par
Rigorous results are the main goal in computer algebra.
However, verification methods use solely floating-point
arithmetic, so that the total computational effort is
not too far from that of a purely (approximate)
numerical method. Nontrivial problems have been solved
using verification methods. For example:\par
Tucker (1999) received the 2004 EMS prize awarded by
the European Mathematical Society for (citation)
`giving a rigorous proof that the Lorenz attractor
exists for the parameter values provided by Lorenz.
This was a long standing challenge to the dynamical
system community, and was included by Smale in his list
of problems for the new millennium. The proof uses
computer estimates with rigorous bounds based on higher
dimensional interval arithmetics.'\par
Sahinidis and Tawaralani (2005) received the 2006
Beale-Orchard-Hays Prize for their package BARON which
(citation) `incorporates techniques from automatic
differentiation, interval arithmetic, and other areas
to yield an automatic, modular, and relatively
efficient solver for the very difficult area of global
optimization'.\par
A main goal of this talk is to introduce the principles
of how to design verification algorithms, and how these
principles differ from those for traditional numerical
algorithms.\par
We begin with a brief discussion of the working tools
of verification methods, in particular floating-point
and interval arithmetic. In particular the development
and limits of verification methods for finite
dimensional problems are discussed in some detail;
problems include dense systems of linear equations,
sparse linear systems, systems of nonlinear equations,
semi-definite programming and other special linear and
nonlinear problems including M-matrices, simple and
multiple roots of polynomials, bounds for simple and
multiple eigenvalues or clusters, and quadrature. We
mention that automatic differentiation tools to compute
the range of gradients, Hessians, Taylor coefficients,
and slopes are necessary. If time permits, verification
methods for continuous problems, namely two-point
boundary value problems and semilinear elliptic
boundary value problems are presented.\par
Throughout the talk, a number of examples of the wrong
use of interval operations are given. In the past such
examples contributed to the dubious reputation of
interval arithmetic, whereas they are, in fact, just a
misuse.\par
Some algorithms are presented in executable
Matlab/INTLAB-code. INTLAB, the Matlab toolbox for
reliable computing and free for academic use, is
developed and written by Rump (1999). It was, for
example, used by Bornemann, Laurie, Wagon, and
Waldvogel (2004) in the solution of half of the
problems of the $10 \times 10$-digit challenge by
Trefethen (2002).",
acknowledgement = ack-nhfb,
}
@InProceedings{Rupp:2010:SIC,
author = "Karl Rupp",
title = "Symbolic integration at compile time in finite element
methods",
crossref = "Watt:2010:IPI",
pages = "347--354",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1838000",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sevilla:2010:PIR,
author = "David Sevilla and Daniel Wachsmuth",
title = "Polynomial integration on regions defined by a
triangle and a conic",
crossref = "Watt:2010:IPI",
pages = "163--170",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837968",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shi:2010:CSR,
author = "Xiaoran Shi and Falai Chen",
title = "Computing the singularities of rational space curves",
crossref = "Watt:2010:IPI",
pages = "171--178",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837970",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Slavici:2010:FML,
author = "Vlad Slavici and Xin Dong and Daniel Kunkle and Gene
Cooperman",
title = "Fast multiplication of large permutations for disk,
flash memory and {RAM}",
crossref = "Watt:2010:IPI",
pages = "355--362",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1838001",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sottile:2010:SSP,
author = "Frank Sottile and Ravi Vakil and Jan Verschelde",
title = "Solving {Schubert} problems with
{Littlewood--Richardson} homotopies",
crossref = "Watt:2010:IPI",
pages = "179--186",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837971",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Strzebonski:2010:CSS,
author = "Adam Strzebo{\'n}ski",
title = "Computation with semialgebraic sets represented by
cylindrical algebraic formulas",
crossref = "Watt:2010:IPI",
pages = "61--68",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837952",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sturm:2010:PQS,
author = "Thomas Sturm and Christoph Zengler",
title = "Parametric quantified {SAT} solving",
crossref = "Watt:2010:IPI",
pages = "77--84",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837954",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tiwari:2010:TRV,
author = "Ashish Tiwari",
title = "Theory of reals for verification and synthesis of
hybrid dynamical systems",
crossref = "Watt:2010:IPI",
pages = "5--6",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837938",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tsarev:2010:TFP,
author = "S. P. Tsarev",
title = "Transformation and factorization of partial
differential systems: applications to stochastic
systems",
crossref = "Watt:2010:IPI",
pages = "11--12",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837942",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2010:FAB,
author = "Mark van Hoeij and Quan Yuan",
title = "Finding all {Bessel} type solutions for linear
differential equations with rational function
coefficients",
crossref = "Watt:2010:IPI",
pages = "37--44",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837948",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A linear differential equation with rational function
coefficients has a Bessel type solution when it is
solvable in terms of $B_v(f)$, $B_{v+1}(f)$. For second
order equations, with rational function coefficients,
$f$ must be a rational function or the square root of a
rational function. An algorithm was given by Debeerst,
van Hoeij, and Koepf, that can compute Bessel type
solutions if and only if $f$ is a rational function. In
this paper we extend this work to the square root case,
resulting in a complete algorithm to find all Bessel
type solutions.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2010:LSI,
author = "Mark van Hoeij and Giles Levy",
title = "{Liouvillian} solutions of irreducible second order
linear difference equations",
crossref = "Watt:2010:IPI",
pages = "297--301",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837991",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vonzurGathen:2010:CCP,
author = "Joachim von zur Gathen and Mark Giesbrecht and
Konstantin Ziegler",
title = "Composition collisions and projective polynomials:
statement of results",
crossref = "Watt:2010:IPI",
pages = "123--130",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837962",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zanoni:2010:ITC,
author = "Alberto Zanoni",
title = "Iterative {Toom--Cook} methods for very unbalanced
long integer multiplication",
crossref = "Watt:2010:IPI",
pages = "319--323",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837995",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider the multiplication of long integers when
one factor is much larger than the other one. We
describe an iterative approach using Toom--Cook
unbalanced methods, which results in the evaluation of
the smaller integer only once. The particular case of
Toom-2.5 is considered in full detail. A further
optimization depending on the parity of the shortest
operand evaluation in 1 is also described. A comparison
with GMP library is also presented.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ananth:2011:BBD,
author = "Prabhanjan Vijendra Ananth and Ambedkar Dukkipati",
title = "Border basis detection is {NP-complete}",
crossref = "Schost:2011:IPI",
pages = "11--18",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993895",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Border basis detection (BBD) is described as follows:
given a set of generators of an ideal, decide whether
that set of generators is a border basis of the ideal
with respect to some order ideal. The motivation for
this problem comes from a similar problem related to
Gr{\"o}bner bases termed as Gr{\"o}bner basis detection (GBD)
which was proposed by Gritzmann and Sturmfels (1993).
GBD was shown to be NP-hard by Sturmfels and Wiegelmann
(1996). In this paper, we investigate the computational
complexity of BBD and show that it is NP-complete.",
acknowledgement = ack-nhfb,
}
@InProceedings{Aparicio-Monforte:2011:FFI,
author = "Ainhoa Aparicio-Monforte and Moulay A. Barkatou and
Sergi Simon and Jacques-Arthur Weil",
title = "Formal first integrals along solutions of differential
systems {I}",
crossref = "Schost:2011:IPI",
pages = "19--26",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993896",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider an analytic vector field x = X (x \right)
and study, via a variational approach, whether it may
possess analytic first integrals. We assume one
solution $ \Gamma $ is known and we study the
successive variational equations along $ \Gamma $.
Constructions in [MRRS07] show that Taylor expansion
coefficients of first integrals appear as rational
solutions of the dual linearized variational equations.
We show that they also satisfy linear ``filter''
conditions. Using this, we adapt the algorithms from
[Bar99, vHW97] to design new ones optimized to this
effect and demonstrate their use. Part of this work
stems from the first author's Ph.D. thesis [AM10].",
acknowledgement = ack-nhfb,
}
@InProceedings{Bembe:2011:VRR,
author = "Daniel Bemb{\'e} and Andr{\'e} Galligo",
title = "Virtual roots of a real polynomial and fractional
derivatives",
crossref = "Schost:2011:IPI",
pages = "27--34",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993897",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "After the works of Gonzales-Vega, Lombardi, Mahe [11],
and of Coste, Lajous, Lombardi, Roy [6], we consider
the virtual roots of a univariate polynomial $f$ with
real coefficients. Using fractional derivatives, we
associate to $f$ a bivariate polynomial $ P(x, t) $
depending on the choice of an origin $a$, then two type
of plan curves we call the FDcurve and stem of $f$. We
show, in the generic case, how to locate the virtual
roots of $f$ on the Budan table and on each of these
curves. The paper is illustrated with examples and
pictures computed with the computer algebra system
Maple.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bernardi:2011:MPD,
author = "Alessandra Bernardi and J{\'e}r{\^o}me Brachat and
Pierre Comon and Bernard Mourrain",
title = "Multihomogeneous polynomial decomposition using moment
matrices",
crossref = "Schost:2011:IPI",
pages = "35--42",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993898",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In the paper, we address the important problem of
tensor decomposition which can be seen as a
generalisation of Singular Value Decomposition for
matrices. We consider general multilinear and
multihomogeneous tensors. We show how to reduce the
problem to a truncated moment matrix problem and we
give a new criterion for flat extension of Quasi-Hankel
matrices. We connect this criterion to the commutation
characterisation of border bases. A new algorithm is
described: it applies for general multihomogeneous
tensors, extending the approach of J. J. Sylvester on
binary forms. An example illustrates the algebraic
operations involved in this approach and how the
decomposition can be recovered from eigenvector
computation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Borwein:2011:SVG,
author = "Jonathan M. Borwein and Armin Straub",
title = "Special values of generalized log-sine integrals",
crossref = "Schost:2011:IPI",
pages = "43--50",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993899",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
abstract = "We study generalized log-sine integrals at special
values. At $ \pi $ and multiples thereof explicit
evaluations are obtained in terms of Nielsen
polylogarithms at $ \pm 1 $. For general arguments we
present algorithmic evaluations involving Nielsen
polylogarithms at related arguments. In particular, we
consider log-sine integrals at $ \pi / 3 $ which
evaluate in terms of polylogarithms at the sixth root
of unity. An implementation of our results for the
computer algebra systems Mathematica and SAGE is
provided.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bright:2011:VRN,
author = "Curtis Bright and Arne Storjohann",
title = "Vector rational number reconstruction",
crossref = "Schost:2011:IPI",
pages = "51--58",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993900",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The final step of some algebraic algorithms is to
reconstruct the common denominator $d$ of a collection
of rational numbers $ (n_i / d)_{1 \leq i \leq n} $
from their images $ (a_i)_{1 \leq i \leq n} \bmod M $,
subject to a condition such as $ 0 < d \leq N $ and $
N_i \leq N $ for a given magnitude bound $N$. Applying
elementwise rational number reconstruction requires
that $ M \in \Omega (N^2) $. Using the gradual
sublattice reduction algorithm of van Hoeij and
Novocin, we show how to perform the reconstruction
efficiently even when the modulus satisfies a
considerably smaller magnitude bound $ M \in \Omega
(N^{1 + 1 / c}) $ for $c$ a small constant, for example
$ 2 \leq c \leq 5 $. Assuming $ c \in O(1) $ the cost
of the approach is $ O(n (\log M)^3) $ bit operations
using the original LLL lattice reduction algorithm, but
is reduced to $ O(n (\log M)^2) $ bit operations by
incorporating the $ L^2 $ variant of Nguyen and Stehle.
As an application, we give a robust method for
reconstructing the rational solution vector of a linear
system from its image, such as obtained by a solver
using $p$-adic lifting.",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgisser:2011:PAC,
author = "Peter B{\"u}rgisser",
title = "Probabilistic analysis of condition numbers",
crossref = "Schost:2011:IPI",
pages = "5--6",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993891",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Condition numbers are well known in numerical linear
algebra. It is less known that this concept also plays
a crucial part in understanding the efficiency of
algorithms in linear programming, convex optimization,
and for solving systems of polynomial equations.
Indeed, the running time of such algorithms may be
often effectively bounded in terms of the condition
underlying the problem. ``Smoothed analysis'', as
suggested by Spielman and Teng, is a blend of
worst-case and average-case probabilistic analysis of
algorithms. The goal is to prove that for all inputs
(even ill-posed ones), and all slight random
perturbations of that input, it is unlikely that the
running time (or condition number) will be large. The
tutorial will present a unifying view on the notion of
condition in linear algebra, convex optimization, and
polynomial equations. We will discuss the role of
condition for the analysis of algorithms as well as
techniques for their probabilistic analysis. For the
latter, geometry plays an important role.",
acknowledgement = ack-nhfb,
}
@InProceedings{Burton:2011:DGV,
author = "Benjamin A. Burton",
title = "Detecting genus in vertex links for the fast
enumeration of $3$-manifold triangulations",
crossref = "Schost:2011:IPI",
pages = "59--66",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993901",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Enumerating all $3$-manifold triangulations of a given
size is a difficult but increasingly important problem
in computational topology. A key difficulty for
enumeration algorithms is that most combinatorial
triangulations must be discarded because they do not
represent topological $3$-manifolds. In this paper we
show how to preempt bad triangulations by detecting
genus in partially-constructed vertex links, allowing
us to prune the enumeration tree substantially. The key
idea is to manipulate the boundary edges surrounding
partial vertex links using expected logarithmic time
operations. Practical testing shows the resulting
enumeration algorithm to be significantly faster, with
up to $ 249 \times $ speed-ups even for small problems
where comparisons are feasible. We also discuss
parallelisation, and describe new data sets that have
been obtained using high-performance computing
facilities.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cabarcas:2011:LAC,
author = "Daniel Cabarcas and Jintai Ding",
title = "Linear algebra to compute syzygies and {Gr{\"o}bner}
bases",
crossref = "Schost:2011:IPI",
pages = "67--74",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993902",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we introduce a new method to avoid zero
reductions in Gr{\"o}bner basis computation. We call
this method LASyz, which stands for Lineal Algebra to
compute Syzygies. LASyz uses exhaustively the
information of both principal syzygies and non-trivial
syzygies to avoid zero reductions. All computation is
done using linear algebra techniques. LASyz is easy to
understand and implement. The method does not require
to compute Gr{\"o}bner bases of subsequences of
generators incrementally and it imposes no restrictions
on the reductions allowed. We provide a complete
theoretical foundation for the LASyz method and we
describe an algorithm to compute Gr{\"o}bner bases for
zero dimensional ideals based on this foundation. A
qualitative comparison with similar algorithms is
provided and the performance of the algorithm is
illustrated with experimental data.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2011:ACT,
author = "Changbo Chen and Marc Moreno Maza",
title = "Algorithms for computing triangular decompositions of
polynomial systems",
crossref = "Schost:2011:IPI",
pages = "83--90",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993904",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "We propose new algorithms for computing triangular
decompositions of polynomial systems incrementally.
With respect to previous works, our improvements are
based on a weakened notion of a polynomial GCD modulo a
regular chain, which permits to greatly simplify and
optimize the sub-algorithms. Extracting common work
from similar expensive computations is also a key
feature of our algorithms. In our experimental results
the implementation of our new algorithms, realized with
the {\tt RegularChains} library in MAPLE, outperforms
solvers with similar specifications by several orders
of magnitude on sufficiently difficult problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2011:CSA,
author = "Changbo Chen and James H. Davenport and Marc Moreno
Maza and Bican Xia and Rong Xiao",
title = "Computing with semi-algebraic sets represented by
triangular decomposition",
crossref = "Schost:2011:IPI",
pages = "75--82",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993903",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This article is a continuation of our earlier work
[3], which introduced triangular decompositions of
semi-algebraic systems and algorithms for computing
them. Our new contributions include theoretical results
based on which we obtain practical improvements for
these decomposition algorithms. We exhibit new results
on the theory of border polynomials of parametric
semi-algebraic systems: in particular a geometric
characterization of its ``true boundary'' (Definition
2). In order to optimize these algorithms, we also
propose a technique, that we call relaxation, which can
simplify the decomposition process and reduce the
number of redundant components in the output. Moreover,
we present procedures for basic set-theoretical
operations on semi-algebraic sets represented by
triangular decomposition. Experimentation confirms the
effectiveness of our techniques.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2011:SCR,
author = "Shaoshi Chen and Ruyong Feng and Guofeng Fu and Ziming
Li",
title = "On the structure of compatible rational functions",
crossref = "Schost:2011:IPI",
pages = "91--98",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993905",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A finite number of rational functions are compatible
if they satisfy the compatibility conditions of a
first-order linear functional system involving
differential, shift and $q$-shift operators. We present
a theorem that describes the structure of compatible
rational functions. The theorem enables us to decompose
a solution of such a system as a product of a rational
function, several symbolic powers, a hyperexponential
function, a hypergeometric term, and a
$q$-hypergeometric term. We outline an algorithm for
computing this product, and present an application.",
acknowledgement = ack-nhfb,
}
@InProceedings{Eder:2011:SBA,
author = "Christian Eder and John Edward Perry",
title = "Signature-based algorithms to compute {Gr{\"o}bner}
bases",
crossref = "Schost:2011:IPI",
pages = "99--106",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993906",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Abstract This paper describes a Buchberger-style
algorithm to compute a Gr{\"o}bner basis of a
polynomial ideal, allowing for a selection strategy
based on ``signatures''. We explain how three recent
algorithms can be viewed as different strategies for
the new algorithm, and how other selection strategies
can be formulated. We describe a fourth as an example.
We analyze the strategies both theoretically and
empirically, leading to some surprising results.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fang:2011:DSO,
author = "Tingting Fang and Mark van Hoeij",
title = "$2$-descent for second order linear differential
equations",
crossref = "Schost:2011:IPI",
pages = "107--114",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993907",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $L$ be a second order linear ordinary differential
equation with coefficients in $ C(x) $. The goal in
this paper is to reduce $L$ to an equation that is
easier to solve. The starting point is an irreducible
$L$, of order two, and the goal is to decide if $L$ is
projectively equivalent to another equation $L$ that is
defined over a subfield $ C (f) $ of $ C(x) $. This
paper treats the case of $2$-descent, which means
reduction to a subfield with index $ [C(x) : C(f)] = 2
$. Although the mathematics has already been treated in
other papers, a complete implementation could not be
given because it involved a step for which we do not
have a complete implementation. The contribution of
this paper is to give an approach that is fully
implementable. Examples illustrate that this algorithm
is very useful for finding closed form solutions
($2$-descent, if it exists, reduces the number of true
singularities from $n$ to at most $ n / 2 + 2 $).",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2011:FAC,
author = "Jean-Charles Faug{\`e}re and Chenqi Mou",
title = "Fast algorithm for change of ordering of
zero-dimensional {Gr{\"o}bner} bases with sparse
multiplication matrices",
crossref = "Schost:2011:IPI",
pages = "115--122",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993908",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $I$ in $ K[x_1, \ldots {}, x_n] $ be a
$0$-dimensional ideal of degree $D$ where $K$ is a
field. It is well-known that obtaining efficient
algorithms for change of ordering of Gr{\"o}bner bases
of $I$ is crucial in polynomial system solving. Through
the algorithm FGLM, this task is classically tackled by
linear algebra operations in $ K[x_1, \ldots {}, x_n] /
I $. With recent progress on Gr{\"o}bner bases
computations, this step turns out to be the bottleneck
of the whole solving process. Our contribution is an
algorithm that takes advantage of the sparsity
structure of multiplication matrices appearing during
the change of ordering. This sparsity structure arises
even when the input polynomial system defining $I$ is
dense. As a by-product, we obtain an implementation
which is able to manipulate $0$-dimensional ideals over
a prime field of degree greater than $ 30 \, 000 $. It
outperforms the Magma\slash Singular\ldots{} FGb
implementations of FGLM. First, we investigate the
particular but important shape position case. The
obtained algorithm performs the change of ordering
within a complexity $ O(D(N i >_1 + n \log (D))) $,
where $ N_1 $ is the number of nonzero entries of a
multiplication matrix. This almost matches the
complexity of computing the minimal polynomial of one
multiplication matrix. Then, we address the general
case and give corresponding complexity results. Our
algorithm is dynamic in the sense that it selects
automatically which strategy to use depending on the
input. Its key ingredients are the Wiedemann algorithm
to handle $1$-dimensional linear recurrence (for the
shape position case), and the Berlekamp--Massey-Sakata
algorithm from Coding Theory to handle
multi-dimensional linearly recurring sequences in the
general case.",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:2011:DII,
author = "Mark Giesbrecht and Daniel S. Roche",
title = "Diversification improves interpolation",
crossref = "Schost:2011:IPI",
pages = "123--130",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993909",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider the problem of interpolating an unknown
multivariate polynomial with coefficients taken from a
finite field or as numerical approximations of complex
numbers. Building on the recent work of Garg and
Schost, we improve on the best-known algorithm for
interpolation over large finite fields by presenting a
Las Vegas randomized algorithm that uses fewer black
box evaluations. Using related techniques, we also
address numerical interpolation of sparse polynomials
with complex coefficients, and provide the first
provably stable algorithm (in the sense of relative
error) for this problem, at the cost of modestly more
evaluations. A key new technique is a randomization
which makes all coefficients of the unknown polynomial
distinguishable, producing what we call a diverse
polynomial. Another departure from most previous
approaches is that our algorithms do not rely on root
finding as a subroutine. We show how these improvements
affect the practical performance with trial
implementations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Greuet:2011:DRI,
author = "Aur{\'e}lien Greuet and Mohab Safey {El Din}",
title = "Deciding reachability of the infimum of a multivariate
polynomial",
crossref = "Schost:2011:IPI",
pages = "131--138",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993910",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $ f \in Q[X_1, \ l d o t {s}, X_n] $ be of degree
$D$. Algorithms for solving the unconstrained global
optimization problem $ f *= \inf_x \in R^n f(x) $ are
of first importance since this problem appears
frequently in numerous applications in engineering
sciences. This can be tackled by either designing
appropriate quantifier elimination algorithms or by
certifying lower bounds on $ f * $ by means of sums of
squares decompositions but there is no efficient
algorithm for deciding if $ f * $ is a minimum. This
paper is dedicated to this important problem. We design
a probabilistic algorithm that decides, for a given $f$
and the corresponding $ f * $, if $ f * $ is reached
over $ R^n $ and computes a point $ x * \in R^n $ such
that $ f(x *) = f * $ if such a point exists. This
algorithm makes use of algebraic elimination algorithms
and real root isolation. If $L$ is the length of a
straight-line program evaluating $f$, algebraic
elimination steps run in $ O(\log (D - 1) n^6 (n L +
n^4) U ((D - 1)^{n + 1})^3) $ arithmetic operations in
$Q$ where $ D = \deg (f) $ and $ U(x) = x (\log (x))^2
\log \log (x) $. Experiments show its practical
efficiency.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2011:ACS,
author = "Leilei Guo and Feng Liu",
title = "An algorithm for computing set-theoretic generators of
an algebraic variety",
crossref = "Schost:2011:IPI",
pages = "139--146",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993911",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Based on Eisenbud's idea (see [Eisenbud, D., Evans,
G., 1973. \booktitle{Every algebraic set in $n$-space
is the intersection of $n$ hypersurfaces}. Invent.
