@Preamble{"
\ifundefined{emdash}
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@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|https://www.math.utah.edu/~beebe/|"}
@String{pub-AP = "Academic Press"}
@String{pub-AP:adr = "New York, NY, USA"}
@String{pub-CAMBRIDGE = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
@String{pub-CLARENDON = "Clarendon"}
@String{pub-CLARENDON:adr = "New York, NY, USA"}
@String{pub-KLUWER = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht,
The Netherlands"}
@String{pub-SIAM = "SIAM Press"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128"}
@Book{Beebe:2017:MFC,
author = "Nelson H. F. Beebe",
title = "The Mathematical-Function Computation Handbook:
Programming Using the {MathCW} Portable Software
Library",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1114",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-64110-2",
ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
(e-book)",
LCCN = "QA75.5-76.95",
bibdate = "Sat Jul 15 19:34:43 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/mupad.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319641096",
acknowledgement = ack-nhfb,
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
tableofcontents = "List of figures / xxv \\
List of tables / xxxi \\
Quick start / xxxv \\
1: Introduction / 1 \\
1.1: Programming conventions / 2 \\
1.2: Naming conventions / 4 \\
1.3: Library contributions and coverage / 5 \\
1.4: Summary / 6 \\
2: Iterative solutions and other tools / 7 \\
2.1: Polynomials and Taylor series / 7 \\
2.2: First-order Taylor series approximation / 8 \\
2.3: Second-order Taylor series approximation / 9 \\
2.4: Another second-order Taylor series approximation /
9 \\
2.5: Convergence of second-order methods / 10 \\
2.6: Taylor series for elementary functions / 10 \\
2.7: Continued fractions / 12 \\
2.8: Summation of continued fractions / 17 \\
2.9: Asymptotic expansions / 19 \\
2.10: Series inversion / 20 \\
2.11: Summary / 22 \\
3: Polynomial approximations / 23 \\
3.1: Computation of odd series / 23 \\
3.2: Computation of even series / 25 \\
3.3: Computation of general series / 25 \\
3.4: Limitations of Cody\slash Waite polynomials / 28
\\
3.5: Polynomial fits with Maple / 32 \\
3.6: Polynomial fits with Mathematica / 33 \\
3.7: Exact polynomial coefficients / 42 \\
3.8: Cody\slash Waite rational polynomials / 43 \\
3.9: Chebyshev polynomial economization / 43 \\
3.10: Evaluating Chebyshev polynomials / 48 \\
3.11: Error compensation in Chebyshev fits / 50 \\
3.12: Improving Chebyshev fits / 51 \\
3.13: Chebyshev fits in rational form / 52 \\
3.14: Chebyshev fits with Mathematica / 56 \\
3.15: Chebyshev fits for function representation / 57
\\
3.16: Extending the library / 57 \\
3.17: Summary and further reading / 58 \\
4: Implementation issues / 61 \\
4.1: Error magnification / 61 \\
4.2: Machine representation and machine epsilon / 62
\\
4.3: IEEE 754 arithmetic / 63 \\
4.4: Evaluation order in C / 64 \\
4.5: The {\tt volatile} type qualifier / 65 \\
4.6: Rounding in floating-point arithmetic / 66 \\
4.7: Signed zero / 69 \\
4.8: Floating-point zero divide / 70 \\
4.9: Floating-point overflow / 71 \\
4.10: Integer overflow / 72 \\
4.11: Floating-point underflow / 77 \\
4.12: Subnormal numbers / 78 \\
4.13: Floating-point inexact operation / 79 \\
4.14: Floating-point invalid operation / 79 \\
4.15: Remarks on NaN tests / 80 \\
4.16: Ulps --- units in the last place / 81 \\
4.17: Fused multiply-add / 85 \\
4.18: Fused multiply-add and polynomials / 88 \\
4.19: Significance loss / 89 \\