Math. 19, 107--112]), we present an algorithm for
computing set-theoretic generators for any algebraic
variety in the affine $n$-space, which consists of at
most $n$ polynomials. With minor modifications, this
algorithm is also valid for projective algebraic
variety in projective $n$-space.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2011:RPL,
author = "Li Guo and William Y. Sit and Ronghua Zhang",
title = "On {Rota}'s problem for linear operators in
associative algebras",
crossref = "Schost:2011:IPI",
pages = "147--154",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993912",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A long standing problem of Gian-Carlo Rota for
associative algebras is the classification of all
linear operators that can be defined on them. In the
1970s, there were only a few known operators, for
example, the derivative operator, the difference
operator, the average operator and the Rota--Baxter
operator. A few more appeared after Rota posed his
problem. However, little progress was made to solve
this problem in general. In part, this is because the
precise meaning of the problem is not so well
understood. In this paper, we propose a formulation of
the problem using the framework of operated algebras
and viewing an associative algebra with a linear
operator as one that satisfies a certain operated
polynomial identity. To narrow our focus more on the
operators that Rota was interested in, we further
consider two particular classes of operators, namely,
those that generalize differential or Rota--Baxter
operators. With the aid of computer algebra, we are
able to come up with a list of these two classes of
operators, and provide some evidence that these lists
may be complete. Our search have revealed quite a few
new operators of these types whose properties are
expected to be similar to the differential operator and
Rota--Baxter operator respectively. Recently, a more
unified approach has emerged in related areas, such as
difference algebra and differential algebra, and
Rota--Baxter algebra and Nijenhuis algebra. The
similarities in these theories can be more efficiently
explored by advances on Rota's problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:2011:CHF,
author = "Somit Gupta and Arne Storjohann",
title = "Computing {Hermite} forms of polynomial matrices",
crossref = "Schost:2011:IPI",
pages = "155--162",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993913",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper presents a new algorithm for computing the
Hermite form of a polynomial matrix. Given a
nonsingular $ n \times n $ matrix $A$ filled with
degree $d$ polynomials with coefficients from a field,
the algorithm computes the Hermite form of $A$ using an
expected number of $ (n^3 d)^{1 + o(1)} $ field
operations. This is the first algorithm that is both
softly linear in the degree $d$ and softly cubic in the
dimension $n$. The algorithm is randomized of the Las
Vegas type.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hart:2011:PPF,
author = "William Hart and Mark van Hoeij and Andrew Novocin",
title = "Practical polynomial factoring in polynomial time",
crossref = "Schost:2011:IPI",
pages = "163--170",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993914",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "State of the art factoring in $ Q[x] $ is dominated in
theory by a combinatorial reconstruction problem while,
excluding some rare polynomials, performance tends to
be dominated by Hensel lifting. We present an algorithm
which gives a practical improvement (less Hensel
lifting) for these more common polynomials. In
addition, factoring has suffered from a 25 year
complexity gap because the best implementations are
much faster in practice than their complexity bounds.
We illustrate that this complexity gap can be closed by
providing an implementation which is comparable to the
best current implementations and for which competitive
complexity results can be proved.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2011:QTC,
author = "Erich L. Kaltofen and Michael Nehring and B. David
Saunders",
title = "Quadratic-time certificates in linear algebra",
crossref = "Schost:2011:IPI",
pages = "171--176",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993915",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present certificates for the positive
semidefiniteness of an $n$ by $n$ matrix $A$, whose
entries are integers of binary length $ \log || A || $,
that can be verified in $ O(n^{(2 + \mu)} (\log || A
||)^{(1 + \mu)}) $ binary operations for any $ \mu > 0
$. The question arises in Hilbert\slash Artin-based
rational sum-of-squares certificates (proofs) for
polynomial inequalities with rational coefficients. We
allow certificates that are validated by Monte Carlo
randomized algorithms, as in Rusins Freivalds's famous
1979 quadratic time certification for the matrix
product. Our certificates occupy $ O(n^{(3 + \mu)}
(\log || A ||)^{(1 + \mu)}) $ bits, from which the
verification algorithm randomly samples a quadratic
amount. In addition, we give certificates of the same
space and randomized validation time complexity for the
Frobenius form, which includes the characteristic and
minimal polynomial. For determinant and rank we have
certificates of essentially-quadratic binary space and
time complexity via Storjohann's algorithms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2011:SBB,
author = "Erich L. Kaltofen and Michael Nehring",
title = "Supersparse black box rational function
interpolation",
crossref = "Schost:2011:IPI",
pages = "177--186",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993916",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a method for interpolating a supersparse
blackbox rational function with rational coefficients,
for example, a ratio of binomials or trinomials with
very high degree. We input a blackbox rational
function, as well as an upper bound on the number of
non-zero terms and an upper bound on the degree. The
result is found by interpolating the rational function
modulo a small prime $p$, and then applying an
effective version of Dirichlet's Theorem on primes in
an arithmetic progression progressively lift the result
to larger primes. Eventually we reach a prime number
that is larger than the inputted degree bound and we
can recover the original function exactly. In a
variant, the initial prime $p$ is large, but the
exponents of the terms are known modulo larger and
larger factors of $ p - 1 $. The algorithm, as
presented, is conjectured to be polylogarithmic in the
degree, but exponential in the number of terms.
Therefore, it is very effective for rational functions
with a small number of non-zero terms, such as the
ratio of binomials, but it quickly becomes ineffective
for a high number of terms. The algorithm is oblivious
to whether the numerator and denominator have a common
factor. The algorithm will recover the sparse form of
the rational function, rather than the reduced form,
which could be dense. We have experimentally tested the
algorithm in the case of under 10 terms in numerator
and denominator combined and observed its conjectured
high efficiency.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaminski:2011:UDC,
author = "Jeremy-Yrmeyahu Kaminski and Yann Sepulcre",
title = "Using discriminant curves to recover a surface of {$
P^4 $} from two generic linear projections",
crossref = "Schost:2011:IPI",
pages = "187--192",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993917",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study how an irreducible smooth and closed
algebraic surface X embedded in CP$^4$, can be
recovered using its projections from two points onto
embedded projective hyperplanes. The different
embeddings are unknown. The only input is the defining
equation of each projected surface. We show how both
the embeddings and the surface in CP$^4$ can be
recovered modulo some action of the group of projective
transformations of CP$^4$. We show how in a generic
situation, a characteristic matrix of the pair of
embeddings can be recovered. Then we use this matrix to
recover the class of the couple of maps and as a
consequence to recover the surface. For a generic
situation, two projections define a surface with two
irreducible components. One component has degree d (d
-1) and the other has degree d, being the original
surface.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kapur:2011:CCG,
author = "Deepak Kapur and Yao Sun and Dingkang Wang",
title = "Computing comprehensive {Gr{\"o}bner} systems and
comprehensive {Gr{\"o}bner} bases simultaneously",
crossref = "Schost:2011:IPI",
pages = "193--200",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993918",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In Kapur et al (ISSAC, 2010), a new method for
computing a comprehensive Gr{\"o}bner system of a
parameterized polynomial system was proposed and its
efficiency over other known methods was effectively
demonstrated. Based on those insights, a new approach
is proposed for computing a comprehensive Gr{\"o}bner basis
of a parameterized polynomial system. The key new idea
is not to simplify a polynomial under various
specialization of its parameters, but rather keep track
in the polynomial, of the power products whose
coefficients vanish; this is achieved by partitioning
the polynomial into two parts- nonzero part and zero
part for the specialization under consideration. During
the computation of a comprehensive Gr{\"o}bner system, for
a particular branch corresponding to a specialization
of parameter values, nonzero parts of the polynomials
dictate the computation, i.e., computing S-polynomials
as well as for simplifying a polynomial with respect to
other polynomials; but the manipulations on the whole
polynomials (including their zero parts) are also
performed. Gr{\"o}bner basis computations on such pairs of
polynomials can also be viewed as Gr{\"o}bner basis
computations on a module. Once a comprehensive Gr{\"o}bner
system is generated, both nonzero and zero parts of the
polynomials are collected from every branch and the
result is a faithful comprehensive Gr{\"o}bner basis, to
mean that every polynomial in a comprehensive Gr{\"o}bner
basis belongs to the ideal of the original
parameterized polynomial system. This technique should
be applicable to other algorithms for computing a
comprehensive Gr{\"o}bner system as well, thus producing
both a comprehensive Gr{\"o}bner system as well as a
faithful comprehensive Gr{\"o}bner basis of a parameterized
polynomial system simultaneously. The approach is
exhibited by adapting the recently proposed method for
computing a comprehensive Gr{\"o}bner system in (ISSAC,
2010) for computing a comprehensive Gr{\"o}bner basis. The
timings on a collection of examples demonstrate that
this new algorithm for computing comprehensive Gr{\"o}bner
bases has better performance than other existing
algorithms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2011:CT,
author = "Manuel Kauers",
title = "The concrete tetrahedron",
crossref = "Schost:2011:IPI",
pages = "7--8",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993892",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We give an overview over computer algebra algorithms
for dealing with symbolic sums, recurrence equations,
generating functions, and asymptotic estimates, and we
will illustrate how to apply these algorithms to
problems arising in discrete mathematics.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kauers:2011:RDB,
author = "Manuel Kauers and Carsten Schneider",
title = "A refined denominator bounding algorithm for
multivariate linear difference equations",
crossref = "Schost:2011:IPI",
pages = "201--208",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993919",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We continue to investigate which polynomials can
possibly occur as factors in the denominators of
rational solutions of a given partial linear difference
equation. In an earlier article we have introduced the
distinction between periodic and aperiodic factors in
the denominator, and we have given an algorithm for
predicting the aperiodic ones. Now we extend this
technique towards the periodic case and present a
refined algorithm which also finds most of the periodic
factors.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kerber:2011:ERR,
author = "Michael Kerber and Michael Sagraloff",
title = "Efficient real root approximation",
crossref = "Schost:2011:IPI",
pages = "209--216",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993920",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider the problem of approximating all real
roots of a square-free polynomial f. Given isolating
intervals, our algorithm refines each of them to a
width at most $ 2^{-L} $, that is, each of the roots is
approximated to $L$ bits after the binary point. Our
method provides a certified answer for arbitrary real
polynomials, only requiring finite approximations of
the polynomial coefficient and choosing a suitable
working precision adaptively. In this way, we get a
correct algorithm that is simple to implement and
practically efficient. Our algorithm uses the quadratic
interval refinement method; we adapt that method to be
able to cope with inaccuracies when evaluating $f$,
without sacrificing its quadratic convergence behavior.
We prove a bound on the bit complexity of our algorithm
in terms of degree, coefficient size and discriminant.
Our bound improves previous work on integer polynomials
by a factor of $ \deg f $ and essentially matches best
known theoretical bounds on root approximation which
are obtained by very sophisticated algorithms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2011:APF,
author = "Yue Li and Gabriel {Dos Reis}",
title = "An automatic parallelization framework for algebraic
computation systems",
crossref = "Schost:2011:IPI",
pages = "233--240",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993923",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper proposes a non-intrusive automatic
parallelization framework for typeful and
property-aware computer algebra systems. Automatic
parallelization remains a promising computer program
transformation for exploiting ubiquitous concurrency
facilities available in modern computers. The framework
uses semantics-based static analysis to extract
reductions in library components based on algebraic
properties. An early implementation shows up to 5 times
speed-up for library functions and homotopy-based
polynomial system solver. The general framework is
applicable to algebraic computation systems and
programming languages with advanced type systems that
support user-defined axioms or annotation systems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2011:ARS,
author = "Hongbo Li and Ruiyong Sun and Shoubin Yao and Ge Li",
title = "Approximate rational solutions torational {ODEs}
defined on discrete differentiable curves",
crossref = "Schost:2011:IPI",
pages = "217--224",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993921",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "In this paper, a new concept is proposed for discrete
differential geometry: discrete n-differentiable curve,
which is a tangent n-jet on a sequence of space points.
A complete method is proposed to solve ODEs of the form
n$^{(m)} = F(r, r', \ldots {}, r^{(n)}, n, n', \ldots
{}, n^{(m - 1)}, u) / G (r, r', \ldots {}, r^{(n)}, n,
n', \ldots {}, n^{(m - 1)}, u)$, where $F$, $G$ are
respectively vector-valued and scalar-valued
polynomials, where $r$ is a discrete curve obtained by
sampling along an unknown smooth curve parametrized by
$u$, and where $n$ is the vector field to be computed
along the curve. Our Maple-13 program outputs an
approximate rational solution with the highest order of
approximation for given data and neighborhood size. The
method is used to compute rotation minimizing frames of
space curves in CAGD. For one-step backward-forward
chasing, a 6th-order approximate rational solution is
found, and 6 is guaranteed to be the highest order of
approximation by rational functions. The theoretical
order of approximation is also supported by numerical
experiments.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2011:SDR,
author = "Wei Li and Xiao-Shan Gao and Cum-Ming Yuan",
title = "Sparse differential resultant",
crossref = "Schost:2011:IPI",
pages = "225--232",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993922",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, the concept of sparse differential
resultant for a differentially essential system of
differential polynomials is introduced and its
properties are proved. In particular, a degree bound
for the sparse differential resultant is given. Based
on the degree bound, an algorithm to compute the sparse
differential resultant is proposed, which is single
exponential in terms of the order, the number of
variables, and the size of the differentially essential
system.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ma:2011:MRG,
author = "Yue Ma and Lihong Zhi",
title = "The minimum-rank gram matrix completion via modified
fixed point continuation method",
crossref = "Schost:2011:IPI",
pages = "241--248",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993924",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The problem of computing a representation for a real
polynomial as a sum of minimum number of squares of
polynomials can be casted as finding a symmetric
positive semidefinite real matrix of minimum rank
subject to linear equality constraints. In this paper,
we propose algorithms for solving the minimum-rank Gram
matrix completion problem, and show the convergence of
these algorithms. Our methods are based on the fixed
point continuation method. We also use the
Barzilai--Borwein technique and a specific linear
combination of two previous iterates to accelerate the
convergence of modified fixed point continuation
algorithms. We demonstrate the effectiveness of our
algorithms for computing approximate and exact rational
sum of squares decompositions of polynomials with
rational coefficients.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mantzaflaris:2011:DCI,
author = "Angelos Mantzaflaris and Bernard Mourrain",
title = "Deflation and certified isolation of singular zeros of
polynomial systems",
crossref = "Schost:2011:IPI",
pages = "249--256",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993925",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We develop a new symbolic-numeric algorithm for the
certification of singular isolated points, using their
associated local ring structure and certified numerical
computations. An improvement of an existing method to
compute inverse systems is presented, which avoids
redundant computation and reduces the size of the
intermediate linear systems to solve. We derive a
one-step deflation technique, from the description of
the multiplicity structure in terms of differentials.
The deflated system can be used in Newton-based
iterative schemes with quadratic convergence. Starting
from a polynomial system and a sufficiently small
neighborhood, we obtain a criterion for the existence
and uniqueness of a singular root of a given
multiplicity structure, applying a well-chosen symbolic
perturbation. Standard verification methods, based e.g.
on interval arithmetic and a fixed point theorem, are
employed to certify that there exists a unique
perturbed system with a singular root in the domain.
Applications to topological degree computation and to
the analysis of real branches of an implicit curve
illustrate the method.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mayr:2011:SEG,
author = "Ernst W. Mayr and Stephan Ritscher",
title = "Space-efficient {Gr{\"o}bner} basis computation
without degree bounds",
crossref = "Schost:2011:IPI",
pages = "257--264",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993926",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The computation of a Gr{\"o}bner basis of a polynomial
ideal is known to be exponential space complete. We
revisit the algorithm by K{\"u}hnle and Mayr using
recent improvements of various degree bounds. The
result is an algorithm which is exponential in the
ideal dimension (rather than the number of
indeterminates). Furthermore, we provide an incremental
version of the algorithm which is independent of the
knowledge of degree bounds. Employing a space-efficient
implementation of Buchberger's S-criterion, the
algorithm can be implemented such that the space
requirement depends on the representation and
Gr{\"o}bner basis degrees of the problem instance
(instead of the worst case) and thus is much lower in
average.",
acknowledgement = ack-nhfb,
}
@InProceedings{Miller:2011:CAE,
author = "Victor S. Miller",
title = "Computational aspects of elliptic curves and modular
forms",
crossref = "Schost:2011:IPI",
pages = "1--2",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993888",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The ultimate motivation for much of the study of
Number Theory is the solution of Diophantine Equations
--- finding integer solutions to systems of equations.
Elliptic curves comprise a large, and important class
of such equations. Throughout the history of their
study Elliptic Curves have always had a strong
algorithmic component. In the early 1960's Birch and
Swinnerton-Dyer developed systematic algorithms to
automate a generalization of a procedure called
``descent'' which went back to Fermat. The data they
obtained was instrumental in formulating their famous
conjecture, which is now one of the Clay Mathematical
Institute's Millenium prizes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Moody:2011:DPJ,
author = "Dustin Moody",
title = "Division polynomials for {Jacobi} quartic curves",
crossref = "Schost:2011:IPI",
pages = "265--272",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993927",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we find division polynomials for Jacobi
quartics. These curves are an alternate model for
elliptic curves to the more common Weierstrass
equation. Division polynomials for Weierstrass curves
are well known, and the division polynomials we find
are analogues for Jacobi quartics. Using the division
polynomials, we show recursive formulas for the n -th
multiple of a point on the quartic curve. As an
application, we prove a type of mean-value theorem for
Jacobi quartics. These results can be extended to other
models of elliptic curves, namely, Jacobi intersections
and Huff curves.",
acknowledgement = ack-nhfb,
}
@InProceedings{Nagasaka:2011:CSG,
author = "Kosaku Nagasaka",
title = "Computing a structured {Gr{\"o}bner} basis
approximately",
crossref = "Schost:2011:IPI",
pages = "273--280",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993928",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "There are several preliminary definitions for a
Gr{\"o}bner basis with inexact input since computing
such a basis is one of the challenging problems in
symbolic-numeric computations for several decades. A
structured Gr{\"o}bner basis is such a basis defined
from the data mining point of view: how to extract a
meaningful result from the given inexact input when the
amount of noise is not small or we do not have enough
information about the input. However, the known
algorithm needs a suitable (unknown) information on
terms required for a variant of the Buchberger
algorithm. In this paper, we introduce an improved
version of the algorithm that does not need any extra
information in advance.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2011:RPM,
author = "Victor Y. Pan and Guoliang Qian and Ai-Long Zheng",
title = "Randomized preconditioning of the {MBA} algorithm",
crossref = "Schost:2011:IPI",
pages = "281--288",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993929",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "MBA algorithm inverts a structured matrix in nearly
linear arithmetic time but requires a serious
restriction on the input class. We remove this
restriction by means of randomization and extend the
progress to some fundamental computations with
polynomials, e.g., computing their GCDs and AGCDs,
where most effective known algorithms rely on
computations with matrices having Toeplitz-like
structure. Furthermore, our randomized algorithms fix
rank deficiency and ill conditioning of general and
structured matrices. At the end we comment on a wide
range of other natural extensions of our progress and
underlying ideas.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pospelov:2011:FFT,
author = "Alexey Pospelov",
title = "{Fast Fourier Transforms} over poor fields",
crossref = "Schost:2011:IPI",
pages = "289--296",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993930",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a new algebraic algorithm for computing the
discrete Fourier transform over arbitrary fields. It
computes DFTs of infinitely many orders $n$ in $ O(n
\log n) $ algebraic operations, while the complexity of
a straightforward application of the known FFT
algorithms can be $ \Omega (n^{1.5}) $ for such $n$.
Our algorithm is a novel combination of the classical
FFT algorithms, and is never slower than any of the
latter. As an application we come up with an efficient
way of computing DFTs of high orders in finite field
extensions which can further boost polynomial
multiplication algorithms. We relate the complexities
of the DFTs of such orders with the complexity of
polynomial multiplication.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sagraloff:2011:SEE,
author = "Michael Sagraloff and Chee K. Yap",
title = "A simple but exact and efficient algorithm for complex
root isolation",
crossref = "Schost:2011:IPI",
pages = "353--360",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993938",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a new exact subdivision algorithm CEVAL for
isolating the complex roots of a square-free polynomial
in any given box. It is a generalization of a previous
real root isolation algorithm called EVAL. Under
suitable conditions, our approach is applicable for
general analytic functions. CEVAL is based on the
simple Bolzano Principle and is easy to implement
exactly. Preliminary experiments have shown its
competitiveness. We further show that, for the
``benchmark problem'' of isolating all roots of a
square-free polynomial with integer coefficients, the
asymptotic complexity of both algorithms EVAL and CEVAL
matches (up a logarithmic term) that of more
sophisticated real root isolation methods which are
based on Descartes' Rule of Signs, Continued Fraction
or Sturm sequence. In particular, we show that the tree
size of EVAL matches that of other algorithms. Our
analysis is based on a novel technique called \Delta
-clusters from which we expect to see further
applications.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sarkar:2011:NRR,
author = "Soumojit Sarkar and Arne Storjohann",
title = "Normalization of row reduced matrices",
crossref = "Schost:2011:IPI",
pages = "297--304",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993931",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper gives a deterministic algorithm to
transform a row reduced matrix to canonical Popov form.
Given as input a row reduced matrix $R$ over $ K[x] $,
$ K a $ field, our algorithm computes the Popov form in
about the same time as required to multiply together
over $ K[x] $ two matrices of the same dimension and
degree as $R$. We also show that the problem of
transforming a row reduced matrix to Popov form is at
least as hard as polynomial matrix multiplication.",
acknowledgement = ack-nhfb,
}
@InProceedings{Saunders:2011:NSE,
author = "B. David Saunders and David Harlan Wood and Bryan S.
Youse",
title = "Numeric-symbolic exact rational linear system solver",
crossref = "Schost:2011:IPI",
pages = "305--312",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993932",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An iterative refinement approach is taken to rational
linear system solving. Such methods produce, for each
entry of the solution vector, a rational approximation
with denominator a power of 2. From this the correct
rational entry can be reconstructed. Our iteration is a
numeric-symbolic hybrid in that it uses an approximate
numeric solver at each step together with a symbolic
(exact arithmetic) residual computation and symbolic
rational reconstruction. The rational solution may be
checked symbolically (exactly). However, there is some
possibility of failure of convergence, usually due to
numeric ill-conditioning. Alternatively, the algorithm
may be used to obtain an extended precision floating
point approximation of any specified precision. In this
case we cannot guarantee the result by rational
reconstruction and an exact solution check, but the
approach gives evidence (not proof) that the
probability of error is extremely small. The chief
contributions of the method and implementation are (1)
confirmed continuation, (2) improved rational
reconstruction, and (3) faster and more robust
performance.",
acknowledgement = ack-nhfb,
}
@InProceedings{She:2011:AAA,
author = "Zhikun She and Bai Xue and Zhiming Zheng",
title = "Algebraic analysis on asymptotic stability of
continuous dynamical systems",
crossref = "Schost:2011:IPI",
pages = "313--320",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993933",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we propose a mechanisable technique for
asymptotic stability analysis of continuous dynamical
systems. We start from linearizing a continuous
dynamical system, solving the Lyapunov matrix equation
and then check whether the solution is positive
definite. For the cases that the Jacobian matrix is not
a Hurwitz matrix, we first derive an algebraizable
sufficient condition for the existence of a Lyapunov
function in quadratic form without linearization. Then,
we apply a real root classification based method step
by step to formulate this derived condition as a
semi-algebraic set such that the semi-algebraic set
only involves the coefficients of the pre-assumed
quadratic form. Finally, we compute a sample point in
the resulting semi-algebraic set for the coefficients
resulting in a Lyapunov function. In this way, we avoid
the use of generic quantifier elimination techniques
for efficient computation. We prototypically
implemented our algorithm based on DISCOVERER. The
experimental results and comparisons demonstrate the
feasibility and promise of our approach.",
acknowledgement = ack-nhfb,
}
@InProceedings{Strzebonski:2011:URR,
author = "Adam Strzebonski and Elias Tsigaridas",
title = "Univariate real root isolation in an extension field",
crossref = "Schost:2011:IPI",
pages = "321--328",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993934",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
abstract = "We present algorithmic, complexity and implementation
results for the problem of isolating the real roots of
a univariate polynomial in $ B_{\alpha} \in L [y] $,
where $ L = Q \alpha $ is a simple algebraic extension
of the rational numbers. We revisit two approaches for
the problem. In the first approach, using resultant
computations, we perform a reduction to a polynomial
with integer coefficients and we deduce a bound of $
O_B(N^{10}) $ for isolating the real roots of $
B_\alpha $, where $N$ is an upper bound on all the
quantities (degree and bitsize) of the input
polynomials. In the second approach we isolate the real
roots working directly on the polynomial of the input.
We compute improved separation bounds for the roots and
we prove that they are optimal, under mild assumptions.