4.20: Error handling and reporting / 89 \\
4.21: Interpreting error codes / 93 \\
4.22: C99 changes to error reporting / 94 \\
4.23: Error reporting with threads / 95 \\
4.24: Comments on error reporting / 95 \\
4.25: Testing function implementations / 96 \\
4.26: Extended data types on Hewlett--Packard HP-UX
IA-64 / 100 \\
4.27: Extensions for decimal arithmetic / 101 \\
4.28: Further reading / 103 \\
4.29: Summary / 104 \\
5: The floating-point environment / 105 \\
5.1: IEEE 754 and programming languages / 105 \\
5.2: IEEE 754 and the mathcw library / 106 \\
5.3: Exceptions and traps / 106 \\
5.4: Access to exception flags and rounding control /
107 \\
5.5: The environment access pragma / 110 \\
5.6: Implementation of exception-flag and
rounding-control access / 110 \\
5.7: Using exception flags: simple cases / 112 \\
5.8: Using rounding control / 115 \\
5.9: Additional exception flag access / 116 \\
5.10: Using exception flags: complex case / 120 \\
5.11: Access to precision control / 123 \\
5.12: Using precision control / 126 \\
5.13: Summary / 127 \\
6: Converting floating-point values to integers / 129
\\
6.1: Integer conversion in programming languages / 129
\\
6.2: Programming issues for conversions to integers /
130 \\
6.3: Hardware out-of-range conversions / 131 \\
6.4: Rounding modes and integer conversions / 132 \\
6.5: Extracting integral and fractional parts / 132 \\
6.6: Truncation functions / 135 \\
6.7: Ceiling and floor functions / 136 \\
6.8: Floating-point rounding functions with fixed
rounding / 137 \\
6.9: Floating-point rounding functions: current
rounding / 138 \\
6.10: Floating-point rounding functions without {\em
inexact\/} exception / 139 \\
6.11: Integer rounding functions with fixed rounding /
140 \\
6.12: Integer rounding functions with current rounding
/ 142 \\
6.13: Remainder / 143 \\
6.14: Why the remainder functions are hard / 144 \\
6.15: Computing {\tt fmod} / 146 \\
6.16: Computing {\tt remainder} / 148 \\
6.17: Computing {\tt remquo} / 150 \\
6.18: Computing one remainder from the other / 152 \\
6.19: Computing the remainder in nonbinary bases / 155
\\
6.20: Summary / 156 \\
7: Random numbers / 157 \\
7.1: Guidelines for random-number software / 157 \\
7.2: Creating generator seeds / 158 \\
7.3: Random floating-point values / 160 \\
7.4: Random integers from floating-point generator /
165 \\
7.5: Random integers from an integer generator / 166
\\
7.6: Random integers in ascending order / 168 \\
7.7: How random numbers are generated / 169 \\
7.8: Removing generator bias / 178 \\
7.9: Improving a poor random number generator / 178 \\
7.10: Why long periods matter / 179 \\
7.11: Inversive congruential generators / 180 \\
7.12: Inversive congruential generators, revisited /
189 \\
7.13: Distributions of random numbers / 189 \\
7.14: Other distributions / 195 \\
7.15: Testing random-number generators / 196 \\
7.16: Applications of random numbers / 202 \\
7.17: The \textsf {mathcw} random number routines / 208
\\
7.18: Summary, advice, and further reading / 214 \\
8: Roots / 215 \\
8.1: Square root / 215 \\
8.2: Hypotenuse and vector norms / 222 \\
8.3: Hypotenuse by iteration / 227 \\
8.4: Reciprocal square root / 233 \\
8.5: Cube root / 237 \\
8.6: Roots in hardware / 240 \\
8.7: Summary / 242 \\
9: Argument reduction / 243 \\
9.1: Simple argument reduction / 243 \\
9.2: Exact argument reduction / 250 \\
9.3: Implementing exact argument reduction / 253 \\
9.4: Testing argument reduction / 265 \\
9.5: Retrospective on argument reduction / 265 \\