For isolating the real roots we consider a modified
Sturm algorithm, and a modified version of Descartes'
algorithm introduced by Sagraloff. For the former we
prove a complexity bound of $ O_B(N^8) $ and for the
latter a bound of $ O_B(N^7) $. We implemented the
algorithms in C as part of the core library of
Mathematica and we illustrate their efficiency over
various data sets. Finally, we present complexity for
the general case of the first approach, where the
coefficients belong to multiple extensions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sturm:2011:VSU,
author = "Thomas Sturm and Ashish Tiwari",
title = "Verification and synthesis using real quantifier
elimination",
crossref = "Schost:2011:IPI",
pages = "329--336",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993935",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present the application of real quantifier
elimination to formal verification and synthesis of
continuous and switched dynamical systems. Through a
series of case studies, we show how first-order
formulas over the reals arise when formally analyzing
models of complex control systems. Existing
off-the-shelf quantifier elimination procedures are not
successful in eliminating quantifiers from many of our
benchmarks. We therefore automatically combine three
established software components: virtual substitution
based quantifier elimination in Reduce/Redlog,
cylindrical algebraic decomposition implemented in
Qepcad, and the simplifier Slfq implemented on top of
Qepcad. We use this combination to successfully analyze
various models of systems including adaptive cruise
control in automobiles, adaptive flight control system,
and the classical inverted pendulum problem studied in
control theory.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sun:2011:GCS,
author = "Yao Sun and Dingkang Wang",
title = "A generalized criterion for signature related
{Gr{\"o}bner} basis algorithms",
crossref = "Schost:2011:IPI",
pages = "337--344",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993936",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A generalized criterion for signature related
algorithms to compute Gr{\"o}bner basis is proposed in
this paper. Signature related algorithms are a popular
kind of algorithms for computing Gr{\"o}bner basis,
including the famous F5 algorithm, the F5C algorithm,
the extended F5 algorithm and the GVW algorithm. The
main purpose of current paper is to study in theory
what kind of criteria is correct in signature related
algorithms and provide a generalized method to develop
new criteria. For this purpose, a generalized criterion
is proposed. The generalized criterion only relies on a
general partial order defined on a set of polynomials.
When specializing the partial order to appropriate
specific orders, the generalized criterion can
specialize to almost all existing criteria of signature
related algorithms. For admissible partial orders, a
proof is presented for the correctness of the algorithm
that is based on this generalized criterion. And the
partial orders implied by the criteria of F5 and GVW
are also shown to be admissible in this paper. More
importantly, the generalized criterion provides an
effective method to check whether a new criterion is
correct as well as to develop new criteria for
signature related algorithms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Szanto:2011:HSN,
author = "Agnes Szanto",
title = "Hybrid symbolic-numeric methods for the solution of
polynomial systems: tutorial overview",
crossref = "Schost:2011:IPI",
pages = "9--10",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993893",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this tutorial we will focus on the solution of
polynomial systems given with inexact coefficients
using hybrid symbolic-numeric methods. In particular,
we will concentrate on systems that are
over-constrained or have roots with multiplicities.
These systems are considered ill-posed or
ill-conditioned by traditional numerical methods and
they try to avoid them. On the other hand, traditional
symbolic methods are not designed to handle
inexactness. Ill-conditioned polynomial equation
systems arise very frequently in many important
applications areas such as geometric modeling, computer
vision, fluid dynamics, etc.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2011:GS,
author = "Mark van Hoeij and J{\"u}rgen Kl{\"u}ners and Andrew
Novocin",
title = "Generating subfields",
crossref = "Schost:2011:IPI",
pages = "345--352",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993937",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a field extension K/k of degree n we are
interested in finding the subfields of K containing k.
There can be more than polynomially many subfields. We
introduce the notion of generating subfields, a set of
up to n subfields whose intersections give the rest. We
provide an efficient algorithm which uses linear
algebra in k or lattice reduction along with
factorization. Our implementation shows that previously
difficult cases can now be handled.",
acknowledgement = ack-nhfb,
}
@InProceedings{Villard:2011:RPL,
author = "Gilles Villard",
title = "Recent progress in linear algebra and lattice basis
reduction",
crossref = "Schost:2011:IPI",
pages = "3--4",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993889",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A general goal concerning fundamental linear algebra
problems is to reduce the complexity estimates to
essentially the same as that of multiplying two
matrices (plus possibly a cost related to the input and
output sizes). Among the bottlenecks one usually finds
the questions of designing a recursive approach and
mastering the sizes of the intermediately computed
data. In this talk we are interested in two special
cases of lattice basis reduction. We consider bases
given by square matrices over $ K[x] $ or $Z$, with,
respectively, the notion of reduced form and LLL
reduction. Our purpose is to introduce basic tools for
understanding how to generalize the Lehmer and
Knuth--Sch{\"o}nhage gcd algorithms for basis
reduction. Over $ K[x] $ this generalization is a key
ingredient for giving a basis reduction algorithm whose
complexity estimate is essentially that of multiplying
two polynomial matrices. Such a problem relation
between integer basis reduction and integer matrix
multiplication is not known. The topic receives a lot
of attention, and recent results on the subject show
that there might be room for progressing on the
question.",
acknowledgement = ack-nhfb,
}
@InProceedings{Abramov:2012:VMS,
author = "S. A. Abramov and D. E. Khmelnov",
title = "On valuations of meromorphic solutions of
arbitrary-order linear difference systems with
polynomial coefficients",
crossref = "vanderHoeven:2012:IPI",
pages = "12--19",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442836",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algorithms for computing lower bounds on valuations
(e.g., orders of the poles) of the components of
meromorphic solutions of arbitrary-order linear
difference systems with polynomial coefficients are
considered. In addition to algorithms based on ideas
which have been already utilized in computer algebra
for treating normal first-order systems, a new
algorithm using tropical calculations is proposed. It
is shown that the latter algorithm is rather fast, and
produces the bounds with good accuracy.",
acknowledgement = ack-nhfb,
}
@InProceedings{Adrovic:2012:CPS,
author = "Danko Adrovic and Jan Verschelde",
title = "Computing {Puiseux} series for algebraic surfaces",
crossref = "vanderHoeven:2012:IPI",
pages = "20--27",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442837",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we outline an algorithmic approach to
compute Puiseux series expansions for algebraic sets.
The series expansions originate at the intersection of
the algebraic set with as many coordinate planes as the
dimension of the algebraic set. Our approach starts
with a polyhedral method to compute cones of normal
vectors to the Newton polytopes of the given polynomial
system that defines the algebraic set. If as many
vectors in the cone as the dimension of the algebraic
set define an initial form system that has isolated
solutions, then those vectors are potential tropisms
for the initial term of the Puiseux series expansion.
Our preliminary methods produce exact representations
for solution sets of the cyclic $n$-roots problem, for
$n = m^2$, corresponding to a result of Backelin.",
acknowledgement = ack-nhfb,
}
@InProceedings{Albrecht:2012:MLD,
author = "Martin R. Albrecht",
title = "The {M4RIE} library for dense linear algebra over
small fields with even characteristic",
crossref = "vanderHoeven:2012:IPI",
pages = "28--34",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442838",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We describe algorithms and implementations for linear
algebra with dense matrices over $ F_2 e $ for $ 2 \leq
e \leq 10 $. Our main contributions are: (1) a
specialisation of precomputation tables to $ F_2 e $,
called Newton--John tables in this work, to avoid
scalar multiplications in Gaussian elimination and
matrix multiplication, (2) an efficient implementation
of Karatsuba-style multiplication for matrices over
extension fields of $ F_2 $ and (3) a description of an
open-source library --- called M4RIE --- providing the
fastest known implementation of dense linear algebra
over $ F_2 e $ with $ 2 \leq e \leq 10 $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2012:CCF,
author = "M. A. Barkatou and T. Cluzeau and C. {El Bacha} and
J.-A. Weil",
title = "Computing closed form solutions of integrable
connections",
crossref = "vanderHoeven:2012:IPI",
pages = "43--50",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442840",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "We present algorithms for computing rational and
hyperexponential solutions of linear $D$-finite partial
differential systems written as integrable connections.
We show that these types of solutions can be computed
recursively by adapting existing algorithms handling
ordinary linear differential systems. We provide an
arithmetic complexity analysis of the algorithms that
we develop. A Maple implementation is available and
some examples and applications are given.",
acknowledgement = ack-nhfb,
}
@InProceedings{Barkatou:2012:SLO,
author = "Moulay A. Barkatou and Clemens G. Raab",
title = "Solving linear ordinary differential systems in
hyperexponential extensions",
crossref = "vanderHoeven:2012:IPI",
pages = "51--58",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442841",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let F be a differential field generated from the
rational functions over some constant field by one
hyperexponential extension. We present an algorithm to
compute the solutions in $F^n$ of systems of $n$
first-order linear ODEs. Solutions in $F$ of a scalar ODE
of higher order can be determined by an algorithm of
Bronstein and Fredet. Our approach avoids reduction to
the scalar case. We also give examples to show how this
can be applied to integration.",
acknowledgement = ack-nhfb,
}
@InProceedings{Berthomieu:2012:RPA,
author = "J{\'e}r{\'e}my Berthomieu and Romain Lebreton",
title = "Relaxed $p$-adic {Hensel} lifting for algebraic
systems",
crossref = "vanderHoeven:2012:IPI",
pages = "59--66",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442842",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In a previous article [1], an implementation of lazy p
-adic integers with a multiplication of quasi-linear
complexity, the so-called relaxed product, was
presented. Given a ring $R$ and an element $p$ in $R$,
we design a relaxed Hensel lifting for algebraic
systems from $R / (p)$ to the $p$-adic completion $R_p$
of $R$. Thus, any root of linear and algebraic regular
systems can be lifted with a quasi-optimal
complexity. We report our implementations in C++ within
the computer algebra system Mathemagix and compare them
with Newton operator. As an application, we solve
linear systems over the integers and compare the
running times with Linbox and IML.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bettale:2012:SPS,
author = "Luk Bettale and Jean-Charles Faug{\`e}re and Ludovic
Perret",
title = "Solving polynomial systems over finite fields:
improved analysis of the hybrid approach",
crossref = "vanderHoeven:2012:IPI",
pages = "67--74",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442843",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Polynomial System Solving (PoSSo) problem is a
fundamental NP-Hard problem in computer algebra. Among
others, PoSSo have applications in area such as coding
theory and cryptology. Typically, the security of
multivariate public-key schemes (MPKC) such as the UOV
cryptosystem of Kipnis, Shamir and Patarin is directly
related to the hardness of PoSSo over finite fields.
The goal of this paper is to further understand the
influence of finite fields on the hardness of PoSSo. To
this end, we consider the so-called hybrid approach.
This is a polynomial system solving method dedicated to
finite fields proposed by Bettale, Faug{\`e}re and
Perret (Journal of Mathematical Cryptography, 2009).
The idea is to combine exhaustive search with
Gr{\"o}bner bases. The efficiency of the hybrid
approach is related to the choice of a trade-off
between the two methods. We propose here an improved
complexity analysis dedicated to quadratic systems.
Whilst the principle of the hybrid approach is simple,
its careful analysis leads to rather surprising and
somehow unexpected results. We prove that the optimal
trade-off (i.e. number of variables to be fixed)
allowing to minimize the complexity is achieved by
fixing a number of variables proportional to the number
of variables of the system considered, denoted n. Under
some natural algebraic assumption, we show that the
asymptotic complexity of the hybrid approach is $
2^{(3.31 - 3.62 \log 2 (q) - 1) n} $, where $q$ is the
size of the field (under the condition in particular
that $ \log (q) \ll n $). This is to date, the best
complexity for solving PoSSo over finite fields (when $
q > 2 $). We have been able to quantify the gain
provided by the hybrid approach compared to a direct
Gr{\" o}bner basis method. For quadratic systems, we
show (assuming a natural algebraic assumption) that
this gain is exponential in the number of variables.
Asymptotically, the gain is $ 2^{1.49 n} $ when both
$n$ and $q$ grow to infinity and $ \log (q) \ll n $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Beukers:2012:HFC,
author = "Frits Beukers",
title = "{$A$}-hypergeometric functions: computational
aspects",
crossref = "vanderHoeven:2012:IPI",
pages = "1--2",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442830",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Biasse:2012:PTA,
author = "Jean-Fran{\c{c}}ois Biasse and Claus Fieker",
title = "A polynomial time algorithm for computing the {HNF} of
a module over the integers of a number field",
crossref = "vanderHoeven:2012:IPI",
pages = "75--82",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442844",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a variation of the modular algorithm for
computing the Hermite Normal Form of an $O_K$-module
presented by Cohen [4], where $O_K$ is the ring of
integers of a number field $K$. An approach presented in
[4] based on reductions modulo ideals was conjectured
to run in polynomial time by Cohen, but so far, no such
proof was available in the literature. In this paper,
we present a modification of the approach of [4] to
prevent the coefficient swell and we rigorously assess
its complexity with respect to the size of the input
and the invariants of the field $K$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Biscani:2012:PSP,
author = "Francesco Biscani",
title = "Parallel sparse polynomial multiplication on modern
hardware architectures",
crossref = "vanderHoeven:2012:IPI",
pages = "83--90",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442845",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a high performance algorithm for the
parallel multiplication of sparse multivariate
polynomials on modern computer architectures. The
algorithm is built on three main concepts: a
cache-friendly hash table implementation for the
storage of polynomial terms in distributed form, a
statistical method for the estimation of the size of
the multiplication result, and the use of Kronecker
substitution as a homomorphic hash function. The
algorithm achieves high performance by promoting data
access patterns that favour temporal and spatial
locality of reference. We present benchmarks comparing
our algorithm to routines of other computer algebra
systems, both in sequential and parallel mode.",
acknowledgement = ack-nhfb,
}
@InProceedings{Blankertz:2012:CCD,
author = "Raoul Blankertz and Joachim von zur Gathen and
Konstantin Ziegler",
title = "Compositions and collisions at degree $ p^2 $",
crossref = "vanderHoeven:2012:IPI",
pages = "91--98",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442846",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A univariate polynomial $f$ over a field is
decomposable if $ f = g o h = g (h) $ for nonlinear
polynomials $g$ and $h$. In order to count the
decomposables, one wants to know the number of
equal-degree collisions of the form $ f = g o h = g * o
h * $ with $ (g, h) /= (g *, h *) $ and $ \deg g = \deg
g * $. Such collisions only occur in the wild case,
where the field characteristic $p$ divides $ \deg f $.
Reasonable bounds on the number of decomposables over a
finite field are known, but they are less sharp in the
wild case, in particular for degree $ p^2 $. We provide
a classification of all polynomials of degree $ p^2 $
with a collision. It yields the exact number of
decomposable polynomials of degree $ p^2 $ over a
finite field of characteristic $p$. We also present an
algorithm that determines whether a given polynomial of
degree $ p^2 $ has a collision or not.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2012:FCC,
author = "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Bruno
Salvy and Ziming Li",
title = "Fast computation of common left multiples of linear
ordinary differential operators",
crossref = "vanderHoeven:2012:IPI",
pages = "99--106",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442847",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study tight bounds and fast algorithms for LCLMs of
several linear differential operators with polynomial
coefficients. We analyse the arithmetic complexity of
existing algorithms for LCLMs, as well as the size of
their outputs. We propose a new algorithm that recasts
the LCLM computation in a linear algebra problem on a
polynomial matrix. This algorithm yields sharp bounds
on the coefficient degrees of the LCLM, improving by
one order of magnitude the best bounds obtained using
previous algorithms. The complexity of the new
algorithm is almost optimal, in the sense that it
nearly matches the arithmetic size of the output.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2012:PSS,
author = "Alin Bostan and Bruno Salvy and Muhammad F. I.
Chowdhury and {\'E}ric Schost and Romain Lebreton",
title = "Power series solutions of singular $ (q)
$-differential equations",
crossref = "vanderHoeven:2012:IPI",
pages = "107--114",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442848",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We provide algorithms computing power series solutions
of a large class of differential or $q$-differential
equations or systems. Their number of arithmetic
operations grows linearly with the precision, up to
logarithmic terms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bournez:2012:CSI,
author = "Olivier Bournez and Daniel S. Gra{\c{c}}a and Amaury
Pouly",
title = "On the complexity of solving initial value problems",
crossref = "vanderHoeven:2012:IPI",
pages = "115--121",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442849",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we prove that computing the solution of
an initial-value problem $ y = p(y) $ with initial
condition $ y (t_0) = y_0 \in R^d $ at time $ t_0 + T $
with precision $ 2^{- \mu } $ where $p$ is a vector of
polynomials can be done in time polynomial in the value
of $T$, $ \mu $ and $ Y = [{\rm equation}] $. Contrary
to existing results, our algorithm works over any
bounded or unbounded domain. Furthermore, we do not
assume any Lipschitz condition on the initial-value
problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2012:ODC,
author = "Shaoshi Chen and Manuel Kauers",
title = "Order-degree curves for hypergeometric creative
telescoping",
crossref = "vanderHoeven:2012:IPI",
pages = "122--129",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442850",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Creative telescoping applied to a bivariate proper
hypergeometric term produces linear recurrence
operators with polynomial coefficients, called
telescopers. We provide bounds for the degrees of the
polynomials appearing in these operators. Our bounds
are expressed as curves in the $ (r, d) $-plane which
assign to every order $r$ a bound on the degree $d$ of
the telescopers. These curves are hyperbolas, which
reflect the phenomenon that higher order telescopers
tend to have lower degree, and vice versa.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2012:TRA,
author = "Shaoshi Chen and Manuel Kauers and Michael F. Singer",
title = "Telescopers for rational and algebraic functions via
residues",
crossref = "vanderHoeven:2012:IPI",
pages = "130--137",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442851",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We show that the problem of constructing telescopers
for rational functions of $ m + 1 $ variables is
equivalent to the problem of constructing telescopers
for algebraic functions of $m$ variables and we present
a new algorithm to construct telescopers for algebraic
functions of two variables. These considerations are
based on analyzing the residues of the input. According
to experiments, the resulting algorithm for rational
functions of three variables is faster than known
algorithms, at least in some examples of combinatorial
interest. The algorithm for algebraic functions implies
a new bound on the order of the telescopers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Comer:2012:SPI,
author = "Matthew T. Comer and Erich L. Kaltofen and Cl{\'e}ment
Pernet",
title = "Sparse polynomial interpolation and {Berlekamp\slash
Massey} algorithms that correct outlier errors in input
values",
crossref = "vanderHoeven:2012:IPI",
pages = "138--145",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442852",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We propose algorithms performing sparse interpolation
with errors, based on Prony's--Ben-Or's {\&} Tiwari's
algorithm, using a Berlekamp/Massey algorithm with
early termination. First, we present an algorithm that
can recover a $t$-sparse polynomial $f$ from a sequence
of values, where some of the values are wrong, spoiled
by either random or misleading errors. Our algorithm
requires bounds $ T \geq t $ and $ E \geq e $, where
$e$ is the number of evaluation errors. It interpolates
$ f(\omega^i) $ for $ i = 1, \ldots {}, 2 T (E + 1) $,
where $ \omega $ is a field element at which each
non-zero term evaluates distinctly. We also investigate
the problem of recovering the minimal linear generator
from a sequence of field elements that are linearly
generated, but where again $ e \leq E $ elements are
erroneous. We show that there exist sequences of $ < 2
t (2 e + 1) $ elements, such that two distinct
generators of length $t$ satisfy the linear recurrence
up to $e$ faults, at least if the field has
characteristic $ /= 2 $. Uniqueness can be proven (for
any field characteristic) for length $ \geq 2 t (2 e +
1) $ of the sequence with e errors. Finally, we present
the Majority Rule Berlekamp/Massey algorithm, which can
recover the unique minimal linear generator of degree
$t$ when given bounds $ T \geq t $ and $ E \geq e $ and
the initial sequence segment of $ 2 T (2 E + 1) $
elements. Our algorithm also corrects the sequence
segment. The Majority Rule algorithm yields a unique
sparse interpolant for the first problem. The
algorithms are applied to sparse interpolation
algorithms with numeric noise, into which we now can
bring outlier errors in the values.",
acknowledgement = ack-nhfb,
}
@InProceedings{Elsheikh:2012:FCS,
author = "Mustafa Elsheikh and Mark Giesbrecht and Andy Novocin
and B. David Saunders",
title = "Fast computation of {Smith} forms of sparse matrices
over local rings",
crossref = "vanderHoeven:2012:IPI",
pages = "146--153",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442853",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present algorithms to compute the Smith Normal Form
of matrices over two families of local rings. The
algorithms use the black-box model which is suitable
for sparse and structured matrices. The algorithms
depend on a number of tools, such as matrix rank
computation over finite fields, for which the
best-known time- and memory-efficient algorithms are
probabilistic. For an $ n \times n $ matrix $A$ over
the ring $ F[z] / (f^e) $, where $ f^e $ is a power of
an irreducible polynomial $ f \in F[z] $ of degree $d$,
our algorithm requires $ O(\eta d e^2 n) $ operations
in $F$, where our black-box is assumed to require $
O(\eta) $ operations in $F$ to compute a matrix-vector
product by a vector over $ F[z] / (f^e) $ (and $ \eta $
is assumed greater than $ n d e $). The algorithm only
requires additional storage for $ O(n d e) $ elements
of $F$. In particular, if $ \eta = O(n d e) $, then our
algorithm requires only $ O(n^2 d^2 e^3) $ operations
in $F$, which is an improvement on known dense methods
for small $d$ and $e$. For the ring $ Z / p^e Z $,
where $p$ is a prime, we give an algorithm which is
time- and memory-efficient when the number of
nontrivial invariant factors is small. We describe a
method for dimension reduction while preserving the
invariant factors. The time complexity is essentially
linear in $ \mu n r e \log p $, where $ \mu $ is the
number of operations in $ Z / p Z $ to evaluate the
black-box (assumed greater than $n$) and $r$ is the
total number of non-zero invariant factors. To avoid
the practical cost of conditioning, we give a Monte
Carlo certificate, which at low cost, provides either a
high probability of success or a proof of failure. The
quest for a time- and memory-efficient solution without
restrictions on the number of nontrivial invariant
factors remains open. We offer a conjecture which may
contribute toward that end.",
acknowledgement = ack-nhfb,
}
@InProceedings{Emeliyanenko:2012:CSB,
author = "Pavel Emeliyanenko and Michael Sagraloff",
title = "On the complexity of solving a bivariate polynomial
system",
crossref = "vanderHoeven:2012:IPI",
pages = "154--161",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442854",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study the complexity of computing the real
solutions of a bivariate polynomial system using the
recently presented algorithm Bisolve [2]. Bisolve is an
elimination method which, in a first step, projects the
solutions of a system onto the $x$- and $y$-axes and,
then, selects the actual solutions from the so induced
candidate set. However, unlike similar algorithms,
Bisolve requires no genericity assumption on the input,
and there is no need for any kind of coordinate
transformation. Furthermore, extensive benchmarks as
presented in [2] confirm that the algorithm is highly
practical, that is, a corresponding C++ implementation
in Cgal outperforms state of the art approaches by a
large factor. In this paper, we focus on the
theoretical complexity of Bisolve. For two polynomials
$ f, g \in Z[x, y] $ of total degree at most n with
integer coefficients bounded by $ 2^\tau $, we show
that Bisolve computes isolating boxes for all real
solutions of the system $ f = g = 0 $ using $ O(n^8 +
n^7 \tau) $ bit operations, thereby improving the
previous record bound for the same task by several
magnitudes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2012:CPG,
author = "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
Pierre-Jean Spaenlehauer",
title = "Critical points and {Gr{\"o}bner} bases: the unmixed
case",
crossref = "vanderHoeven:2012:IPI",
pages = "162--169",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442855",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We consider the problem of computing critical points
of the restriction of a polynomial map to an algebraic
variety. This is of first importance since the global
minimum of such a map is reached at a critical point.
Thus, these points appear naturally in non-convex
polynomial optimization which occurs in a wide range of
scientific applications (control theory, chemistry,
economics,\ldots{}). Critical points also play a
central role in recent algorithms of effective real
algebraic geometry. Experimentally, it has been
observed that Gr{\"o}bner basis algorithms are
efficient to compute such points. Therefore, recent
software based on the so-called Critical Point Method
are built on Gr{\"o}bner bases engines. Let $ f_1,
\ldots {}, f_p $ be polynomials in $ Q[x_1, \ldots {},
x_n] $ of degree $D$, $ V \subset C^n $ be their
complex variety and $ \pi_1 $ be the projection map $
(x_1, \ldots {}, x_n) \to x_1 $. The critical points of
the restriction of $ \pi_1 $ to $V$ are defined by the
vanishing of $ f_1, \ldots {}, f_p $ and some maximal
minors of the Jacobian matrix associated to $ f_1,
\ldots {}, f_p $. Such a system is algebraically
structured: the ideal it generates is the sum of a
determinantal ideal and the ideal generated by $ f_1,
\ldots {}, f_p $. We provide the first complexity
estimates on the computation of Gr{\"o}bner bases of
such systems defining critical points. We prove that
under genericity assumptions on $ f_1, \ldots {}, f_p
$, the complexity is polynomial in the generic number
of critical points, i.e. $ D^p(D - 1)^{n - p} (n - 1 /
p - 1) $. More particularly, in the quadratic case $ D
= 2 $, the complexity of such a Gr{\"o}bner basis
computation is polynomial in the number of variables
$n$ and exponential in $p$. We also give experimental
evidence supporting these theoretical results.",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2012:SPS,
author = "Jean-Charles Faug{\`e}re and Jules Svartz",
title = "Solving polynomial systems globally invariant under an
action of the symmetric group and application to the
equilibria of {$N$} vortices in the plane",
crossref = "vanderHoeven:2012:IPI",
pages = "170--178",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442856",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We propose an efficient algorithm to solve polynomial
systems of which equations are globally invariant under
an action of the symmetric group G$_N$ acting on the
variable x$_i$ with \sigma (x$_i$) = x$_{ \sigma
(i)}$ and the number of variables is a multiple of N.
For instance, we can assume that swapping two variables
(or two pairs of variables) in one equation gives rise
to another equation of the system (perhaps changing the
sign). The idea is to apply many times divided
difference operators to the original system in order to
obtain a new system of equations involving only the
symmetric functions of a subset of the variables. The
next step is to solve the system using Gr{\"o}bner
techniques; this is usually several order faster than
computing the Gr{\"o}bner basis of the original system
since the number of solutions of the corresponding
ideal, which is always finite has been divided by at
least N!. To illustrate the algorithm and to
demonstrate its efficiency, we apply the method to a
well known physical problem called equilibria positions
of vortices. This problem has been studied for almost
150 years and goes back to works by von Helmholtz and
Lord Kelvin. Assuming that all vortices have same
vorticity, the problem can be reformulated as a system
of polynomial equations invariant under an action of
G$_N$. Using numerical methods, physicists have been
able to compute solutions up to N \leq 7 but it was an
open challenge to check whether the set of solution is
complete. Direct naive approach of Gr{\"o}bner bases
techniques give rise to hard-to-solve polynomial
system: for instance, when N = 5, it takes several days
to compute the Gr{\"o}bner basis and the number of
solutions is 2060. By contrast, applying the new
algorithm to the same problem gives rise to a system of
17 solutions that can be solved in less than 0.1 sec.
Moreover, we are able to compute all equilibria when N
\leq 7.",
acknowledgement = ack-nhfb,
}
@InProceedings{Garcia:2012:RIA,
author = "Maria Emilia Alonso Garcia and Andr{\'e} Galligo",
title = "A root isolation algorithm for sparse univariate
polynomials",
crossref = "vanderHoeven:2012:IPI",
pages = "35--42",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442839",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "We consider a univariate polynomial f with real
coefficients having a high degree $N$ but a rather
small number $ d + 1 $ of monomials, with $ d \ll N $.
Such a sparse polynomial has a number of real root
smaller or equal to $d$. Our target is to find for each
real root of $f$ an interval isolating this root from
the others. The usual subdivision methods, relying
either on Sturm sequences or M{\"o}bius transform
followed by Descartes' rule of sign, destruct the
sparse structure. Our approach relies on the
generalized Budan--Fourier theorem of Coste, Lajous,
Lombardi, Roy [8] and the techniques developed in
Galligo [12]. To such a $f$ is associated a set of $ d
+ 1 $ $F$-derivatives. The Budan=-Fourier function $
V_f(x) $ counts the sign changes in the sequence of
$F$-derivatives of the $f$ evaluated at $x$. The values
at which this function jumps are called the $F$-virtual
roots of $f$, these include the real roots of $f$. We
also consider the augmented $F$-virtual roots of $f$
and introduce a genericity property which eases our
study. We present a real root isolation method and an
algorithm which has been implemented in Maple. We rely
on an improved generalized Budan--Fourier count applied
to both the input polynomial and its reciprocal,
together with Newton like approximation steps. The
paper is illustrated with examples and pictures.",
acknowledgement = ack-nhfb,
}
@InProceedings{Garoufalidis:2012:TQH,
author = "Stavros Garoufalidis and Christoph Koutschan",
title = "Twisting $q$-holonomic sequences by complex roots of
unity",
crossref = "vanderHoeven:2012:IPI",
pages = "179--186",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442857",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A sequence $ f_n (q) $ is $q$-holonomic if it
satisfies a nontrivial linear recurrence with
coefficients polynomials in $q$ and $ q^n $. Our main
theorems state that $q$-holonomicity is preserved under
twisting, i.e., replacing $q$ by $ \omega q $ where $
\omega $ is a complex root of unity, and under the
substitution $ q > q^\alpha $ where $ \alpha $ is a
rational number. Our proofs are constructive, work in
the multivariate setting of \partial -finite sequences
and are implemented in the Mathematica package {\tt
HolonomicFunctions}. Our results are illustrated by
twisting natural $q$-holonomic sequences which appear
in quantum topology, namely the colored Jones
polynomial of pretzel knots and twist knots. The
recurrence of the twisted colored Jones polynomial can
be used to compute the asymptotics of the Kashaev
invariant of a knot at an arbitrary complex root of
unity.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gleixner:2012:IAL,
author = "Ambros M. Gleixner and Daniel E. Steffy and Kati
Wolter",
title = "Improving the accuracy of linear programming solvers
with iterative refinement",
crossref = "vanderHoeven:2012:IPI",
pages = "187--194",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442858",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We describe an iterative refinement procedure for
computing extended precision or exact solutions to
linear programming problems (LPs). Arbitrarily precise
solutions can be computed by solving a sequence of
closely related LPs with limited precision arithmetic.
The LPs solved share the same constraint matrix as the
original problem instance and are transformed only by
modification of the objective function, right-hand
side, and variable bounds. Exact computation is used to
compute and store the exact representation of the
transformed problems, while numeric computation is used
for solving LPs. At all steps of the algorithm the LP
bases encountered in the transformed problems
correspond directly to LP bases in the original problem
description. We demonstrate that this algorithm is
effective in practice for computing extended precision
solutions and that this leads to direct improvement of
the best known methods for solving LPs exactly over the
rational numbers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2012:CIH,
author = "Feng Guo and Erich L. Kaltofen and Lihong Zhi",
title = "Certificates of impossibility of {Hilbert--Artin}
representations of a given degree for definite
polynomials and functions",
crossref = "vanderHoeven:2012:IPI",
pages = "195--202",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442859",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We deploy numerical semidefinite programming and
conversion to exact rational inequalities to certify
that for a positive semidefinite input polynomial or
rational function, any representation as a fraction of
sums-of-squares of polynomials with real coefficients
must contain polynomials in the denominator of degree
no less than a given input lower bound. By Artin's
solution to Hilbert's 17th problems, such
representations always exist for some denominator
degree. Our certificates of infeasibility are based on
the generalization of Farkas's Lemma to semidefinite
programming. The literature has many famous examples of
impossibility of SOS representability including
Motzkin's, Robinson's, Choi's and Lam's polynomials,
and Reznick's lower degree bounds on uniform
denominators, e.g., powers of the sum-of-squares of
each variable. Our work on exact certificates for
positive semidefiniteness allows for non-uniform
denominators, which can have lower degree and are often
easier to convert to exact identities. Here we
demonstrate our algorithm by computing certificates of
impossibilities for an arbitrary sum-of-squares
denominator of degree 2 and 4 for some symmetric
sextics in 4 and 5 variables, respectively. We can also
certify impossibility of base polynomials in the
denominator of restricted term structure, for instance
as in Landau's reduction by one less variable.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hubert:2012:RIS,
author = "Evelyne Hubert and George Labahn",
title = "Rational invariants of scalings from {Hermite} normal
forms",
crossref = "vanderHoeven:2012:IPI",
pages = "219--226",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442862",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Scalings form a class of group actions that have both
theoretical and practical importance. A scaling is
accurately described by an integer matrix. Tools from
linear algebra are exploited to compute a minimal
generating set of rational invariants, trivial
rewriting and rational sections for such a group
action. The primary tools used are Hermite normal forms
and their unimodular multipliers. With the same line of
ideas, a complete solution to the scaling symmetry
reduction of a polynomial system is also presented.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ishikawa:2012:ZHA,
author = "Masao Ishikawa and Christoph Koutschan",
title = "{Zeilberger}'s holonomic ansatz for {Pfaffians}",
crossref = "vanderHoeven:2012:IPI",
pages = "227--233",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442863",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A variation of Zeilberger's holonomic ansatz for
symbolic determinant evaluations is proposed which is
tailored to deal with Pfaffians. The method is also
applicable to determinants of skew-symmetric matrices,
for which the original approach does not work. As
Zeilberger's approach is based on the Laplace expansion
(cofactor expansion) of the determinant, we derive our
approach from the cofactor expansion of the Pfaffian.
To demonstrate the power of our method, we prove, using
computer algebra algorithms, some conjectures proposed
in the paper ``Pfaffian decomposition and a Pfaffian
analogue of q -Catalan Hankel determinants'' by
Ishikawa, Tagawa, and Zeng. A minor summation formula
related to partitions and Motzkin paths follows as a
corollary.",
acknowledgement = ack-nhfb,
}
@InProceedings{Koiran:2012:UBR,
author = "Pascal Koiran",
title = "Upper bounds on real roots and lower bounds for the
permanent",
crossref = "vanderHoeven:2012:IPI",
pages = "8--8",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442833",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lebreton:2012:AUD,
author = "Romain Lebreton and {\'E}ric Schost",
title = "Algorithms for the universal decomposition algebra",
crossref = "vanderHoeven:2012:IPI",
pages = "234--241",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442864",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $k$ be a field and let $ f \in k [T] $ be a
polynomial of degree $n$. The universal decomposition
algebra $A$ is the quotient of $ k[X_1, \ldots {}, X_n]
$ by the ideal of symmetric relations (those
polynomials that vanish on all permutations of the
roots of $f$). We show how to obtain efficient
algorithms to compute in $A$. We use a univariate
representation of $A$, i.e. an isomorphism of the form
$ A k [T] / Q (T) $, since in this representation,
arithmetic operations in $A$ are known to be
quasi-optimal. We give details for two related
algorithms, to find the isomorphism above, and to
compute the characteristic polynomial of any element of
$A$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lella:2012:EIA,
author = "Paolo Lella",
title = "An efficient implementation of the algorithm computing
the {Borel}-fixed points of a {Hilbert} scheme",
crossref = "vanderHoeven:2012:IPI",
pages = "242--248",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442865",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Borel-fixed ideals play a key role in the study of
Hilbert schemes. Indeed each component and each
intersection of components of a Hilbert scheme contains
at least one Borel-fixed point, i.e. a point
corresponding to a subscheme defined by a Borel-fixed
ideal. Moreover Borel-fixed ideals have good
combinatorial properties, which make them very
interesting in an algorithmic perspective. In this
paper, we propose an implementation of the algorithm
computing all the saturated Borel-fixed ideals with
number of variables and Hilbert polynomial assigned,
introduced from a theoretical point of view in the
paper ``Segment ideals and Hilbert schemes of points'',
Discrete Mathematics 311 (2011).",
acknowledgement = ack-nhfb,
}
@InProceedings{Levandovskyy:2012:ECA,
author = "Viktor Levandovskyy",
title = "Elements of computer-algebraic analysis",
crossref = "vanderHoeven:2012:IPI",
pages = "9--10",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442834",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algebraic Analysis has been coined as a term in the
mid 50's by the Japanese group led by Mikio Sato. In
recent years many constructions of Algebraic Analysis
have been approached from a computer-algebraic point of
view, with algorithms and their implementations.
Extension of such an interaction from linear
differential operators to linear difference, q
-difference, q -differential and other linear operators
we call Computer-Algebraic Analysis. The major object
of study are systems of linear functional equations,
their properties, solutions (including those in terms
of generalized functions) and behaviour.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ma:2012:CRS,
author = "Yue Ma and Lihong Zhi",
title = "Computing real solutions of polynomial systems via
low-rank moment matrix completion",
crossref = "vanderHoeven:2012:IPI",
pages = "249--256",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442866",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we propose a new algorithm for
computing real roots of polynomial equations or a
subset of real roots in a given semi-algebraic set
described by additional polynomial inequalities. The
algorithm is based on using modified fixed point
continuation method for solving Lasserre's hierarchy of
moment relaxations. We establish convergence properties
for our algorithm. For a large-scale polynomial system
with only few real solutions in a given area, we can
extract them quickly. Moreover, for a polynomial system
with an infinite number of real solutions, our
algorithm can also be used to find some isolated real
solutions or real solutions on the manifolds.",
acknowledgement = ack-nhfb,
}
@InProceedings{McCarron:2012:SHQ,
author = "James McCarron",
title = "Small homogeneous quandles",
crossref = "vanderHoeven:2012:IPI",
pages = "257--264",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442867",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We derive an algorithm for computing all the
homogeneous quandles of a given order n provided that a
list of the transitive permutation groups of degree n
are known. We discuss the implementation of the
algorithm, and use it to enumerate the number of
isomorphism classes of homogeneous quandles up to order
23 and compute representatives for each class. We also
completely determine the homogeneous quandles of prime
order. As a by-product, we are able to confirm an
independent calculation of the connected quandles of
order at most 30 by Vendramin and, based on this, to
compute the number of isomorphism classes of simple
quandles to the same order.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mourrain:2012:BBR,
author = "Bernard Mourrain and Philippe Tr{\'e}buchet",
title = "Border basis representation of a general quotient
algebra",
crossref = "vanderHoeven:2012:IPI",
pages = "265--272",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442868",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we generalized the construction of
border bases to non-zero dimensional ideals for normal
forms compatible with the degree, tackling the
remaining obstacle for a general application of border
basis methods. First, we give conditions to have a
border basis up to a given degree. Next, we describe a
new stopping criteria to determine when the reduction
with respect to the leading terms is a normal form.
This test based on the persistence and regularity
theorems of Gotzmann yields a new algorithm for
computing a border basis of any ideal, which proceeds
incrementally degree by degree until its regularity. We
detail it, prove its correctness, present its
implementation and report some experimentations which
illustrate its practical good behavior.",
acknowledgement = ack-nhfb,
}
@InProceedings{Oaku:2012:ACD,
author = "Toshinori Oaku",
title = "An algorithm to compute the differential equations for
the logarithm of a polynomial",
crossref = "vanderHoeven:2012:IPI",
pages = "273--280",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442869",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present an algorithm to compute the annihilator of
(i.e., the linear differential equations for) the
multi-valued analytic function $ f^\lambda (\log f)^m $
in the Weyl algebra $ D_n $ for a given non-constant
polynomial $f$, a non-negative integer $m$, and a
complex number $ \lambda $. This algorithm essentially
consists of the differentiation with respect to $s$ of
the annihilator of $ f^s $ in the ring $ D_n[s] $ and
ideal quotient computation in $ D_n $. The obtained
differential equations constitute what is called a
holonomic system in $D$-module theory. Hence combined
with the integration algorithm for $D$-modules, this
enables us to compute a holonomic system for the
integral of a function involving the logarithm of a
polynomial with respect to some variables.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pauderis:2012:DUC,
author = "Colton Pauderis and Arne Storjohann",
title = "Deterministic unimodularity certification",
crossref = "vanderHoeven:2012:IPI",
pages = "281--288",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442870",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The asymptotically fastest algorithms for many linear
algebra problems on integer matrices, including solving
a system of linear equations and computing the
determinant, use high-order lifting. Currently,
high-order lifting requires the use of a randomized
shifted number system to detect and avoid
error-producing carries. By interleaving quadratic and
linear lifting, we devise a new algorithm for
high-order lifting that allows us to work in the usual
symmetric range modulo p, thus avoiding randomization.
As an application, we give a deterministic algorithm to
assay if an n x n integer matrix A is unimodular. The
cost of the algorithm is O ((\log n) n$^{ \omega }$
M(\log n + \log|| A ||)) bit operations, where || A ||
denotes the largest entry in absolute value, and M(t)
is the cost of multiplying two integers bounded in bit
length by t.",
acknowledgement = ack-nhfb,
}
@InProceedings{Romero:2012:PBT,
author = "Ana Romero and Francis Sergeraert",
title = "Programming before theorizing, a case study",
crossref = "vanderHoeven:2012:IPI",
pages = "289--296",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442871",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper relates how a ``simple'' result in
combinatorial homotopy eventually led to a totally new
understanding of basic theorems in Algebraic Topology,
namely the Eilenberg--Zilber theorem, the twisted
Eilenberg--Zilber theorem, and finally the
Eilenberg-MacLane correspondance between the
Classifying Space and Bar constructions. In the last
case, it was an amazing lucky consequence of
computations based on conjectures not yet proved. The
key new tool used in this context is Robin Forman's
Discrete Vector Fields theory.",
acknowledgement = ack-nhfb,
}
@InProceedings{Roune:2012:PGB,
author = "Bjarke Hammersholt Roune and Michael Stillman",
title = "Practical {Gr{\"o}bner} basis computation",
crossref = "vanderHoeven:2012:IPI",
pages = "203--210",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442860",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We report on our experiences exploring state of the
art Gr{\"o}bner basis computation. We investigate
signature based algorithms in detail. We also introduce
new practical data structures and computational
techniques for use in both signature based Gr{\"o}bner
basis algorithms and more traditional variations of the
classic Buchberger algorithm. Our conclusions are based
on experiments using our new freely available open
source standalone C++ library.",
acknowledgement = ack-nhfb,
}
@InProceedings{Roy:2012:CDC,
author = "Marie-Fran{\c{c}}oise Roy",
title = "Complexity of deciding connectivity in real algebraic
sets: recent results and future research directions",
crossref = "vanderHoeven:2012:IPI",
pages = "3--5",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442831",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The number of connected components of a real algebraic
set defined in $R^k$ by equations of degree $d$ is
$O(d)^k$ which is polynomial in the degree, and singly
exponential in the number of variables. Moreover it is
very easy to design algebraic sets defined by
polynomials of degree $2 d$ in $k$ variables with
$O(d)^k$ connected components.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sagraloff:2012:WNM,
author = "Michael Sagraloff",
title = "When {Newton} meets {Descartes}: a simple and fast
algorithm to isolate the real roots of a polynomial",
crossref = "vanderHoeven:2012:IPI",
pages = "297--304",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442872",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We introduce a novel algorithm denoted NewDsc to
isolate the real roots of a univariate square-free
polynomial f with integer coefficients. The algorithm
iteratively subdivides an initial interval which is
known to contain all real roots of f and performs exact
(rational) operations on the coefficients of f in each
step. For the subdivision strategy, we combine
Descartes' Rule of Signs and Newton iteration. More
precisely, instead of using a fixed subdivision
strategy such as bisection in each iteration, a Newton
step based on the number of sign variations for an
actual interval is considered, and, only if the Newton
step fails, we fall back to bisection. Following this
approach, quadratic convergence towards the real roots
is achieved in most iterations. In terms of complexity,
our method induces a recursion tree of almost optimal
size $ O (n \cdot \log (n \tau)) $, where $n$ denotes
the degree of the polynomial and \tau the bitsize of
its coefficients. The latter bound constitutes an
improvement by a factor of \tau upon all existing
subdivision methods for the task of isolating the real
roots. We further provide a detailed complexity
analysis which shows that NewDsc needs only $ {\tilde
O}(n^3 \tau) $ bit operations to isolate all real roots
of f. In comparison to existing asymptotically fast
numerical algorithms (e.g. the algorithms by V. Pan and
A. Sch{\"o}nhage), NewDsc is much easier to access and,
due to its similarities to the classical Descartes
method, it seems to be well suited for an efficient
implementation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Scheiblechner:2012:ERC,
author = "Peter Scheiblechner",
title = "Effective {de Rham} cohomology: the hypersurface
case",
crossref = "vanderHoeven:2012:IPI",
pages = "305--310",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442873",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We prove an effective bound for the degrees of
generators of the algebraic de Rham cohomology of
smooth affine hypersurfaces. In particular, we show
that the de Rham cohomology $ H^p_{dR}(X) $ of a smooth
hypersurface $X$ of degree $d$ in $ C^n $ can be
generated by differential forms of degree $ d^{O(pn)}
$. This result is relevant for the algorithmic
computation of the cohomology, but is also motivated by
questions in the theory of ordinary differential
equations related to the infinitesimal Hilbert 16th
problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Seress:2012:CCR,
author = "{\'A}kos Seress",
title = "Construction of $2$-closed {$M$}-representations",
crossref = "vanderHoeven:2012:IPI",
pages = "311--318",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442874",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The sporadic simple group Monster, denoted by M, acts
on the Griess algebra, which is a real vector space of
dimension 196,884, equipped with a positive definite
scalar product and a bilinear, commutative, and
non-associative algebra product. Certain properties of
this linear representation of M, together with
properties (discovered by Conway and Miyamoto) of
idempotents in the Griess algebra that correspond to 2A
involutions in M, have been defined by Ivanov as the
M-representation of the Monster. This definition
enables us to talk about M-representations of arbitrary
groups G that are generated by involutions. In general,
an M-representation may or may not exist, but if G is
isomorphic to a subgroup of the Monster and a
representation is isomorphic to the corresponding
subalgebra of the Griess algebra then we say that the
M-representation is based on an embedding of G in the
Monster. In this paper, we describe a generic
theoretical procedure to construct M-representations,
and a GAP computer program that implements the
procedure. It turns out that in many cases the
representations are based on embeddings in the Monster,
thereby providing a valuable tool of studying
subalgebras of the Griess algebra that were
unaccessible in the 196,884-dimensional setting.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sharma:2012:NOT,
author = "Vikram Sharma and Chee K. Yap",
title = "Near optimal tree size bounds on a simple real root
isolation algorithm",
crossref = "vanderHoeven:2012:IPI",
pages = "319--326",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442875",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The problem of isolating all real roots of a
square-free integer polynomial $ f(X) $ inside any
given interval $ I_0 $ is a fundamental problem. EVAL
is a simple and practical exact numerical algorithm for
this problem: it recursively bisects $ I_0 $, and any
sub-interval $ I \subseteq I_0 $, until a certain
numerical predicate $ C_0 (I) V C_1 (I) $ holds on each
$I$. We prove that the size of the recursion tree is $
O(d (L + r + \log d)) $ where $f$ has degree $d$, its
coefficients have absolute values $ < 2^L $, and $ I_0
$ contains $r$ roots of $f$. In the range $ L \geq d $,
our bound is the sharpest known, and provably optimal.