10: Exponential and logarithm / 267 \\
10.1: Exponential functions / 267 \\
10.2: Exponential near zero / 273 \\
10.3: Logarithm functions / 282 \\
10.4: Logarithm near one / 290 \\
10.5: Exponential and logarithm in hardware / 292 \\
10.6: Compound interest and annuities / 294 \\
10.7: Summary / 298 \\
11: Trigonometric functions / 299 \\
11.1: Sine and cosine properties / 299 \\
11.2: Tangent properties / 302 \\
11.3: Argument conventions and units / 304 \\
11.4: Computing the cosine and sine / 306 \\
11.5: Computing the tangent / 310 \\
11.6: Trigonometric functions in degrees / 313 \\
11.7: Trigonometric functions in units of $ \pi $ / 315
\\
11.8: Computing the cosine and sine together / 320 \\
11.9: Inverse sine and cosine / 323 \\
11.10: Inverse tangent / 331 \\
11.11: Inverse tangent, take two / 336 \\
11.12: Trigonometric functions in hardware / 338 \\
11.13: Testing trigonometric functions / 339 \\
11.14: Retrospective on trigonometric functions / 340
\\
12: Hyperbolic functions / 341 \\
12.1: Hyperbolic functions / 341 \\
12.2: Improving the hyperbolic functions / 345 \\
12.3: Computing the hyperbolic functions together / 348
\\
12.4: Inverse hyperbolic functions / 348 \\
12.5: Hyperbolic functions in hardware / 350 \\
12.6: Summary / 352 \\
13: Pair-precision arithmetic / 353 \\
13.1: Limitations of pair-precision arithmetic / 354
\\
13.2: Design of the pair-precision software interface /
355 \\
13.3: Pair-precision initialization / 356 \\
13.4: Pair-precision evaluation / 357 \\
13.5: Pair-precision high part / 357 \\
13.6: Pair-precision low part / 357 \\
13.7: Pair-precision copy / 357 \\
13.8: Pair-precision negation / 358 \\
13.9: Pair-precision absolute value / 358 \\
13.10: Pair-precision sum / 358 \\
13.11: Splitting numbers into pair sums / 359 \\
13.12: Premature overflow in splitting / 362 \\
13.13: Pair-precision addition / 365 \\
13.14: Pair-precision subtraction / 367 \\
13.15: Pair-precision comparison / 368 \\
13.16: Pair-precision multiplication / 368 \\
13.17: Pair-precision division / 371 \\
13.18: Pair-precision square root / 373 \\
13.19: Pair-precision cube root / 377 \\
13.20: Accuracy of pair-precision arithmetic / 379 \\
13.21: Pair-precision vector sum / 384 \\
13.22: Exact vector sums / 385 \\
13.23: Pair-precision dot product / 385 \\
13.24: Pair-precision product sum / 386 \\
13.25: Pair-precision decimal arithmetic / 387 \\
13.26: Fused multiply-add with pair precision / 388 \\
13.27: Higher intermediate precision and the FMA / 393
\\
13.28: Fused multiply-add without pair precision / 395
\\
13.29: Fused multiply-add with multiple precision / 401
\\
13.30: Fused multiply-add, Boldo/\penalty
\exhyphenpenalty Melquiond style / 403 \\
13.31: Error correction in fused multiply-add / 406 \\
13.32: Retrospective on pair-precision arithmetic / 407
\\
14: Power function / 411 \\
14.1: Why the power function is hard to compute / 411
\\
14.2: Special cases for the power function / 412 \\
14.3: Integer powers / 414 \\
14.4: Integer powers, revisited / 420 \\
14.5: Outline of the power-function algorithm / 421 \\
14.6: Finding $a$ and $p$ / 423 \\
14.7: Table searching / 424 \\
14.8: Computing $\log_n(g/a)$ / 426 \\
14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
14.10: Exact products / 430 \\
14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
14.12: Computing $n^{w_2}$ / 437 \\
14.13: The choice of $q$ / 438 \\
14.14: Testing the power function / 438 \\
14.15: Retrospective on the power function / 440 \\
15: Complex arithmetic primitives / 441 \\
15.1: Support macros and type definitions / 442 \\