Our results are closely paralleled by recent bounds on
EVAL by Sagraloff--Yap (ISSAC 2011) and Burr--Krahmer
(2012). In the range $ L \leq d $, our bound is
incomparable with those of Sagraloff--Yap or
Burr--Krahmer. Similar to the Burr--Krahmer proof, we
exploit the technique of ``continuous amortization''
from Burr--Krahmer--Yap (2009), namely to bound the
tree size by an integral $ \int_I O G(x) \, d x $ over
a suitable ``charging function'' $ G(x) $. We give an
application of this feature to the problem of
ray-shooting (i.e., finding smallest root in a given
interval).",
acknowledgement = ack-nhfb,
}
@InProceedings{Slavici:2012:EPM,
author = "Vlad Slavici and Daniel Kunkle and Gene Cooperman and
Stephen Linton",
title = "An efficient programming model for memory-intensive
recursive algorithms using parallel disks",
crossref = "vanderHoeven:2012:IPI",
pages = "327--334",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442876",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In order to keep up with the demand for solutions to
problems with ever-increasing data sets, both academia
and industry have embraced commodity computer clusters
with locally attached disks or SANs as an inexpensive
alternative to supercomputers. With the advent of tools
for parallel disks programming, such as MapReduce,
STXXL and Roomy --- that allow the developer to focus
on higher-level algorithms --- the programmer
productivity for memory-intensive programs has
increased many-fold. However, such parallel tools were
primarily targeted at iterative programs. We propose a
programming model for migrating recursive RAM-based
legacy algorithms to parallel disks. Many
memory-intensive symbolic algebra algorithms are most
easily expressed as recursive algorithms. In this case,
the programming challenge is multiplied, since the
developer must re-structure such an algorithm with two
criteria in mind: converting a naturally recursive
algorithm into an iterative algorithm, while
simultaneously exposing any potential data parallelism
(as needed for parallel disks). This model alleviates
the large effort going into the design phase of an
external memory algorithm. Research in this area over
the past 10 years has focused on per-problem solutions,
without providing much insight into the connection
between legacy algorithms and out-of-core algorithms.
Our method shows how legacy algorithms employing
recursion and non-streaming memory access can be more
easily translated into efficient parallel disk-based
algorithms. We demonstrate the ideas on a largest
computation of its kind: the determinization via subset
construction and minimization of very large
nondeterministic finite set automata (NFA). To our
knowledge, this is the largest subset construction
reported in the literature. Determinization for large
NFA has long been a large computational hurdle in the
study of permutation classes defined by token passing
networks. The programming model was used to design and
implement an efficient NFA determinization algorithm
that solves the next stage in analyzing token passing
networks representing two stacks in series.",
acknowledgement = ack-nhfb,
}
@InProceedings{Strassen:2012:ASM,
author = "Volker Strassen",
title = "Asymptotic spectrum and matrix multiplication",
crossref = "vanderHoeven:2012:IPI",
pages = "6--7",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442832",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The minimal number of arithmetic operations sufficient
to multiply matrices of order m by an algebraic circuit
has the form m$^{\omega + o(1)}$, where o(1) goes to
zero when m tends to infinity. \omega is called the
exponent of matrix multiplication. Asymptotically, it
controls the complexity of almost all significant
computational tasks of linear algebra. The desire to
determine \omega has been the main motivation for
investigating the complexity of bilinear maps in
general.",
acknowledgement = ack-nhfb,
}
@InProceedings{Strzebonski:2012:SPS,
author = "Adam Strzebo{\'n}ski",
title = "Solving polynomial systems over semialgebraic sets
represented by cylindrical algebraic formulas",
crossref = "vanderHoeven:2012:IPI",
pages = "335--342",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442877",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Cylindrical algebraic formulas are an explicit
representation of semialgebraic sets as finite unions
of cylindrically arranged disjoint cells bounded by
graphs of algebraic functions. We present a version of
the Cylindrical Algebraic Decomposition (CAD) algorithm
customized for solving systems of polynomial equations
and inequalities over semialgebraic sets given in this
representation. The algorithm can also be used to solve
conjunctions of polynomial conditions in an incremental
manner. We show application examples and give an
empirical comparison of incremental and direct CAD
computation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Strzebonski:2012:URR,
author = "Adam Strzebo{\'n}ski and Elias P. Tsigaridas",
title = "Univariate real root isolation in multiple extension
fields",
crossref = "vanderHoeven:2012:IPI",
pages = "343--350",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442878",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
abstract = "We present algorithmic, complexity and implementation
results for the problem of isolating the real roots of
a univariate polynomial in $ B_\alpha \in L [y] $,
where $ L = Q(\alpha_1, \ldots {}, \alpha_l) $ is an
algebraic extension of the rational numbers. Our bounds
are single exponential in $l$ and match the ones
presented in [34] for the case $ l = 1 $. We consider
two approaches. The first, indirect approach, using
multivariate resultants, computes a univariate
polynomial with integer coefficients, among the real
roots of which are the real roots of $ B_\alpha $. The
Boolean complexity of this approach is $ O_B(N^{4 l +
4}) $, where $N$ is the maximum of the degrees and the
coefficient bitsize of the involved polynomials. The
second, direct approach, tries to solve the polynomial
directly, without reducing the problem to a univariate
one. We present an algorithm that generalizes Sturm
algorithm from the univariate case, and modified
versions of well known solvers that are either
numerical or based on Descartes' rule of sign. We
achieve a Boolean complexity of $ O_B $ [equation],
respectively. We implemented the algorithms in C as
part of the core library of Mathematica and we
illustrate their efficiency over various data sets.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sullivant:2012:AS,
author = "Seth Sullivant",
title = "Algebraic statistics",
crossref = "vanderHoeven:2012:IPI",
pages = "11--11",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442835",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algebraic statistics advocates polynomial algebra as a
tool for addressing problems in statistics and its
applications. This connection is based on the fact that
most statistical models are defined either
parametrically or implicitly via polynomial equations.
The idea is summarized by the phrase ``Statistical
models are semialgebraic sets''. My tutorial will
consist of a detailed study of two examples where the
algebra/statistics connection has proven especially
useful: in the study of phylogenetic models and in the
analysis of contingency tables.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sun:2012:SBA,
author = "Yao Sun and Dingkang Wang and Xiaodong Ma and Yang
Zhang",
title = "A signature-based algorithm for computing
{Gr{\"o}bner} bases in solvable polynomial algebras",
crossref = "vanderHoeven:2012:IPI",
pages = "351--358",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442879",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Signature-based algorithms, including F5, F5C, G2V and
GVW, are efficient algorithms for computing Gr{\"o}bner
bases in commutative polynomial rings. In this paper,
we present a signature-based algorithm to compute
Gr{\"o}bner bases in solvable polynomial algebras which
include usual commutative polynomial rings and some
non-commutative polynomial rings like Weyl algebra. The
generalized Rewritten Criterion (discussed in Sun and
Wang, ISSAC 2011) is used to reject redundant
computations. When this new algorithm uses the partial
order implied by GVW, its termination is proved without
special assumptions on computing orders of critical
pairs. Data structures similar to F5 can be used to
speed up this new algorithm, and Gr{\"o}bner bases of
syzygy modules of input polynomials can be obtained
from the outputs easily. Experimental data show that
most redundant computations can be avoided in this new
algorithm.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderHoeven:2012:CMB,
author = "Joris van der Hoeven and Gr{\'e}goire Lecerf",
title = "On the complexity of multivariate blockwise polynomial
multiplication",
crossref = "vanderHoeven:2012:IPI",
pages = "211--218",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442861",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this article, we study the problem of multiplying
two multivariate polynomials which are somewhat but not
too sparse, typically like polynomials with convex
supports. We design and analyze an algorithm which is
based on blockwise decomposition of the input
polynomials, and which performs the actual
multiplication in an FFT model or some other more
general so called ``evaluated model''. If the input
polynomials have total degrees at most d, then, under
mild assumptions on the coefficient ring, we show that
their product can be computed with $O(s^{1.5337})$ ring
operations, where $s$ denotes the number of all the
monomials of total degree at most $2 d$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhang:2012:FDO,
author = "Mingbo Zhang and Yong Luo",
title = "Factorization of differential operators with ordinary
differential polynomial coefficients",
crossref = "vanderHoeven:2012:IPI",
pages = "359--365",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442880",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we present an algorithm to factor a
differential operator $ L = \sigma^n + c_{n - 1}
\sigma^{n - 1} + \cdot \cdot \cdot + c_1 \sigma + c_0 $
with coefficients $ c_i $ in $ C \{ y \} $, where $C$
is a constant field and $ C \{ y \} $ is the ordinary
differential polynomial ring over $C$. Also, we discuss
the applications of the algorithm in decomposing
nonlinear differential polynomials and factoring
differential operators with coefficients in the
extension field of $C$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhou:2012:CMN,
author = "Wei Zhou and George Labahn and Arne Storjohann",
title = "Computing minimal nullspace bases",
crossref = "vanderHoeven:2012:IPI",
pages = "366--373",
year = "2012",
DOI = "https://doi.org/10.1145/2442829.2442881",
bibdate = "Fri Mar 14 13:49:05 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we present a deterministic algorithm for
the computation of a minimal nullspace basis of an $ m
\times n $ input matrix of univariate polynomials over
a field $K$ with $ m \eq n $. This algorithm computes a
minimal nullspace basis of a degree $d$ input matrix
with a cost of $ O \tilde (n_\omega \lceil m d / n
\rceil) $ field operations in $K$. Here the soft-$O$
notation is Big-$O$ with $ \log $ factors removed while
$ \omega $ is the exponent of matrix multiplication.
The same algorithm also works in the more general
situation on computing a shifted minimal nullspace
basis, with a given degree shift [equation] whose
entries bound the corresponding column degrees of the
input matrix. In this case if $ \rho $ is the sum of
the $m$ largest entries of $s$, then a $s$-minimal
right nullspace basis can be computed with a cost of $
O \tilde (n^\omega \rho / m) $ field operations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Arnold:2013:NTF,
author = "Andrew Arnold",
title = "A new truncated {Fourier Transform} algorithm",
crossref = "Monagan:2013:IPI",
pages = "15--22",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465957",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Truncated Fourier Transforms (TFTs), first introduced
by van der Hoeven, refer to a family of algorithms that
attempt to smooth ``jumps'' in complexity exhibited by
FFT algorithms. We present an in-place TFT whose time
complexity, measured in terms of ring operations, is
asymptotically equivalent to existing not-in-place TFT
methods. We also describe a transformation that maps
between two families of TFT algorithms that use
different sets of evaluation points.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bach:2013:ACS,
author = "Eric Bach and Jonathan P. Sorenson",
title = "Approximately counting semismooth integers",
crossref = "Monagan:2013:IPI",
pages = "23--30",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465933",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An integer $n$ is $ (y, z) $-semismooth if $ n = p m $
where $m$ is an integer with all prime divisors $ \geq
y $ and $p$ is $1$ or a prime $ \geq z $. Large
quantities of semismooth integers are utilized in
modern integer factoring algorithms, such as the number
field sieve, that incorporate the so-called large prime
variant. Thus, it is useful for factoring practitioners
to be able to estimate the value of $ \Psi (x, y, z) $,
the number of $ (y, z) $-semismooth integers up to $x$,
so that they can better set algorithm parameters and
minimize running times, which could be weeks or months
on a cluster supercomputer. In this paper, we explore
several algorithms to approximate $ \Psi (x, y, z) $
using a generalization of Buchstab's identity with
numeric integration.",
acknowledgement = ack-nhfb,
}
@InProceedings{Basson:2013:EEL,
author = "Romain Basson and Reynald Lercier and Christophe
Ritzenthaler and Jeroen Sijsling",
title = "An explicit expression of the {L{\"u}roth} invariant",
crossref = "Monagan:2013:IPI",
pages = "31--36",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465507",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this short note, we give an algorithm that returns
an explicit expression of the L{\"u}roth invariant in
terms of the Dixmier-Ohno invariants of plane quartic
curves. We also obtain an explicit factorized
expression on the locus of Ciani quartics in terms of
the coefficients. After this calculation, we extend our
methods to answer two open theoretical questions
concerning the sub-locus of singular L{\"u}roth
quartics.",
acknowledgement = ack-nhfb,
}
@InProceedings{Berthe:2013:MGP,
author = "Val{\'e}rie Berth{\'e} and Jean Creusefond and
Lo{\"\i}ck Lhote and Brigitte Vall{\'e}e",
title = "Multiple {GCDs}. {Probabilistic} analysis of the plain
algorithm",
crossref = "Monagan:2013:IPI",
pages = "37--44",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465512",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper provides a probabilistic analysis of an
algorithm which computes the gcd of l inputs (with l
\geq 2), with a succession of l --- 1 phases, each of
them being the Euclid algorithm on two entries. This
algorithm is both basic and natural, and two kinds of
inputs are studied: polynomials over the finite field
F$_q$ and integers. The analysis exhibits the precise
probabilistic behaviour of the main parameters, namely
the number of iterations in each phase and the
evolution of the length of the current gcd along the
execution. We first provide an average-case analysis.
Then we make it even more precise by a distributional
analysis. Our results rigorously exhibit two phenomena:
(i) there is a strong difference between the first
phase, where most of the computations are done and the
remaining phases; (ii) there is a strong similarity
between the polynomial and integer cases, as can be
expected.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bessonov:2013:ICP,
author = "Mariya Bessonov and Alexey Ovchinnikov and Maxwell
Shapiro",
title = "Integrability conditions for parameterized linear
difference equations",
crossref = "Monagan:2013:IPI",
pages = "45--52",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465942",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study integrability conditions for systems of
parameterized linear difference equations and related
properties of linear differential algebraic groups. We
show that isomonodromicity of such a system is
equivalent to isomonodromicity with respect to each
parameter separately under a linearly differentially
closed assumption on the field of differential
parameters. Due to our result, it is no longer
necessary to solve non-linear differential equations to
verify isomonodromicity, which will improve efficiency
of computation with these systems. Moreover, it is not
possible to further strengthen this result by removing
the requirement on the parameters, as we show by giving
a counterexample. We also discuss the relation between
isomonodromicity and the properties of the associated
parameterized difference Galois group.",
acknowledgement = ack-nhfb,
}
@InProceedings{Betten:2013:RCC,
author = "Anton Betten",
title = "Rainbow cliques and the classification of small
{BLT-sets}",
crossref = "Monagan:2013:IPI",
pages = "53--60",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465508",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In Finite Geometry, a class of objects known as
BLT-sets play an important role. They are points on the
Q (4, q) quadric satisfying a condition on triples.
This paper is a contribution to the difficult problem
of classifying these sets up to isomorphism, i.e., up
to the action of the automorphism group of the quadric.
We reduce the classification problem of these sets to
the problem of classifying rainbow cliques in graphs.
This allows us to classify BLT-sets for all orders q in
the range 31 to 67.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bi:2013:SLR,
author = "Jingguo Bi and Qi Cheng and J. Maurice Rojas",
title = "Sub-linear root detection, and new hardness results,
for sparse polynomials over finite fields",
crossref = "Monagan:2013:IPI",
pages = "61--68",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465514",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a deterministic $ 2^{O(t)} q^{t - 2 / t - 1
+ o (1)} $ algorithm to decide whether a univariate
polynomial $f$, with exactly $t$ monomial terms and
degree $ < q $, has a root in $ F_q $. Our method is
the first with complexity sub-linear in $q$ when $t$ is
fixed. We also prove a structural property for the
nonzero roots in $ F_q $ of any $t$-nomial: the nonzero
roots always admit a partition into no more than $ 2
\sqrt t - 1 (q - 1)^{t - 2 / t - 1} $ cosets of two
subgroups $ S_1 \subseteq S_2 $ of $ F*_q $. This can
be thought of as a finite field analogue of Descartes'
Rule. A corollary of our results is the first
deterministic sub-linear algorithm for detecting common
degree one factors of $k$-tuples of $t$-nomials in $
F_q[x] $ when $k$ and $t$ are fixed. When $t$ is not
fixed we show that, for $p$ prime, detecting roots in $
F_p $ for $f$ is NP-hard with respect to
BPP-reductions. Finally, we prove that if the
complexity of root detection is sub-linear (in a
refined sense), relative to the straight-line program
encoding, then $ {\rm NEXP} \subseteq P / {\em poly}
$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Boady:2013:TRS,
author = "Mark Boady and Pavel Grinfeld and Jeremy Johnson",
title = "A term rewriting system for the calculus of moving
surfaces",
crossref = "Monagan:2013:IPI",
pages = "69--76",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2466576",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The calculus of moving surfaces (CMS) is an analytic
framework that extends the tensor calculus to deforming
manifolds. We have applied the CMS to a number of
boundary variation problems using a Term Rewrite System
(TRS). The TRS is used to convert the initial CMS
expression into a form that can be evaluated. The CMS
produces expressions that are true for all coordinate
spaces. This makes it very powerful but applications
remain limited by a rapid growth in the size of
expressions. We have extended results on existing
problems to orders that had been previously
intractable. In this paper, we describe our TRS and our
method for evaluating CMS expressions on a specific
coordinate system. Our work has already provided new
insight into problems of current interest to
researchers in the CMS.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2013:CET,
author = "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and {\'E}lie
de Panafieu",
title = "Complexity estimates for two uncoupling algorithms",
crossref = "Monagan:2013:IPI",
pages = "85--92",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465941",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Uncoupling algorithms transform a linear differential
system of first order into one or several scalar
differential equations. We examine two approaches to
uncoupling: the cyclic-vector method (CVM) and the
Danilevski-Barkatou-Z{\"u}rcher algorithm (DBZ). We
give tight size bounds on the scalar equations produced
by CVM, and design a fast variant of CVM whose
complexity is quasi-optimal with respect to the output
size. We exhibit a strong structural link between CVM
and DBZ enabling to show that, in the generic case, DBZ
has polynomial complexity and that it produces a single
equation, strongly related to the output of CVM. We
prove that algorithm CVM is faster than DBZ by almost
two orders of magnitude, and provide experimental
results that validate the theoretical complexity
analyses.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2013:CTR,
author = "Alin Bostan and Pierre Lairez and Bruno Salvy",
title = "Creative telescoping for rational functions using the
{Griffiths--Dwork} method",
crossref = "Monagan:2013:IPI",
pages = "93--100",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465935",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Creative telescoping algorithms compute linear
differential equations satisfied by multiple integrals
with parameters. We describe a precise and elementary
algorithmic version of the Griffiths--Dwork method for
the creative telescoping of rational functions. This
leads to bounds on the order and degree of the
coefficients of the differential equation, and to the
first complexity result which is single exponential in
the number of variables. One of the important features
of the algorithm is that it does not need to compute
certificates. The approach is vindicated by a prototype
implementation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bostan:2013:HRC,
author = "Alin Bostan and Shaoshi Chen and Fr{\'e}d{\'e}ric
Chyzak and Ziming Li and Guoce Xin",
title = "{Hermite} reduction and creative telescoping for
hyperexponential functions",
crossref = "Monagan:2013:IPI",
pages = "77--84",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465946",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a new reduction algorithm that
simultaneously extends Hermite's reduction for rational
functions and the Hermite-like reduction for
hyperexponential functions. It yields a unique additive
decomposition that allows to decide hyperexponential
integrability. Based on this reduction algorithm, we
design a new algorithm to compute minimal telescopers
for bivariate hyperexponential functions. One of its
main features is that it can avoid the costly
computation of certificates. Its implementation
outperforms Maple's function DEtools[Zeilberger]. We
also derive an order bound on minimal telescopers that
is tighter than the known ones.",
acknowledgement = ack-nhfb,
}
@InProceedings{Boulier:2013:IDF,
author = "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire and
Georg Regensburger and Markus Rosenkranz",
title = "On the integration of differential fractions",
crossref = "Monagan:2013:IPI",
pages = "101--108",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465934",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we provide a differential algebra
algorithm for integrating fractions of differential
polynomials. It is not restricted to differential
fractions that are the derivatives of other
differential fractions. The algorithm leads to new
techniques for representing differential fractions,
which may help converting differential equations to
integral equations (as for example used in parameter
estimation).",
acknowledgement = ack-nhfb,
}
@InProceedings{Bouzidi:2013:RUR,
author = "Yacine Bouzidi and Sylvain Lazard and Marc Pouget and
Fabrice Rouillier",
title = "Rational univariate representations of bivariate
systems and applications",
crossref = "Monagan:2013:IPI",
pages = "109--116",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465519",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We address the problem of solving systems of two
bivariate polynomials of total degree at most d with
integer coefficients of maximum bitsize \tau We suppose
known a linear separating form (that is a linear
combination of the variables that takes different
values at distinct solutions of the system) and focus
on the computation of a Rational Univariate
Representation (RUR). We present an algorithm for
computing a RUR with worst-case bit complexity in $
{\tilde O}_B (d^7 + d^6 \tau) $ and bound the bitsize
of its coefficients by $ {\tilde O}(d^2 + d \tau) $
(where $ {\tilde O}_B $ refers to bit complexities and
$ {\tilde O} $ to complexities where polylogarithmic
factors are omitted). We show in addition that
isolating boxes of the solutions of the system can be
computed from the RUR with $ {\tilde O}_B (d^8 + d^7
\tau) $ bit operations. Finally, we show how a RUR can
be used to evaluate the sign of a bivariate polynomial
(of degree at most $d$ and bitsize at most $ \tau $)
at one real solution of the system in $ {\tilde O}_B
(d^8 + d^7 \tau) $ bit operations and at all the $
\Theta (d^2) $ solutions in only $ O(d) $ times that
for one solution.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bouzidi:2013:SLF,
author = "Yacine Bouzidi and Sylvain Lazard and Marc Pouget and
Fabrice Rouillier",
title = "Separating linear forms for bivariate systems",
crossref = "Monagan:2013:IPI",
pages = "117--124",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465518",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present an algorithm for computing a separating
linear form of a system of bivariate polynomials with
integer coefficients, that is a linear combination of
the variables that takes different values when
evaluated at distinct (complex) solutions of the
system. In other words, a separating linear form
defines a shear of the coordinate system that sends the
algebraic system in generic position, in the sense that
no two distinct solutions are vertically aligned. The
computation of such linear forms is at the core of most
algorithms that solve algebraic systems by computing
rational parameterizations of the solutions and,
moreover, the computation of a separating linear form
is the bottleneck of these algorithms, in terms of
worst-case bit complexity. Given two bivariate
polynomials of total degree at most $d$ with integer
coefficients of bitsize at most $ \tau $, our algorithm
computes a separating linear form in $ {\tilde O}_B (d^8
+ d^7 \tau + d^5 \tau^2) $ bit operations in the worst
case, where the previously known best bit complexity
for this problem was $ {\tilde O}_B (d^{10} + d^9 \tau)
$ (where $ {\tilde O} $ refers to the complexity where
polylogarithmic factors are omitted and $ {\tilde O}_B
$ refers to the bit complexity)",
acknowledgement = ack-nhfb,
}
@InProceedings{Bradford:2013:CAD,
author = "Russell Bradford and James H. Davenport and Matthew
England and Scott McCallum and David Wilson",
title = "Cylindrical algebraic decompositions for boolean
combinations",
crossref = "Monagan:2013:IPI",
pages = "125--132",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465516",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "This article makes the key observation that when using
cylindrical algebraic decomposition (CAD) to solve a
problem with respect to a set of polynomials, it is not
always the signs of those polynomials that are of
paramount importance but rather the truth values of
certain quantifier free formulae involving them. This
motivates our definition of a Truth Table Invariant CAD
(TTICAD). We generalise the theory of equational
constraints to design an algorithm which will
efficiently construct a TTICAD for a wide class of
problems, producing stronger results than when using
equational constraints alone. The algorithm is
implemented fully in Maple and we present promising
results from experimentation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brown:2013:CSO,
author = "Christopher W. Brown",
title = "Constructing a single open cell in a cylindrical
algebraic decomposition",
crossref = "Monagan:2013:IPI",
pages = "133--140",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465952",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper presents an algorithm that, roughly
speaking, constructs a single open cell from a
cylindrical algebraic decomposition (CAD). The
algorithm takes as input a point and a set of
polynomials, and computes a description of an open
cylindrical cell containing the point in which the
input polynomials have constant non-zero sign, provided
the point is sufficiently generic. The paper reports on
a few example computations carried out by a test
implementation of the algorithm, which demonstrate the
functioning of the algorithm and illustrate the sense
in which it is more efficient than following the usual
``open CAD'' approach. Interest in the problem of
computing a single cell from a CAD is motivated by a
2012 paper of Jovanovic and de Moura that require
solving this problem repeatedly as a key step in NLSAT
system. However, the example computations raise the
possibility that repeated application of the new method
may in fact be more efficient than the usual open CAD
approach, both in time and space, for a broad range of
problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chattopadhyay:2013:FBL,
author = "Arkadev Chattopadhyay and Bruno Grenet and Pascal
Koiran and Natacha Portier and Yann Strozecki",
title = "Factoring bivariate lacunary polynomials without
heights",
crossref = "Monagan:2013:IPI",
pages = "141--148",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465932",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present an algorithm which computes the multilinear
factors of bivariate lacunary polynomials. It is based
on a new Gap theorem which allows to test whether $
P(X) = \Sigma^k_{j = 1} \alpha_j X^{\alpha j}(1 + X)^{
= beta j} $ is identically zero in polynomial time. The
algorithm we obtain is more elementary than the one by
Kaltofen and Koiran (ISSAC'05) since it relies on the
valuation of polynomials of the previous form instead
of the height of the coefficients. As a result, it can
be used to find some linear factors of bivariate
lacunary polynomials over a field of large finite
characteristic in probabilistic polynomial time.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2013:DEO,
author = "Shaoshi Chen and Maximilian Jaroschek and Manuel
Kauers and Michael F. Singer",
title = "Desingularization explains order-degree curves for ore
operators",
crossref = "Monagan:2013:IPI",
pages = "157--164",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465510",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Desingularization is the problem of finding a left
multiple of a given Ore operator in which some factor
of the leading coefficient of the original operator is
removed. An order-degree curve for a given Ore operator
is a curve in the $ (r, d) $-plane such that for all
points $ (r, d) $ above this curve, there exists a left
multiple of order $r$ and degree $d$ of the given
operator. We give a new proof of a desingularization
result by Abramov and van Hoeij for the shift case, and
show how desingularization implies order-degree curves
which are extremely accurate in examples.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2013:NVH,
author = "Jingwei Chen and Damien Stehl{\'e} and Gilles
Villard",
title = "A new view on {HJLS} and {PSLQ}: sums and projections
of lattices",
crossref = "Monagan:2013:IPI",
pages = "149--156",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465936",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The HJLS and PSLQ algorithms are the de facto
standards for discovering non-trivial integer relations
between a given tuple of real numbers. In this work, we
provide a new interpretation of these algorithms, in a
more general and powerful algebraic setup: we view them
as special cases of algorithms that compute the
intersection between a lattice and a vector subspace.
Further, we extract from them the first algorithm for
manipulating finitely generated additive subgroups of a
Euclidean space, including projections of lattices and
finite sums of lattices. We adapt the analyses of HJLS
and PSLQ to derive correctness and convergence
guarantees.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cohn:2013:SES,
author = "Henry Cohn",
title = "Solving equations with size constraints for the
solutions",
crossref = "Monagan:2013:IPI",
pages = "1--2",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465927",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DeFeo:2013:FAA,
author = "Luca {De Feo} and Javad Doliskani and Eric Schost",
title = "Fast algorithms for $l$-adic towers over finite
fields",
crossref = "Monagan:2013:IPI",
pages = "165--172",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465956",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Inspired by previous work of Shoup, Lenstra-De Smit
and Couveignes-Lercier, we give fast algorithms to
compute in the first levels of the $l$-adic closure of
a finite field. In many cases, our algorithms have
quasi-linear complexity.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dickenstein:2013:CDR,
author = "Alicia Dickenstein and Ioannis Z. Emiris and Vissarion
Fisikopoulos",
title = "Combinatorics of $4$-dimensional resultant polytopes",
crossref = "Monagan:2013:IPI",
pages = "173--180",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465937",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Newton polytope of the resultant, or resultant
polytope, characterizes the resultant polynomial more
precisely than total degree. The combinatorics of
resultant polytopes are known in the Sylvester case
[Gelfand et al.90] and up to dimension 3 [Sturmfels
94]. We extend this work by studying the combinatorial
characterization of 4-dimensional resultant polytopes,
which show a greater diversity and involve
computational and combinatorial challenges. In
particular, our experiments, based on software respol
for computing resultant polytopes, establish lower
bounds on the maximal number of faces. By studying
mixed subdivisions, we obtain tight upper bounds on the
maximal number of facets and ridges, thus arriving at
the following maximal f-vector: (22,66,66,22), i.e.
vector of face cardinalities. Certain general features
emerge, such as the symmetry of the maximal f-vector,
which are intriguing but still under investigation. We
establish a result of independent interest, namely that
the f-vector is maximized when the input supports are
sufficiently generic, namely full dimensional and
without parallel edges. Lastly, we offer a
classification result of all possible 4-dimensional
resultant polytopes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dumas:2013:SCR,
author = "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and Ziad
Sultan",
title = "Simultaneous computation of the row and column rank
profiles",
crossref = "Monagan:2013:IPI",
pages = "181--188",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465517",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Gaussian elimination with full pivoting generates a
PLUQ matrix decomposition. Depending on the strategy
used in the search for pivots, the permutation matrices
can reveal some information about the row or the column
rank profiles of the matrix. We propose a new pivoting
strategy that makes it possible to recover at the same
time both row and column rank profiles of the input
matrix and of any of its leading sub-matrices. We
propose a rank-sensitive and quad-recursive algorithm
that computes the latter PLUQ triangular decomposition
of an $m \times n$ matrix of rank $r$ in $O(m n
r^{\omega - 2})$ field operations, with \omega the
exponent of matrix multiplication. Compared to the LEU
decomposition by Malashonock, sharing a similar
recursive structure, its time complexity is rank
sensitive and has a lower leading constant. Over a word
size finite field, this algorithm also improves the
practical efficiency of previously known
implementations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Eder:2013:SRG,
author = "Christian Eder and Bjarke Hammersholt Roune",
title = "Signature rewriting in {Gr{\"o}bner} basis
computation",
crossref = "Monagan:2013:IPI",
pages = "331--338",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465522",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We introduce the RB algorithm for Gr{\"o}bner basis
computation, a simpler yet equivalent algorithm to
F5GEN. RB contains the original unmodified F5 algorithm
as a special case, so it is possible to study and
understand F5 by considering the simpler RB. We present
simple yet complete proofs of this fact and of F5's
termination and correctness. RB is parametrized by a
rewrite order and it contains many published algorithms
as special cases, including SB. We prove that SB is the
best possible instantiation of RB in the following
sense. Let X be any instantiation of RB (such as F5).
Then the S-pairs reduced by SB are always a subset of
the S-pairs reduced by X and the basis computed by SB
is always a subset of the basis computed by X.",
acknowledgement = ack-nhfb,
}
@InProceedings{ElDin:2013:CPM,
author = "Mohab Safey {El Din}",
title = "Critical point methods and effective real algebraic
geometry: new results and trends",
crossref = "Monagan:2013:IPI",
pages = "5--6",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465928",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2013:CCG,
author = "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
Thibaut Verron",
title = "On the complexity of computing {Gr{\"o}bner} bases for
quasi-homogeneous systems",
crossref = "Monagan:2013:IPI",
pages = "189--196",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465943",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $K$ be a field and $(f_1, \ldots{}, f_n) \subset
K[X_1, \ldots{}, X_n]$ be a sequence of
quasi-homogeneous polynomials of respective weighted
degrees $(d_1, \ldots{}, d_n)$ w.r.t a system of
weights ($w_1$, \ldots{}, $w_n$). Such systems are
likely to arise from a lot of applications, including
physics or cryptography. We design strategies for
computing Gr{\"o}bner bases for quasi-homogeneous
systems by adapting existing algorithms for homogeneous
systems to the quasi-homogeneous case. Overall, under
genericity assumptions, we show that for a generic
zero-dimensional quasi homogeneous system, the
complexity of the full strategy is polynomial in the
weighted B{\'e}zout bound $\Pi_{i =1}^n d^i / \Pi _{i
=1}^n w^i$. We provide some experimental results based
on generic systems as well as systems arising from a
cryptography problem. They show that taking advantage
of the quasi-homogeneous structure of the systems allow
us to solve systems that were out of reach
otherwise.",
acknowledgement = ack-nhfb,
}
@InProceedings{Faugere:2013:GBI,
author = "Jean-Charles Faugere and Jules Svartz",
title = "{Gr{\"o}bner} bases of ideals invariant under a
commutative group: the non-modular case",
crossref = "Monagan:2013:IPI",
pages = "347--354",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465944",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We propose efficient algorithms to compute the
Gr{\"o}bner basis of an ideal I subset k [ x$_1$,\ldots{},
x$_n$ ] globally invariant under the action of a
commutative matrix group G, in the non-modular case
(where char (k) doesn't divide | G |). The idea is to
simultaneously diagonalize the matrices in G, and apply
a linear change of variables on I corresponding to the
base-change matrix of this diagonalization. We can now
suppose that the matrices acting on I are diagonal.
This action induces a grading on the ring R=k [
x$_1$,\ldots{}, x$_n$ ], compatible with the degree, indexed
by a group related to G, that we call G -degree. The
next step is the observation that this grading is
maintained during a Gr{\"o}bner basis computation or
even a change of ordering, which allows us to split the
Macaulay matrices into | G | submatrices of roughly the
same size. In the same way, we are able to split the
canonical basis of R/I (the staircase) if I is a
zero-dimensional ideal. Therefore, we derive abelian
versions of the classical algorithms F$_4$, F$_5$ or
FGLM. Moreover, this new variant of F$_4$ / F$_5$
allows complete parallelization of the linear algebra
steps, which has been successfully implemented. On
instances coming from applications (NTRU crypto-system
or the Cyclic-n problem), a speed-up of more than 400
can be obtained. For example, a Gr{\"o}bner basis of
the Cyclic-11 problem can be solved in less than 8
hours with this variant of F$_4$. Moreover, using this
method, we can identify new classes of polynomial
systems that can be solved in polynomial time.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2013:CRS,
author = "Qingdong Guo and Mohab Safey {El Din} and Lihong Zhi",
title = "Computing rational solutions of linear matrix
inequalities",
crossref = "Monagan:2013:IPI",
pages = "197--204",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465949",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Consider a $ (D \times D) $ symmetric matrix $A$ whose
entries are linear forms in $ Q[X^1, \ldots {}, X_k] $
with coefficients of bit size $ \leq \tau $. We provide
an algorithm which decides the existence of rational
solutions to the linear matrix inequality $ A \geq 0 $
and outputs such a rational solution if it exists. This
problem is of first importance: it can be used to
compute algebraic certificates of positivity for
multivariate polynomials. Our algorithm runs within $
(k < =)^{O(1)} 2^{O(\min (k, D))} D^2 D^O (D^2) $ bit
operations; the bit size of the output solution is
dominated by $ \tau^{O(1)} 2^{O(\min (k, D))} D^2 $.
These results are obtained by designing algorithmic
variants of constructions introduced by Klep and
Schweighofer. This leads to the best complexity bounds
for deciding the existence of sums of squares with
rational coefficients of a given polynomial. We have
implemented the algorithm; it has been able to tackle
Scheiderer's example of a multivariate polynomial that
is a sum of squares over the reals but not over the
rationals; providing the first computer validation of
this counter-example to Sturmfels' conjecture.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hulpke:2013:CST,
author = "Alexander J. Hulpke",
title = "Calculation of the subgroups of a trivial-fitting
group",
crossref = "Monagan:2013:IPI",
pages = "205--210",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465525",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We describe an algorithm to determine representatives
of the conjugacy classes of subgroups of a
Trivial-Fitting group, this case being the one prior
algorithms reduce to. As a subtask we describe an
algorithm for determining conjugacy classes of
complements to an arbitrary normal subgroup if the
factor group is solvable.",
acknowledgement = ack-nhfb,
}
@InProceedings{Johansson:2013:FHS,
author = "Fredrik Johansson and Manuel Kauers and Marc
Mezzarobba",
title = "Finding hyperexponential solutions of linear {ODEs} by
numerical evaluation",
crossref = "Monagan:2013:IPI",
pages = "211--218",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465513",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a new algorithm for computing
hyperexponential solutions of linear ordinary
differential equations with polynomial coefficients.
The algorithm relies on interpreting formal series
solutions at the singular points as analytic functions
and evaluating them numerically at some common ordinary
point. The numerical data is used to determine a small
number of combinations of the formal series that may
give rise to hyperexponential solutions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:2013:SMF,
author = "Erich L. Kaltofen and Zhengfeng Yang",
title = "Sparse multivariate function recovery from values with
noise and outlier errors",
crossref = "Monagan:2013:IPI",
pages = "219--226",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465524",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Error-correcting decoding is generalized to
multivariate sparse rational function recovery from
evaluations that can be numerically inaccurate and
where several evaluations can have severe errors
(``outliers''). The generalization of the
Berlekamp-Welch decoder to exact Cauchy interpolation
of univariate rational functions from values with
faults is by Kaltofen and Pernet in 2012. We give a
different univariate solution based on structured
linear algebra that yields a stable decoder with
floating point arithmetic. Our multivariate polynomial
and rational function interpolation algorithm combines
Zippel's symbolic sparse polynomial interpolation
technique [Ph.D. Thesis MIT 1979] with the numeric
algorithm by Kaltofen, Yang, and Zhi [Proc. SNC 2007],
and removes outliers (``cleans up data'') through
techniques from error correcting codes. Our
multivariate algorithm can build a sparse model from a
number of evaluations that is linear in the sparsity of
the model.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawano:2013:QFT,
author = "Yasuhito Kawano and Hiroshi Sekigawa",
title = "{Quantum Fourier Transform} over symmetric groups",
crossref = "Monagan:2013:IPI",
pages = "227--234",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465940",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper proposes an O (n$^4$) quantum Fourier
transform (QFT) algorithm over symmetric group S$_n$,
the fastest QFT algorithm of its kind. We propose a
fast Fourier transform algorithm over symmetric group
S$_n$, which consists of O (n$^3$) multiplications of
unitary matrices, and then transform it into a quantum
circuit form. The QFT algorithm can be applied to
constructing the standard algorithm of the hidden
subgroup problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kunwar:2013:SOD,
author = "Vijay Jung Kunwar and Mark van Hoeij",
title = "Second order differential equations with
hypergeometric solutions of degree three",
crossref = "Monagan:2013:IPI",
pages = "235--242",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465953",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let L be a second order linear homogeneous
differential equation with rational function
coefficients. The goal in this paper is to solve L in
terms of hypergeometric function 2F1(a,b;c|f) where f
is a rational function of degree 3.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lamban:2013:CSM,
author = "Laureano Lamb{\'a}n and Francisco J.
Mart{\'\i}n-Mateos and Julio Rubio and Jos{\'e}-Luis
Ruiz-Reina",
title = "Certified symbolic manipulation: bivariate simplicial
polynomials",
crossref = "Monagan:2013:IPI",
pages = "243--250",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465515",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Certified symbolic manipulation is an emerging new
field where programs are accompanied by certificates
that, suitably interpreted, ensure the correctness of
the algorithms. In this paper, we focus on algebraic
algorithms implemented in the proof assistant ACL2,
which allows us to verify correctness in the same
programming environment. The case study is that of
bivariate simplicial polynomials, a data structure used
to help the proof of properties in Simplicial Topology.
Simplicial polynomials can be computationally
interpreted in two ways. As symbolic expressions, they
can be handled algorithmically, increasing the
automation in ACL2 proofs. As representations of
functional operators, they help proving properties of
categorical morphisms. As an application of this second
view, we present the definition in ACL2 of some
morphisms involved in the Eilenberg-Zilber reduction, a
central part of the Kenzo computer algebra system. We
have proved the ACL2 implementations are correct and
tested that they get the same results as Kenzo does.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lebreton:2013:CSB,
author = "Romain Lebreton and Esmaeil Mehrabi and Eric Schost",
title = "On the complexity of solving bivariate systems: the
case of non-singular solutions",
crossref = "Monagan:2013:IPI",
pages = "251--258",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465950",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We give an algorithm for solving bivariate polynomial
systems over either k (T)[ X,Y ] or Q [ X,Y ] using a
combination of lifting and modular composition
techniques.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lenstra:2013:LS,
author = "Hendrik Lenstra",
title = "Lattices with symmetry",
crossref = "Monagan:2013:IPI",
pages = "3--4",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465929",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Levandovskyy:2013:ECG,
author = "Viktor Levandovskyy and Grischa Studzinski and
Benjamin Schnitzler",
title = "Enhanced computations of {Gr{\"o}bner} bases in free
algebras as a new application of the letterplace
paradigm",
crossref = "Monagan:2013:IPI",
pages = "259--266",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465948",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Recently, the notion of ``letterplace correspondence''
between ideals in the free associative algebra KX and
certain ideals in the so-called letterplace ring KXP
has evolved. We continue this research direction,
started by La Scala and Levandovskyy, and present novel
ideas, supported by the implementation, for effective
computations with ideals in the free algebra by
utilizing the generalized letterplace correspondance.
In particular, we provide a direct algorithm to compute
Gr{\"o}bner bases of non-graded ideals. Surprisingly, we
realize its behavior as ``homogenizing without a
homogenization variable''. Moreover, we develop new
shift-invariant data structures for this family of
algorithms and discuss about them. Furthermore we
generalize the famous criteria of Gebauer-M{\"o}ller to
the non-commutative setting and show the benefits for
the computation by allowing to skip unnecessary
critical pairs. The methods are implemented in the
computer algebra system Singular. We present a
comparison of performance of our implementation with
the corresponding implementations in the systems Magma
[BCP97] and GAP [GAP13] on the representative set of
nontrivial examples.",
acknowledgement = ack-nhfb,
}
@InProceedings{Levin:2013:MDD,
author = "Alexander B. Levin",
title = "Multivariate difference-differential dimension
polynomials and new invariants of
difference-differential field extensions",
crossref = "Monagan:2013:IPI",
pages = "267--274",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465521",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We introduce a method of characteristic sets with
respect to several term orderings for
difference-differential polynomials. Using this
technique, we obtain a method of computation of
multivariate dimension polynomials of finitely
generated difference-differential field extensions.
Furthermore, we find new invariants of such extensions
and show how the computation of multivariate
difference-differential polynomials is applied to the
equivalence problem for systems of algebraic
difference-differential equations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2013:SDR,
author = "Wei Li and Chun-Ming Yuan and Xiao-Shan Gao",
title = "Sparse difference resultant",
crossref = "Monagan:2013:IPI",
pages = "275--282",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465509",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, the concept of sparse difference
resultant for a Laurent transformally essential system
of Laurent difference polynomials is introduced and its
properties are proved. In particular, order and degree
bounds for the sparse difference resultant are given.
Based on these bounds, an algorithm to compute the
sparse difference resultant is proposed, which is
single exponential in terms of the number of variables,
the Jacobi number, and the size of the system. Also,
the precise order, degree, a determinant
representation, and a Poisson-type product formula for
the difference resultant are given.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mehlhorn:2013:AFR,
author = "Kurt Mehlhorn and Michael Sagraloff and Pengming
Wang",
title = "From approximate factorization to root isolation",
crossref = "Monagan:2013:IPI",
pages = "283--290",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465523",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present an algorithm for isolating all roots of an
arbitrary complex polynomial $p$ which also works in
the presence of multiple roots provided that arbitrary
good approximations of the coefficients of $p$ and the
number of distinct roots are given. Its output consists
of pairwise disjoint disks each containing one of the
distinct roots of p, and its multiplicity. The
algorithm uses approximate factorization as a
subroutine. For the case, where Pan's algorithm [16] is
used for the factorization, we derive complexity bounds
for the problems of isolating and refining all roots
which are stated in terms of the geometric locations of
the roots only. Specializing the latter bounds to a
polynomial of degree d and with integer coefficients of
bitsize less than $ \tau $, we show that $ {\tilde
O}(d^3 + d^2 \tau + d \kappa) $ bit operations are
sufficient to compute isolating disks of size less than
$ 2^- \kappa $ for all roots of p, where $ \kappa $ is
an arbitrary positive integer. Our new algorithm has an
interesting consequence on the complexity of computing
the topology of a real algebraic curve specified as the
zero set of a bivariate integer polynomial and for
isolating the real solutions of a bivariate system. For
input polynomials of degree $n$ and bitsize $ \tau $,
the currently best running time improves from $ {\tilde
O}(n^9 \tau + n^8 \tau^2) $ (deterministic) to $
{\tilde O}(n^6 + n^5 \tau) $ (randomized) for topology
computation and from $ {\tilde O}(n^8 + n^7 \tau) $
(deterministic) to $ {\tilde O}(n^6 + n^5 \tau) $
(randomized) for solving bivariate systems.d",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2013:BCR,
author = "Victor Y. Pan and Elias P. Tsigaridas",
title = "On the boolean complexity of real root refinement",
crossref = "Monagan:2013:IPI",
pages = "299--306",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465938",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We assume that a real square-free polynomial $A$ has a
degree $d$, a maximum coefficient bitsize \tau and a
real root lying in an isolating interval and having no
nonreal roots nearby (we quantify this assumption).
Then, we combine the Double Exponential Sieve algorithm
(also called the Bisection of the Exponents), the
bisection, and Newton iteration to decrease the width
of this inclusion interval by a factor of $ t = 2^{-L}
$. The algorithm has Boolean complexity $ {\tilde O}_B
(d^2 \tau + d L) $. Our algorithms support the same
complexity bound for the refinement of $r$ roots, for
any $ r < = d $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2013:TFA,
author = "Senshan Pan and Yupu Hu and Baocang Wang",
title = "The termination of the {$ F5 $} algorithm revisited",
crossref = "Monagan:2013:IPI",
pages = "291--298",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465520",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The F5 algorithm [8] is generally believed as one of
the fastest algorithms for computing Gr{\"o}bner bases.
However, its termination problem is still unclear. The
crux lies in the non-determinacy of the F5 in selecting
which from the critical pairs of the same degree. In
this paper, we construct a generalized algorithm F5GEN
which contain the F5 as its concrete implementation.
Then we prove the correct termination of the F5GEN
algorithm. That is to say, for any finite set of
homogeneous polynomials, the F5 terminates correctly.",
acknowledgement = ack-nhfb,
}
@InProceedings{Parrilo:2013:CAG,
author = "Pablo A. Parrilo",
title = "Convex algebraic geometry and semidefinite
optimization",
crossref = "Monagan:2013:IPI",
pages = "9--10",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2466575",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In the past decade there has been a surge of interest
in algebraic approaches to optimization problems
defined by multivariate polynomials. Fundamental
mathematical challenges that arise in this area include
understanding the structure of nonnegative polynomials,
the interplay between efficiency and complexity of
different representations of algebraic sets, and the
development of effective algorithms. Remarkably, and
perhaps unexpectedly, convexity provides a new
viewpoint and a powerful framework for addressing these
questions. This naturally brings us to the intersection
of algebraic geometry, optimization, and convex
geometry, with an emphasis on algorithms and
computation. This emerging area has become known as
convex algebraic geometry. This tutorial will focus on
basic and recent developments in convex algebraic
geometry, and the associated computational methods
based on semidefinite programming for optimization
problems involving polynomial equations and
inequalities. There has been much recent progress, by
combining theoretical results in real algebraic
geometry with semidefinite programming to develop
effective computational approaches to these problems.
We will make particular emphasis on sum of squares
decompositions, general duality properties,
infeasibility certificates,
approximation/inapproximability results, as well as
survey the many exciting developments that have taken
place in the last few years.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pauderis:2013:CIS,
author = "Colton Pauderis and Arne Storjohann",
title = "Computing the invariant structure of integer matrices:
fast algorithms into practice",
crossref = "Monagan:2013:IPI",
pages = "307--314",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465955",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We present a new heuristic algorithm for computing the
determinant of a nonsingular $ n \times n $ integer
matrix. Extensive empirical results from a highly
optimized implementation show the running time grows
approximately as $ n^3 \log n $, even for input
matrices with a highly nontrivial Smith invariant
structure. We extend the algorithm to compute the
Hermite form of the input matrix. Both the determinant
and Hermite form algorithm certify correctness of the
computed results.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pillwein:2013:TCP,
author = "Veronika Pillwein",
title = "Termination conditions for positivity proving
procedures",
crossref = "Monagan:2013:IPI",
pages = "315--322",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465945",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Proving positivity of a sequence given by a linear
recurrence with polynomial coefficients (P-finite
recurrence) is a non-trivial task for both humans and
computers. Algorithms dealing with this task are rare
or non-existent. One method that was introduced in the
last decade by Gerhold and Kauers succeeds on many
examples, but termination of this procedure has been
proven so far only up to order three for special cases.