15.2: Complex absolute value / 443 \\
15.3: Complex addition / 445 \\
15.4: Complex argument / 445 \\
15.5: Complex conjugate / 446 \\
15.6: Complex conjugation symmetry / 446 \\
15.7: Complex conversion / 448 \\
15.8: Complex copy / 448 \\
15.9: Complex division: C99 style / 449 \\
15.10: Complex division: Smith style / 451 \\
15.11: Complex division: Stewart style / 452 \\
15.12: Complex division: Priest style / 453 \\
15.13: Complex division: avoiding subtraction loss /
455 \\
15.14: Complex imaginary part / 456 \\
15.15: Complex multiplication / 456 \\
15.16: Complex multiplication: error analysis / 458 \\
15.17: Complex negation / 459 \\
15.18: Complex projection / 460 \\
15.19: Complex real part / 460 \\
15.20: Complex subtraction / 461 \\
15.21: Complex infinity test / 462 \\
15.22: Complex NaN test / 462 \\
15.23: Summary / 463 \\
16: Quadratic equations / 465 \\
16.1: Solving quadratic equations / 465 \\
16.2: Root sensitivity / 471 \\
16.3: Testing a quadratic-equation solver / 472 \\
16.4: Summary / 474 \\
17: Elementary functions in complex arithmetic / 475
\\
17.1: Research on complex elementary functions / 475
\\
17.2: Principal values / 476 \\
17.3: Branch cuts / 476 \\
17.4: Software problems with negative zeros / 478 \\
17.5: Complex elementary function tree / 479 \\
17.6: Series for complex functions / 479 \\
17.7: Complex square root / 480 \\
17.8: Complex cube root / 485 \\
17.9: Complex exponential / 487 \\
17.10: Complex exponential near zero / 492 \\
17.11: Complex logarithm / 495 \\
17.12: Complex logarithm near one / 497 \\
17.13: Complex power / 500 \\
17.14: Complex trigonometric functions / 502 \\
17.15: Complex inverse trigonometric functions / 504
\\
17.16: Complex hyperbolic functions / 509 \\
17.17: Complex inverse hyperbolic functions / 514 \\
17.18: Summary / 520 \\
18: The Greek functions: gamma, psi, and zeta / 521 \\
18.1: Gamma and log-gamma functions / 521 \\
18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
18.3: Polygamma functions / 547 \\
18.4: Incomplete gamma functions / 560 \\
18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
18.6: An Italian excursion: Fibonacci numbers / 575 \\
18.7: A German gem: the Riemann zeta function / 579 \\
18.8: Further reading / 590 \\
18.9: Summary / 591 \\
19: Error and probability functions / 593 \\
19.1: Error functions / 593 \\
19.2: Scaled complementary error function / 598 \\
19.3: Inverse error functions / 600 \\
19.4: Normal distribution functions and inverses / 610
\\
19.5: Summary / 617 \\
20: Elliptic integral functions / 619 \\
20.1: The arithmetic-geometric mean / 619 \\
20.2: Elliptic integral functions of the first kind /
624 \\
20.3: Elliptic integral functions of the second kind /
627 \\
20.4: Elliptic integral functions of the third kind /
630 \\
20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
20.7: Historical algorithms for elliptic integrals /
643 \\
20.8: Auxiliary functions for elliptic integrals / 645
\\
20.9: Computing the elliptic auxiliary functions / 648
\\
20.10: Historical elliptic functions / 650 \\
20.11: Elliptic functions in software / 652 \\
20.12: Applications of elliptic auxiliary functions /
653 \\
20.13: Elementary functions from elliptic auxiliary
functions / 654 \\
20.14: Computing elementary functions via $R_C(x,y)$ /
655 \\
20.15: Jacobian elliptic functions / 657 \\
20.16: Inverses of Jacobian elliptic functions / 664
\\
20.17: The modulus and the nome / 668 \\
20.18: Jacobian theta functions / 673 \\
20.19: Logarithmic derivatives of the Jacobian theta