Here we present an analysis that extends the previously
known termination results on recurrences of order
three, and also provides termination conditions for
recurrences of higher order.",
acknowledgement = ack-nhfb,
}
@InProceedings{Raab:2013:IUF,
author = "Clemens G. Raab",
title = "Integration of unspecified functions and families of
iterated integrals",
crossref = "Monagan:2013:IPI",
pages = "323--330",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465939",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An algorithm for parametric elementary integration
over differential fields constructed by a
differentially transcendental extension is given. It
extends current versions of Risch's algorithm to this
setting and is based on some first ideas of Graham H.
Campbell transferring his method to more formal grounds
and making it parametric, which allows to compute
relations among definite integrals. Apart from
differentially transcendental functions, such as the
gamma function or the zeta function, also unspecified
functions and certain families of iterated integrals
such as the polylogarithms can be modeled in such
differential fields.",
acknowledgement = ack-nhfb,
}
@InProceedings{Steffy:2013:ELI,
author = "Daniel E. Steffy",
title = "Exact linear and integer programming: tutorial
abstract",
crossref = "Monagan:2013:IPI",
pages = "11--12",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465931",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This tutorial surveys state-of-the-art algorithms and
computational methods for computing exact solutions to
linear and mixed-integer programming problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderHoeven:2013:IMC,
author = "Joris van der Hoeven and Gr{\'e}goire Lecerf",
title = "Interfacing {{\tt MATHEMAGIX}} with {C++}",
crossref = "Monagan:2013:IPI",
pages = "363--370",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465511",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we give a detailed description of the
interface between the MATHEMAGIX language and C++. In
particular, we describe the mechanism which allows us
to import a C++ template library (which only permits
static instantiation) as a fully generic MATHEMAGIX
template library.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderHoeven:2013:SFT,
author = "Joris van der Hoeven and Romain Lebreton and {\'E}ric
Schost",
title = "Structured {FFT} and {TFT}: symmetric and lattice
polynomials",
crossref = "Monagan:2013:IPI",
pages = "355--362",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465526",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we consider the problem of efficient
computations with structured polynomials. We provide
complexity results for computing Fourier Transform and
Truncated Fourier Transform of symmetric polynomials,
and for multiplying polynomials supported on a
lattice.",
acknowledgement = ack-nhfb,
}
@InProceedings{vanHoeij:2013:CFU,
author = "Mark van Hoeij",
title = "The complexity of factoring univariate polynomials
over the rationals: tutorial abstract",
crossref = "Monagan:2013:IPI",
pages = "13--14",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2479779",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This tutorial will explain the algorithm behind the
currently fastest implementations for univariate
factorization over the rationals. The complexity will
be analyzed; it turns out that modifications were
needed in order to prove a polynomial time complexity
while preserving the best practical performance. The
complexity analysis leads to two results: (1) it shows
that the practical performance on common inputs can be
improved without harming the worst case performance,
and (2) it leads to an improved complexity, not only
for factoring, but for LLL reduction as well.",
acknowledgement = ack-nhfb,
}
@InProceedings{Wolfram:2013:CAY,
author = "Stephen Wolfram",
title = "Computer algebra: a $ 32 $-year update",
crossref = "Monagan:2013:IPI",
pages = "7--8",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465930",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wu:2013:FPR,
author = "Wenyuan Wu and Greg Reid",
title = "Finding points on real solution components and
applications to differential polynomial systems",
crossref = "Monagan:2013:IPI",
pages = "339--346",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465954",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper we extend complex homotopy methods to
finding witness points on the irreducible components of
real varieties. In particular we construct such witness
points as the isolated real solutions of a constrained
optimization problem. First a random hyperplane
characterized by its random normal vector is chosen.
Witness points are computed by a polyhedral homotopy
method. Some of them are at the intersection of this
hyperplane with the components. Other witness points
are the local critical points of the distance from the
plane to components. A method is also given for
constructing regular witness points on components, when
the critical points are singular. The method is
applicable to systems satisfying certain regularity
conditions. Illustrative examples are given. We show
that the method can be used in the consistent
initialization phase of a popular method due to Pryce
and Pantelides for preprocessing differential algebraic
equations for numerical solution.",
acknowledgement = ack-nhfb,
}
@InProceedings{Yang:2013:VEB,
author = "Zhengfeng Yang and Lihong Zhi and Yijun Zhu",
title = "Verified error bounds for real solutions of
positive-dimensional polynomial systems",
crossref = "Monagan:2013:IPI",
pages = "371--378",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465951",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In this paper, we propose two algorithms for verifying
the existence of real solutions of positive-dimensional
polynomial systems. The first one is based on the
critical point method and the homotopy continuation
method. It targets for verifying the existence of real
roots on each connected component of an algebraic
variety $V \cap R^n$ defined by polynomial equations.
The second one is based on the low-rank moment matrix
completion method and aims for verifying the existence
of at least one real roots on $V \cap R^n$. Combined
both algorithms with the verification algorithms for
zero-dimensional polynomial systems, we are able to
find verified real solutions of positive-dimensional
polynomial systems very efficiently for a large set of
examples.",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhou:2013:CCB,
author = "Wei Zhou and George Labahn",
title = "Computing column bases of polynomial matrices",
crossref = "Monagan:2013:IPI",
pages = "379--386",
year = "2013",
DOI = "https://doi.org/10.1145/2465506.2465947",
bibdate = "Fri Mar 14 14:33:44 MDT 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Given a matrix of univariate polynomials over a field
$K$, its columns generate a $ K[x] $-module. We call
any basis of this module a column basis of the given
matrix. Matrix gcds and matrix normal forms are
examples of such module bases. In this paper we present
a deterministic algorithm for the computation of a
column basis of an $ m \times n $ input matrix with $ m
\leq n $. If $s$ is the average column degree of the
input matrix, this algorithm computes a column basis
with a cost of $ {\tilde O}(n m^{\omega - 1} s) $ field
operations in $K$. Here the soft-$O$ notation is
Big-$O$ with log factors removed while $ \omega $ is
the exponent of matrix multiplication. Note that the
average column degree $s$ is bounded by the commonly
used matrix degree that is also the maximum column
degree of the input matrix.",
acknowledgement = ack-nhfb,
}
@Proceedings{Jenks:1976:SPA,
editor = "Richard D. Jenks",
booktitle = "{Symsac '76: proceedings of the 1976 ACM Symposium on
Symbolic and Algebraic Computation, August 10--12,
1976, Yorktown Heights, New York}",
title = "{Symsac '76: proceedings of the 1976 ACM Symposium on
Symbolic and Algebraic Computation, August 10--12,
1976, Yorktown Heights, New York}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "384",
year = "1976",
LCCN = "QA155.7.E4 A15 1976",
bibdate = "Tue Jul 26 09:04:45 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
price = "US\$20.00",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Ng:1979:SAC,
editor = "Edward W. Ng",
booktitle = "{Symbolic and algebraic computation: EUROSAM '79, an
International Symposium on Symbolic and Algebraic
Manipulation, Marseille, France, June 1979}",
title = "{Symbolic and algebraic computation: EUROSAM '79, an
International Symposium on Symbolic and Algebraic
Manipulation, Marseille, France, June 1979}",
volume = "72",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 557",
year = "1979",
CODEN = "LNCSD9",
ISBN = "0-387-09519-5",
ISBN-13 = "978-0-387-09519-6",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA155.7.E4 E88 1979",
bibdate = "Fri Apr 12 07:14:47 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "algebra --- data processing --- congresses",
}
@Proceedings{Wang:1981:SPA,
editor = "Paul S. Wang",
booktitle = "{SYMSAC '81: proceedings of the 1981 ACM Symposium on
Symbolic and Algebraic Computation, Snowbird, Utah,
August 5--7, 1981}",
title = "{SYMSAC '81: proceedings of the 1981 ACM Symposium on
Symbolic and Algebraic Computation, Snowbird, Utah,
August 5--7, 1981}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xi + 249",
year = "1981",
ISBN = "0-89791-047-8",
ISBN-13 = "978-0-89791-047-7",
LCCN = "QA155.7.E4 A28 1981",
bibdate = "Fri Feb 09 12:29:36 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/macsyma.bib;
http://www.math.utah.edu/pub/tex/bib/sigsam.bib",
note = "ACM order no. 505810",
price = "US\$23.00",
acknowledgement = ack-nhfb,
tableofcontents = "The basis of a computer system for modern algebra /
John J. Cannon \\
A language for computational algebra / Richard D.
Jenks, Barry M. Trager \\
Characterization of VAX Macsyma / John K. Foderaro,
Richard J. Fateman \\
SMP - A Symbolic Manipulation Program / Chris A. Cole,
Stephen Wolfram \\
An extension of Liouville s theorem on integration in
finite terms / M. F. Singer, B. D. Saunders, B. F.
Caviness \\
Formal solutions of differential equations in the
neighborhood of singular points (Regular and Irregular)
/ J. Della Dora, E. Tournier \\
Elementary first integrals of differential equations /
M. J. Prelle, M. F. Singer \\
A technique for solving ordinary differential equations
using Riemann s P-functions / Shunro Watanabe \\
Using Lie transformation groups to find closed form
solutions to first order ordinary differential
equations / Bruce Char \\
The computational complexity of continued fractions /
V. Strassen \\
Newton s iteration and the sparse Hensel algorithm
(Extended Abstract) / Richard Zippel \\
Automatic generation of finite difference equations and
Fourier stability analyses / Michael C. Wirth \\
An algorithmic classification of geometries in general
relativity / Jan E. Aman, Anders Karlhede \\
Formulation of design rules for NMR imaging coil by
using symbolic manipulation / John F. Schenck, M. A.
Hussain \\
Computation for conductance distributions of
percolation lattice cells / Rabbe Fogelholm \\
Breuer s grow factor algorithm in computer algebra / J.
A. van Hulzen \\
An implementation of Kovacic s algorithm for solving
second order linear homogeneous differential equations
/ B. David Saunders \\
Implementing a polynomial factorization and GCD package
/ P. M. A. Moore, A. C. Norman \\
Note on probabilistic algorithms in integer and
polynomial arithmetic / Michael Kaminski \\
A case study in interlanguage communication: Fast LISP
polynomial operations written in C / Richard J. Fateman
\\
On the application of Array Processors to symbol
manipulation / R. Beardsworth \\
The optimization of user programs for an Algebraic
Manipulation System / P. D. Pearce, R. J. Hickst \\
Views on transportability of Lisp and Lisp-based
systems / Richard J. Fateman \\
Algebraic constructions for algorithms (Extended
Abstract) / S. Winograd \\
A cancellation free algorithm, with factoring
capabilities, for the efficient solution of large
sparse sets of equations / J. Smit \\
Efficient Gaussian elimination method for symbolic
determinants and linear systems (Extended Abstract) /
Tateaki Sasaki, Hirokazu Murao \\
Parallelism in algebraic computation and parallel
algorithms for symbolic linear systems / Tateaki
Sasaki, Yasumasa Kanada \\
Algebraic computation for the masses / Joel Moses \\
Construction of nilpotent Lie algebras over arbitrary
fields / Robert E. Beck, Bernard Kolman \\
Algorithms for central extensions of Lie algebras
Robert E. Beck, Bernard Kolman \\
Computing an invariant subring of $k[X,Y]$ / Rosalind
Neuman \\
Double cosets and searching small groups / Gregory
Butler \\
A generalized class of polynomials that are hard to
factor / Erich Kaltofen, David R. Musser, B. David
Saunders \\
Some inequalities about univariate polynomials /
Maurice Mignotte \\
Factorization over finitely generated fields / James H.
Davenport, Barry M. Trager \\
On solving systems of algebraic equations via ideal
bases and elimination theory / Michael E. Pohst, David
Y. Y. Yun \\
A p-adic algorithm for univariate partial fractions /
Paul S. Wang \\
Use of VLSI in algebraic computation: Some suggestions
H. T. Kung \\
An algebraic front-end for the production and use of
numeric programs / Douglas H. Lanam \\
Computer algebra and numerical integration / Richard J.
Fateman \\
Tracing occurrences of patterns in symbolic
computations / F. Gardin, J. A. Campbell \\
The automatic derivation of periodic solutions to a
class of weakly nonlinear differential equations / John
Fitch \\
User-based integration software / John Fitch.",
}
@Proceedings{Char:1986:PSS,
editor = "Bruce W. Char",
booktitle = "{Proceedings of the 1986 Symposium on Symbolic and
Algebraic Computation: Symsac '86, July 21--23, 1986,
Waterloo, Ontario}",
title = "{Proceedings of the 1986 Symposium on Symbolic and
Algebraic Computation: Symsac '86, July 21--23, 1986,
Waterloo, Ontario}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "254",
year = "1986",
ISBN = "0-89791-199-7 (paperback)",
ISBN-13 = "978-0-89791-199-3 (paperback)",
LCCN = "QA155.7.E4 A281 1986",
bibdate = "Thu Mar 12 07:35:00 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order no. 505860.",
acknowledgement = ack-nhfb,
keywords = "Algebra --- Data processing --- Congresses;
Programming languages (Electronic computers) ---
Congresses",
}
@Proceedings{Gianni:1989:SAC,
editor = "P. (Patrizia) Gianni",
booktitle = "{Symbolic and algebraic computation: International
Symposium ISSAC '88, Rome, Italy, July 4--8, 1988:
proceedings}",
title = "{Symbolic and algebraic computation: International
Symposium ISSAC '88, Rome, Italy, July 4--8, 1988:
proceedings}",
volume = "358",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 543",
year = "1989",
ISBN = "3-540-51084-2",
ISBN-13 = "978-3-540-51084-0",
LCCN = "QA76.95 .I571 1988",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "Conference held jointly with AAECC-6.",
series = ser-LNCS,
abstract = "The following topics were dealt with: differential
algebra; applications; Gr{\"o}bner bases; differential
equations; algorithmic number theory; algebraic
geometry; computational geometry; computational logic;
systems; and arithmetic.",
acknowledgement = ack-nhfb,
classification = "C1110 (Algebra); C4100 (Numerical analysis); C7310
(Mathematics)",
confdate = "4--8 July 1988",
conflocation = "Rome, Italy",
keywords = "Differential algebra; Applications; Gr{\"o}bner bases;
Differential equations; Algorithmic number theory;
Algebraic geometry; Computational geometry;
Computational logic; Systems; Arithmetic",
pubcountry = "West Germany",
thesaurus = "Algebra; Computational geometry; Differential
equations; Formal logic; Mathematics computing; Theorem
proving",
}
@Proceedings{Gonnet:1989:PAI,
editor = "Gaston H. Gonnet",
booktitle = "{Proceedings of the ACM-SIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation: ISSAC
'89 / July 17--19, 1989, Portland, Oregon}",
title = "{Proceedings of the ACM-SIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation: ISSAC
'89 / July 17--19, 1989, Portland, Oregon}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "399",
year = "1989",
ISBN = "0-89791-325-6",
ISBN-13 = "978-0-89791-325-6",
LCCN = "QA76.95.I59 1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number: 505890. English and French.",
price = "US\$29.00",
abstract = "The following topics were dealt with: differential
equations; linear difference equations; functional
equivalence; series solutions; factorization; Las Vegas
primality test; matrix algebra; rational mappings;
Knuth--Bendix procedure and Buchberger algorithm;
symbolic algebra; lockup tables; derivations
polynomials; Pad{\'e}--Hermite Forms; $p$-adic
approximations; nonlinear equations; defect;
Sturm--Habicht sequence; MINION; REDUCE; code
optimization; IRENA; MACSYMA; GENCRAY; AIPI; Fourier
series; functions; integration; education; stability;
normal forms; curves; geometry; root isolation;
triangle inequalities; parallel algorithms; rewriting
systems; and theorem proving.",
acknowledgement = ack-nhfb,
classification = "C1110 (Algebra); C1120 (Analysis); C4100 (Numerical
analysis); C4200 (Computer theory); C7310
(Mathematics)",
confdate = "17--19 July 1989",
conflocation = "Portland, OR, USA",
confsponsor = "ACM",
keywords = "AIPI; algebra --- data processing --- congresses;
Buchberger algorithm; Code optimization; computational
complexity --- congresses; Curves; Defect; Derivations;
Differential equations; Education; Factorization;
Fourier series; Functional equivalence; Functions;
GENCRAY; Geometry; Integration; IRENA; Knuth--Bendix
procedure; Las Vegas primality test; Linear difference
equations; Lockup tables; MACSYMA; Matrix algebra;
MINION; Nonlinear equations; Normal forms; P-adic
approximations; Pad{\'e}--Hermite Forms; Parallel
algorithms; Polynomials; Rational mappings; REDUCE;
Rewriting systems; Root isolation; Series solutions;
Stability; Sturm--Habicht sequence; Symbolic algebra;
Theorem proving, mathematics --- data processing ---
congresses; Triangle inequalities",
pubcountry = "USA",
thesaurus = "Algebra; Computation theory; Functions; Mathematics
computing; Numerical analysis; Series [mathematics];
Symbol manipulation",
}
@Proceedings{Mora:1989:AAA,
editor = "T. Mora",
booktitle = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 6th International Conference,
AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
title = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 6th International Conference,
AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
volume = "357",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 480",
year = "1989",
ISBN = "3-540-51083-4",
ISBN-13 = "978-3-540-51083-3",
LCCN = "QA268 .A35 1988",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "Conference held jointly with ISSAC '88.",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
confdate = "4--8 July 1988",
conflocation = "Rome, Italy",
pubcountry = "West Germany",
}
@Proceedings{Watanabe:1990:IPI,
editor = "Shunro Watanabe and Morio Nagata",
booktitle = "{ISSAC '90: proceedings of the International Symposium
on Symbolic and Algebraic Computation: August 20--24,
1990, Tokyo, Japan}",
title = "{ISSAC '90: proceedings of the International Symposium
on Symbolic and Algebraic Computation: August 20--24,
1990, Tokyo, Japan}",
publisher = pub-ACM # " and " # pub-AW,
address = pub-ACM:adr # " and " # pub-AW:adr,
pages = "ix + 307",
year = "1990",
ISBN = "0-89791-401-5 (ACM), 0-201-54892-5 (Addison-Wesley)",
ISBN-13 = "978-0-89791-401-7 (ACM), 978-0-201-54892-1
(Addison-Wesley)",
LCCN = "QA76.95 .I57 1990",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The following topics were dealt with: foundations of
symbolic computation; computational logics; systems;
algorithms on polynomials; integration and differential
equations; and algorithms on geometry.",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
confdate = "20--24 Aug. 1990",
conflocation = "Tokyo, Japan",
confsponsor = "Inf. Processing Soc. Japan; Japan Soc. Software Sci.
Technol.; ACM",
keywords = "algebra --- data processing --- congresses;
Algorithms; Computational geometry; Computational
logics; Differential equations; Geometry; Integration;
mathematics --- data processing --- congresses;
Polynomials; Symbolic computation; Systems",
pubcountry = "USA",
thesaurus = "Algorithm theory; Computational geometry; Formal
logic; Symbol manipulation",
}
@Proceedings{Watt:1991:IPI,
editor = "Stephen M. Watt",
booktitle = "{ISSAC '91: proceedings of the 1991 International
Symposium on Symbolic and Algebraic Computation, July
15--17, 1991, Bonn, Germany}",
title = "{ISSAC '91: proceedings of the 1991 International
Symposium on Symbolic and Algebraic Computation, July
15--17, 1991, Bonn, Germany}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 468",
year = "1991",
ISBN = "0-89791-437-6",
ISBN-13 = "978-0-89791-437-6",
LCCN = "QA 76.95 I59 1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/magma.bib",
abstract = "The following topics were dealt with: algorithms for
symbolic mathematical computation; languages, systems
and packages; computational geometry, group theory and
number theory; automatic theorem proving and
programming; interface of symbolics, numerics and
graphics; applications in mathematics, science and
engineering; and symbolic and algebraic computation in
education.",
acknowledgement = ack-nhfb,
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4210
(Formal logic); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
confdate = "15--17 July 1991",
conflocation = "Bonn, Germany",
confsponsor = "ACM",
keywords = "algebra --- data processing --- congresses; Algebraic
computation; Algorithms; Automatic theorem proving;
Computational geometry; Education; Engineering;
Graphics; Group theory; Languages; Mathematics;
mathematics --- data processing --- congresses; Number
theory; Programming; Science; Symbolic mathematical
computation; Symbolics",
pubcountry = "USA",
thesaurus = "Computational complexity; Formal languages;
Interpolation; Number theory; Polynomials; Symbol
manipulation",
}
@Proceedings{Wang:1992:PII,
editor = "Paul S. Wang",
booktitle = "{Proceedings of ISSAC '92. International Symposium on
Symbolic and Algebraic Computation}",
title = "{Proceedings of ISSAC '92. International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 406",
year = "1992",
ISBN = "0-89791-489-9 (soft cover), 0-89791-490-2 (hard
cover)",
ISBN-13 = "978-0-89791-489-5 (soft cover), 978-0-89791-490-1
(hard cover)",
LCCN = "QA76.95.I59 1992",
bibdate = "Thu Sep 26 05:51:45 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number: 505920.",
abstract = "The following topics were dealt with: symbolic
computation; differential equations; differs-integral
software; algebraic algorithms; algebraic software;
real algebraics and root isolation; groups and number
theory; systems and interfaces.",
acknowledgement = ack-nhfb,
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
confdate = "27--29 July 1992",
conflocation = "Berkeley, CA, USA",
confsponsor = "ACM",
keywords = "Algebraic algorithms; Algebraic software; Differential
equations; Differs-integral software; Groups theory;
Interfaces; Number theory; Real algebraics; Root
isolation; Symbolic computation",
pubcountry = "USA",
thesaurus = "Differential equations; Mathematics computing; Symbol
manipulation",
}
@Proceedings{ACM:1993:PFA,
editor = "{ACM}",
booktitle = "{Proceedings of the Fourth ACM SIGPLAN Symposium on
Principles and Practice of Parallel Programming, PPOPP:
San Diego, California, May 19--22, 1993}",
title = "{Proceedings of the Fourth ACM SIGPLAN Symposium on
Principles and Practice of Parallel Programming, PPOPP:
San Diego, California, May 19--22, 1993}",
volume = "28(7)",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 259",
year = "1993",
ISBN = "0-89791-589-5",
ISBN-13 = "978-0-89791-589-2",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
LCCN = "QA76.642.A27 1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "ACM SIGPLAN Notices",
acknowledgement = ack-nhfb,
sponsor = "Association for Computing Machinery; Special Interest
Group on Programming Languages.",
standardno = "1",
}
@Proceedings{Bronstein:1993:IPI,
editor = "Manuel Bronstein",
booktitle = "{ISSAC'93: proceedings of the 1993 International
Symposium on Symbolic and Algebraic Computation, July
6--8, 1993, Kiev, Ukraine}",
title = "{ISSAC'93: proceedings of the 1993 International
Symposium on Symbolic and Algebraic Computation, July
6--8, 1993, Kiev, Ukraine}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 321",
year = "1993",
ISBN = "0-89791-604-2",
ISBN-13 = "978-0-89791-604-2",
LCCN = "QA 76.95 I59 1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number: 505930.",
abstract = "The following topics were dealt with: algebraic
solutions of equations; computer algebra systems;
algorithm theory and complexity; automated theorem
proving; polynomials; and matrix algebra.",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory); C7310 (Mathematics computing)",
confdate = "6--8 July 1993",
conflocation = "Kiev, Ukraine",
confsponsor = "ACM",
keywords = "algebra --- data processing --- congresses; Algorithm
theory; Automated theorem proving; Complexity; Computer
algebra; mathematics --- data processing ---
congresses; Matrix algebra; Polynomials",
pubcountry = "USA",
source = "ISSAC '93",
sponsor = "Association for Computing Machinery.",
thesaurus = "Computational complexity; Mathematics computing;
Matrix algebra; Polynomials; Symbol manipulation;
Theorem proving",
}
@Proceedings{Halstead:1993:PSC,
editor = "Robert H. Halstead and Takayasu Ito",
booktitle = "{Parallel symbolic computing: languages, systems, and
applications: US\slash Japan workshop, Cambridge, MA,
USA, October 14--17, 1992: proceedings}",
title = "{Parallel symbolic computing: languages, systems, and
applications: US\slash Japan workshop, Cambridge, MA,
USA, October 14--17, 1992: proceedings}",
number = "748",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 417",
year = "1993",
ISBN = "0-387-57396-8, 3-540-57396-8",
ISBN-13 = "978-0-387-57396-0, 978-3-540-57396-8",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.58.P3785 1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Proceedings{Sincovec:1993:PSS,
editor = "Richard F. Sincovec",
booktitle = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, Norfolk, VA,
March, 1993}",
title = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, Norfolk, VA,
March, 1993}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xix + 1041 + iv",
year = "1993",
ISBN = "0-89871-315-3",
ISBN-13 = "978-0-89871-315-2",
LCCN = "QA76.58.S55 1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
sponsor = "Society for Industrial and Applied Mathematics.",
}
@Proceedings{ACM:1994:IPI,
editor = "{ACM}",
booktitle = "{ISSAC '94: Proceedings of the 1994 International
Symposium on Symbolic and Algebraic Computation: July
20--22, 1994, Oxford, England, United Kingdom}",
title = "{ISSAC '94: Proceedings of the 1994 International
Symposium on Symbolic and Algebraic Computation: July
20--22, 1994, Oxford, England, United Kingdom}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 359",
year = "1994",
ISBN = "0-89791-638-7",
ISBN-13 = "978-0-89791-638-7",
LCCN = "QA76.95.I59 1994",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
confdate = "20--22 July 1994",
conflocation = "Oxford, UK",
confsponsor = "ACM",
pubcountry = "USA",
}
@Proceedings{Adleman:1994:ANT,
editor = "L. M. Adleman and M.-D. Huang",
booktitle = "{Algorithmic Number Theory. First International
Symposium, ANTS-I. Proceedings}",
title = "{Algorithmic Number Theory. First International
Symposium, ANTS-I. Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 322",
year = "1994",
ISBN = "0-387-58691-1 (New York), 3-540-58691-1 (Berlin)",
ISBN-13 = "978-0-387-58691-5 (New York), 978-3-540-58691-3
(Berlin)",
LCCN = "QA241.A43 1994",
bibdate = "Thu Sep 26 05:50:11 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
confdate = "6--9 May 1994",
conflocation = "Ithaca, NY, USA",
pubcountry = "Germany",
}
@Proceedings{Hong:1994:FIS,
editor = "Hoon Hong",
booktitle = "{First International Symposium on Parallel Symbolic
Computation, PASCO '94, Hagenberg\slash Linz, Austria,
September 26--28, 1994}",
title = "{First International Symposium on Parallel Symbolic
Computation, PASCO '94, Hagenberg\slash Linz, Austria,
September 26--28, 1994}",
volume = "5",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xiii + 431",
year = "1994",
ISBN = "981-02-2040-5",
ISBN-13 = "978-981-02-2040-2",
LCCN = "QA76.642.I58 1994",
bibdate = "Thu Mar 12 07:55:38 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "Lecture notes series in computing",
acknowledgement = ack-nhfb,
alttitle = "Parallel symbolic computation",
keywords = "Parallel programming (Computer science) ---
Congresses.",
}
@Proceedings{Aityan:1995:PNP,
editor = "S. K. Aityan",
booktitle = "{Proceedings of neural, parallel and scientific
computations: proceedings of the First International
Conference on Neural, Parallel and Scientific
Computations held at Morehouse College, Atlanta, USA,
May 28--31, 1995}",
title = "{Proceedings of neural, parallel and scientific
computations: proceedings of the First International
Conference on Neural, Parallel and Scientific
Computations held at Morehouse College, Atlanta, USA,
May 28--31, 1995}",
volume = "1",
publisher = "Dynamic Publishers, Inc",
address = "Atlanta, GA",
pages = "xi + 506",
year = "1995",
ISBN = "0-9640398-9-3, 0-9640398-8-5",
ISBN-13 = "978-0-9640398-9-6, 978-0-9640398-8-9",
LCCN = "QA76.87 .I58 1995",
bibdate = "Sat Mar 11 16:48:03 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "Proceedings of Neural Parallel and Scientific
Computations",
acknowledgement = ack-nhfb,
}
@Proceedings{Ferreira:1995:PAI,
editor = "Afonso Ferreira and Jose D. P. Rolim",
booktitle = "{Parallel algorithms for irregularly structured
problems: second international workshop, IRREGULAR 95,
Lyon, France, September 4--6, 1995: proceedings}",
title = "{Parallel algorithms for irregularly structured
problems: second international workshop, IRREGULAR 95,
Lyon, France, September 4--6, 1995: proceedings}",
volume = "980",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 409",
year = "1995",
CODEN = "LNCSD9",
ISBN = "3-540-60321-2",
ISBN-13 = "978-3-540-60321-4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.642 .I59 1995",
bibdate = "Fri Apr 12 07:41:32 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "computer algorithms --- congresses; parallel
programming (computer science) --- congresses",
xxvolume = "4005092982",
}
@Proceedings{IEEE:1995:PEI,
editor = "{IEEE}",
booktitle = "{Proceedings of the Eighth IEEE Symposium on
Computer-Based Medical Systems / June 9--10, 1995,
Lubbock, Texas}",
title = "{Proceedings of the Eighth IEEE Symposium on
Computer-Based Medical Systems / June 9--10, 1995,
Lubbock, Texas}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 348",
year = "1995",
ISBN = "0-8186-7117-3",
ISBN-13 = "978-0-8186-7117-3",
LCCN = "R858.A2 I155 1995",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "IEEE catalog number 95CH35813.",
acknowledgement = ack-nhfb,
confdate = "9--10 June 1995",
conflocation = "Lubbock, TX, USA",
confsponsor = "IEEE Comput. Soc. Tech. Committee on Comput. Med.;
IEEE South Plains Sect.; SPIE - Int. Soc. Opt. Eng.;
Texas Tech Univ.; Texas Tech Univ. Health Sci. Center",
pubcountry = "USA",
}
@Proceedings{Levelt:1995:IPI,
editor = "A. H. M. Levelt",
booktitle = "{ISSAC '95: Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation: July
10--12, 1995, Montr{\'e}al, Canada}",
title = "{ISSAC '95: Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation: July
10--12, 1995, Montr{\'e}al, Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xviii + 314",
year = "1995",
ISBN = "0-89791-699-9",
ISBN-13 = "978-0-89791-699-8",
LCCN = "QA 76.95 I59 1995",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number: 505950",
series = "ISSAC -PROCEEDINGS- 1995",
abstract = "The following topics were dealt with: differential
equations; visualisation; algebraic numbers;
algorithms; systems; polynomial and differential
algebra; seminumerical methods; greatest common
divisors; and.",
acknowledgement = ack-nhfb,
classification = "C4100 (Numerical analysis); C4170 (Differential
equations); C7310 (Mathematics computing)",
confdate = "10--12 July 1995",
conflocation = "Montr{\'e}al, Que., Canada",
confsponsor = "ACM",
keywords = "algebra --- data processing --- congresses; Algebraic
numbers; Algorithms; Differential algebra; Differential
equations; Greatest common divisors; mathematics ---
data processing --- congresses; Polynomial;
Seminumerical methods; Systems; Visualisation",
pubcountry = "USA",
source = "ISSAC '95",
thesaurus = "Data visualisation; Differential equations; Group
theory; Numerical analysis; Symbol manipulation",
}
@Proceedings{Briot:1996:OBP,
editor = "Jean-Pierre Briot and Jean-Marc Geib and Akinori
Yonezawa",
booktitle = "{Object-based parallel and distributed computation:
France--Japan Workshop, OBPDC '95, Tokyo, Japan, June
21--23, 1995: selected papers}",
title = "{Object-based parallel and distributed computation:
France--Japan Workshop, OBPDC '95, Tokyo, Japan, June
21--23, 1995: selected papers}",
volume = "1107",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 348",
year = "1996",
ISBN = "3-540-61487-7 (softcover)",
ISBN-13 = "978-3-540-61487-6 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.64 .F7 1995",
bibdate = "Sat Dec 21 16:06:37 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
annote = "Data parallel programming in the parallel
object-oriented language OCore / Hiroki Konaka \ldots{}
[et al.] -- Polymorphic matrices in Paladin / Frederic
Guidec and Jean-Marc Jezequel -- Programming and
debugging for massive parallelism: the case for a
parallel object-oriented language A-NETL / Takanobu
Baba, Tsutomu Yoshinaga, and Takahiro Furuta --
Schematic: a concurrent object-oriented extension to
Scheme / Kenjiro Taura and Akinori Yonezawa -- (Thread
and object)-oriented distributed programming /
Jean-Marc Geib \ldots{} [et al.] -- Distributed and
object oriented symbolic programming in April / Keith
L. Clark and Frank G. McCabe -- Reactive programming
Eiffel// / Denis Caromel and Yves Roudier -- Proofs,
concurrent objects, and computations in a FILL
framework / Didier Galmiche and Eric Boudinet --
Modular description and verification of concurrent
objects / Jean-Paul Bahsoun, Stephan Merz, and Corinne
Servieres - - CHORUS/COOL: CHORUS object oriented
technology / Christian Jacquemot, Peter Strarup Jensen,
and Stephane Carrez -- Adaptive operating system design
using reflection / Rodger Lea, Yasuhiko Yokote, and
Jun-ichiro Itoh -- Isatis: a customizable distributed
object-based runtime system / Michel Ban{\^a}tre
\ldots{} [et al.] -- Lessons from designing and
implementing GARF / Rachid Guerraoui, Benoit Garbinato,
and Karim Mazouni -- Design and implementation of DROL
runtime environment on real-time Mach kernel / Kazunori
Takashio, Hidehisa Shitomi, and Mario Tokoro -- ActNet:
the actor model applied to mobile robotic environments
/ Philippe Darche, Pierre-Guillaume Raverdy, and Eric
Commelin -- Component-based programming and application
management with Olan / Luc Bellissard \ldots{} [et al.]
-- The version management architecture of an
object-oriented distributed systems environment: OZ++ /
Michiharu Tsukamoto \ldots{} [et al.] -- Formal
semantics of agent evolution in language Flage /
Yasuyuki Tahara \ldots{} [et al.].",
keywords = "Electronic data processing -- Distributed processing;
Object-oriented programming (Computer science);
Parallel processing (Electronic computers)",
}
@Proceedings{Calmet:1996:DIS,
editor = "Jacques Calmet and Carla Limongelli",
booktitle = "{Design and implementation of symbolic computation
systems: International Symposium, DISCO '96, Karlsruhe,
Germany, September 18--20, 1996: proceedings}",
title = "{Design and implementation of symbolic computation
systems: International Symposium, DISCO '96, Karlsruhe,
Germany, September 18--20, 1996: proceedings}",
volume = "1128",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 356",
year = "1996",
ISBN = "3-540-61697-7 (softcover)",
ISBN-13 = "978-3-540-61697-9 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.9.S88I576 1996",
bibdate = "Thu Mar 12 12:25:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "Automatic theorem proving --- Congresses.; Mathematics
--- Data processing --- Congresses.; System design ---
Congresses.",
}
@Proceedings{LakshmanYN:1996:IPI,
editor = "{Lakshman Y. N.}",
booktitle = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
title = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xvii + 313",
year = "1996",
ISBN = "0-89791-796-0",
ISBN-13 = "978-0-89791-796-4",
LCCN = "QA 76.95 I59 1996",
bibdate = "Thu Mar 12 08:00:14 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
sponsor = "ACM; Special Interest Group in Symbolic and Algebraic
Manipulation (SIGSAM). ACM; Special Interest Group on
Numerical Mathematics (SIGNUM).",
}
@Proceedings{Baral:1997:LPN,
editor = "C. Baral and V. S. Kreinovich and V. Lifschitz and M.
Gelfond",
booktitle = "{Logic programming, non-monotonic reasoning and
reasoning about actions: Symposium --- November 1995,
El Paso, TX}",
title = "{Logic programming, non-monotonic reasoning and
reasoning about actions: Symposium --- November 1995,
El Paso, TX}",
volume = "21(2)",
publisher = "Baltzer Science",
address = "Basel, Switzerland",
pages = "????",
year = "1997",
ISSN = "1012-2443",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "Annals of Mathematics and Artificial Intelligence",
acknowledgement = ack-nhfb,
}
@Proceedings{Kuchlin:1997:PPS,
editor = "Wolfgang W. K{\"u}chlin",
booktitle = "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
proceedings of the 1997 International Symposium on
Symbolic and Algebraic Computation}",
title = "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
proceedings of the 1997 International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 414",
year = "1997",
ISBN = "0-89791-875-4",
ISBN-13 = "978-0-89791-875-6",
LCCN = "QA76.95",
bibdate = "Sat Mar 23 12:41:32 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/258726/",
acknowledgement = ack-nhfb,
}
@Proceedings{Lengauer:1997:EPP,
editor = "Christian Lengauer and Martin Griebl and Sergei
Gorlatch",
booktitle = "{Euro-Par'97, parallel processing: third International
Euro-Par Conference, Passau, Germany, August 26--29,
1997: proceedings}",
title = "{Euro-Par'97, parallel processing: third International
Euro-Par Conference, Passau, Germany, August 26--29,
1997: proceedings}",
volume = "1300",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxx + 1380",
year = "1997",
ISBN = "3-540-63440-1 (paperback)",
ISBN-13 = "978-3-540-63440-9 (paperback)",
LCCN = "QA76.58.I5535 1997",
bibdate = "Mon Aug 25 10:50:15 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "Parallel processing (Electronic computers) --
Congresses.",
}
@Proceedings{Buchberger:1998:YGB,
editor = "Bruno Buchberger and Franz Winkler",
booktitle = "33 years of Gr{\"o}bner bases: Gr{\"o}bner bases and
applications: Conference --- February 1998, Linz,
Austria",
title = "33 years of Gr{\"o}bner bases: Gr{\"o}bner bases and
applications: Conference --- February 1998, Linz,
Austria",
number = "251",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "viii + 552",
year = "1998",
ISBN = "0-521-63298-6",
ISBN-13 = "978-0-521-63298-0",
LCCN = "QA251.3.G76 1998",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "London Mathematical Society Lecture Note Series",
acknowledgement = ack-nhfb,
sponsor = "Research Institute for Symbolic Computation.",
}
@Proceedings{Gloor:1998:IPI,
editor = "Oliver Gloor",
booktitle = "{ISSAC 98: Proceedings of the 1998 International
Symposium on Symbolic and Algebraic Computation, August
13--15, 1998, University of Rostock, Germany}",
title = "{ISSAC 98: Proceedings of the 1998 International
Symposium on Symbolic and Algebraic Computation, August
13--15, 1998, University of Rostock, Germany}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 327",
year = "1998",
ISBN = "1-58113-002-3",
ISBN-13 = "978-1-58113-002-7",
LCCN = "QA155.7.E4 E88 1998",
bibdate = "Wed Sep 16 17:13:58 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Dooley:1999:IJS,
editor = "Sam Dooley",
booktitle = "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
Vancouver, BC, Canada: proceedings of the 1999
International Symposium on Symbolic and Algebraic
Computation}",
title = "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
Vancouver, BC, Canada: proceedings of the 1999
International Symposium on Symbolic and Algebraic
Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 311",
year = "1999",
ISBN = "1-58113-073-2",
ISBN-13 = "978-1-58113-073-7",
LCCN = "QA76.95 .I57 1999",
bibdate = "Sat Mar 11 16:51:59 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Traverso:2000:IAU,
editor = "Carlo Traverso",
booktitle = "{ISSAC 2000: 7--9 August 2000, University of St.
Andrews, Scotland: proceedings of the 2000
International Symposium on Symbolic and Algebraic
Computation}",
title = "{ISSAC 2000: 7--9 August 2000, University of St.
Andrews, Scotland: proceedings of the 2000
International Symposium on Symbolic and Algebraic
Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 309",
year = "2000",
ISBN = "1-58113-218-2",
ISBN-13 = "978-1-58113-218-2",
LCCN = "QA76.95.I59 2000",
bibdate = "Tue Apr 17 09:12:53 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number 505000.",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/345542/",
acknowledgement = ack-nhfb,
}
@Proceedings{Mourrain:2001:IJU,
editor = "Bernard Mourrain",
booktitle = "{ISSAC 2001: July 22--25, 2001, University of Western
Ontario, London, Ontario, Canada: proceedings of the
2001 International Symposium on Symbolic and Algebraic
Computation}",
title = "{ISSAC 2001: July 22--25, 2001, University of Western
Ontario, London, Ontario, Canada: proceedings of the
2001 International Symposium on Symbolic and Algebraic
Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xii + 352",
year = "2001",
ISBN = "1-58113-417-7",
ISBN-13 = "978-1-58113-417-9",
LCCN = "QA76.95.I59 2001",
bibdate = "Wed May 15 14:30:19 2002",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number 505010.",
acknowledgement = ack-nhfb,
}
@Proceedings{Mora:2002:IPI,
editor = "Teo Mora",
booktitle = "{ISSAC 2002: Proceedings of the 2002 International
Symposium on Symbolic and Algebraic Computation, July
07--10, 2002, Universit{\'e} de Lille, Lille, France}",
title = "{ISSAC 2002: Proceedings of the 2002 International
Symposium on Symbolic and Algebraic Computation, July
07--10, 2002, Universit{\'e} de Lille, Lille, France}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xx + 276",
year = "2002",
ISBN = "1-58113-484-3",
ISBN-13 = "978-1-58113-484-1",
LCCN = "QA76.95",
bibdate = "Fri Nov 22 16:20:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.lifl.fr/ISSAC2002/",
acknowledgement = ack-nhfb,
}
@Proceedings{Senda:2003:IPI,
editor = "J. Rafael Senda",
booktitle = "{ISSAC 2003: Proceedings of the 2003 International
Symposium on Symbolic and Algebraic Computation, August
3--6, 2003, Drexel University, Philadelphia, PA, USA}",
title = "{ISSAC 2003: Proceedings of the 2003 International
Symposium on Symbolic and Algebraic Computation, August
3--6, 2003, Drexel University, Philadelphia, PA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 273",
year = "2003",
ISBN = "1-58113-641-2",
ISBN-13 = "978-1-58113-641-8",
LCCN = "QA76.95",
bibdate = "Sat Dec 13 18:18:22 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number 505030.",
acknowledgement = ack-nhfb,
}
@Proceedings{Gutierrez:2004:IJU,
editor = "Jaime Gutierrez",
booktitle = "{ISAAC 2004: July 4--7, 2004, University of Cantabria,
Santander, Spain: proceedings of the 2004 International
Symposium on Symbolic and Algebraic Computation}",
title = "{ISAAC 2004: July 4--7, 2004, University of Cantabria,
Santander, Spain: proceedings of the 2004 International
Symposium on Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xii + 328",
year = "2004",
ISBN = "1-58113-827-X",
ISBN-13 = "978-1-58113-827-6",
LCCN = "QA76.95 .I57 2004",
bibdate = "Fri Oct 21 06:33:01 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Symbolic and Algebraic
Computation (2004 : Santander, Spain)",
}
@Proceedings{Kauers:2005:IJB,
editor = "Manuel Kauers",
booktitle = "{ISSAC '05: July 24--27, 2005, Beijing, China:
Proceedings of the 2005 International Symposium on
Symbolic and Algebraic Computation}",
title = "{ISSAC '05: July 24--27, 2005, Beijing, China:
Proceedings of the 2005 International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiv + 372",
year = "2005",
ISBN = "1-59593-095-7",
ISBN-13 = "978-1-59593-095-8",
LCCN = "????",
bibdate = "Fri Oct 21 07:01:24 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM Order Number 505050.",
acknowledgement = ack-nhfb,
}
@Proceedings{Trager:2006:PIS,
editor = "Barry Trager",
booktitle = "{Proceedings of the 2006 International Symposium on
Symbolic and Algebraic Computation, Genoa, Italy July
09--12, 2006}",
title = "{Proceedings of the 2006 International Symposium on
Symbolic and Algebraic Computation, Genoa, Italy July
09--12, 2006}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2006",
ISBN = "1-59593-276-3",
ISBN-13 = "978-1-59593-276-1",
LCCN = "????",
bibdate = "Wed Aug 23 09:44:27 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number 505060.",
acknowledgement = ack-nhfb,
}
@Proceedings{Brown:2007:PIS,
editor = "C. W. Brown",
booktitle = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
title = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
(CD-ROM)",
LCCN = "QA76.5 S98 2007",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
note = "ACM order number 505070.",
acknowledgement = ack-nhfb,
}
@Proceedings{Jeffrey:2008:PAM,
editor = "David Jeffrey",
booktitle = "{Proceedings of the 21st annual meeting of the
International Symposium on Symbolic Computation, ISSAC
2008, July 20--23, 2008, Hagenberg, Austria}",
title = "{Proceedings of the 21st annual meeting of the
International Symposium on Symbolic Computation, ISSAC
2008, July 20--23, 2008, Hagenberg, Austria}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 338",
year = "2008",
ISBN = "1-59593-904-0",
ISBN-13 = "978-1-59593-904-3",
LCCN = "????",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{May:2009:PIS,
editor = "John P. May",
booktitle = "{Proceedings of the 2009 international symposium on
Symbolic and algebraic computation, KIAS, Seoul, Korea,
July 28--31, 2009}",
title = "{Proceedings of the 2009 international symposium on
Symbolic and algebraic computation, KIAS, Seoul, Korea,
July 28--31, 2009}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xi + 389",
year = "2009",
ISBN = "1-60558-609-9",
ISBN-13 = "978-1-60558-609-0",
LCCN = "????",
bibdate = "Fri Jun 20 08:53:37 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Watt:2010:IPI,
editor = "Stephen M. Watt",
booktitle = "{ISSAC 2010: Proceedings of the 2010 International
Symposium on Symbolic and Algebraic Computation, July
25--28, 2010, Munich, Germany}",
title = "{ISSAC 2010: Proceedings of the 2010 International
Symposium on Symbolic and Algebraic Computation, July
25--28, 2010, Munich, Germany}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiv + 363",
year = "2010",
ISBN = "1-4503-0150-9",
ISBN-13 = "978-1-4503-0150-3",
LCCN = "QA76.95 .I59 2010",
bibdate = "Fri Jun 17 08:11:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Schost:2011:IPI,
editor = "{\'E}ric Schost and Ioannis Z. Emiris",
booktitle = "{ISSAC 2011: Proceedings of the 2011 International
Symposium on Symbolic and Algebraic Computation, June
7--11, 2011, San Jose, CA, USA}",
title = "{ISSAC 2011: Proceedings of the 2011 International
Symposium on Symbolic and Algebraic Computation, June
7--11, 2011, San Jose, CA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "362 (est.)",
year = "2011",
ISBN = "1-4503-0675-6",
ISBN-13 = "978-1-4503-0675-1",
LCCN = "QA76.95 .I59 2011",
bibdate = "Fri Mar 14 12:24:11 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{vanderHoeven:2012:IPI,
editor = "Joris van der Hoeven and Mark van Hoeij",
booktitle = "{ISSAC 2012: Proceedings of the 2012 International
Symposium on Symbolic and Algebraic Computation, July
22--25, 2012, Grenoble, France}",
title = "{ISSAC 2012: Proceedings of the 2012 International
Symposium on Symbolic and Algebraic Computation, July
22--25, 2012, Grenoble, France}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2012",
ISBN = "1-4503-1269-1",
ISBN-13 = "978-1-4503-1269-1",
LCCN = "QA76.95 .I59 2012",
bibdate = "Fri Mar 14 12:24:11 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Monagan:2013:IPI,
editor = "Michael Monagan and Gene Cooperman and Mark
Giesbrecht",
booktitle = "{ISSAC 2013: Proceedings of the 2013 International
Symposium on Symbolic and Algebraic Computation, June
26--29, 2013, Boston, MA, USA}",
title = "{ISSAC 2013: Proceedings of the 2013 International
Symposium on Symbolic and Algebraic Computation, June
26--29, 2013, Boston, MA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "387 (est.)",
year = "2013",
ISBN = "1-4503-2059-7",
ISBN-13 = "978-1-4503-2059-7",
LCCN = "QA76.95 .I59 2013",
bibdate = "Fri Mar 14 12:24:11 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
acknowledgement = ack-nhfb,
}