functions / 675 \\
20.20: Neville theta functions / 678 \\
20.21: Jacobian Eta, Theta, and Zeta functions / 679
\\
20.22: Weierstrass elliptic functions / 682 \\
20.23: Weierstrass functions by duplication / 689 \\
20.24: Complete elliptic functions, revisited / 690 \\
20.25: Summary / 691 \\
21: Bessel functions / 693 \\
21.1: Cylindrical Bessel functions / 694 \\
21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
21.4: Experiments with recurrences for $J_0(x)$ / 705
\\
21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
21.6: Computing $J_n(x)$ / 710 \\
21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
21.8: Computing $Y_n(x)$ / 715 \\
21.9: Improving Bessel code near zeros / 716 \\
21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
21.14: Properties of spherical Bessel functions / 731
\\
21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
21.17: Modified spherical Bessel functions / 743 \\
21.18: Software for Bessel-function sequences / 755 \\
21.19: Retrospective on Bessel functions / 761 \\
22: Testing the library / 763 \\
22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
22.4: Testing cylindrical Bessel functions / 769 \\
22.5: Testing exponent/\penalty \exhyphenpenalty
significand manipulation / 769 \\
22.6: Testing inline assembly code / 769 \\
22.7: Testing with Maple / 770 \\
22.8: Testing floating-point arithmetic / 773 \\
22.9: The Berkeley Elementary Functions Test Suite /
774 \\
22.10: The AT\&T floating-point test package / 775 \\
22.11: The Antwerp test suite / 776 \\
22.12: Summary / 776 \\
23: Pair-precision elementary functions / 777 \\
23.1: Pair-precision integer power / 777 \\
23.2: Pair-precision machine epsilon / 779 \\
23.3: Pair-precision exponential / 780 \\
23.4: Pair-precision logarithm / 787 \\
23.5: Pair-precision logarithm near one / 793 \\
23.6: Pair-precision exponential near zero / 793 \\
23.7: Pair-precision base-$n$ exponentials / 795 \\
23.8: Pair-precision trigonometric functions / 796 \\
23.9: Pair-precision inverse trigonometric functions /
801 \\
23.10: Pair-precision hyperbolic functions / 804 \\
23.11: Pair-precision inverse hyperbolic functions /
808 \\
23.12: Summary / 808 \\
24: Accuracy of the Cody\slash Waite algorithms / 811
\\
25: Improving upon the Cody\slash Waite algorithms /
823 \\
25.1: The Bell Labs libraries / 823 \\
25.2: The {Cephes} library / 823 \\
25.3: The {Sun} libraries / 824 \\
25.4: Mathematical functions on EPIC / 824 \\
25.5: The GNU libraries / 825 \\
25.6: The French libraries / 825 \\
25.7: The NIST effort / 826 \\
25.8: Commercial mathematical libraries / 826 \\
25.9: Mathematical libraries for decimal arithmetic /
826 \\
25.10: Mathematical library research publications / 826
\\
25.11: Books on computing mathematical functions / 827
\\
25.12: Summary / 828 \\
26: Floating-point output / 829 \\
26.1: Output character string design issues / 830 \\
26.2: Exact output conversion / 831 \\
26.3: Hexadecimal floating-point output / 832 \\
26.4: Octal floating-point output / 850 \\
26.5: Binary floating-point output / 851 \\
26.6: Decimal floating-point output / 851 \\
26.7: Accuracy of output conversion / 865 \\
26.8: Output conversion to a general base / 865 \\
26.9: Output conversion of Infinity / 866 \\
26.10: Output conversion of NaN / 866 \\
26.11: Number-to-string conversion / 867 \\
26.12: The {\tt printf} family / 867 \\
26.13: Summary / 878 \\
27: Floating-point input / 879 \\
27.1: Binary floating-point input / 879 \\
27.2: Octal floating-point input / 894 \\
27.3: Hexadecimal floating-point input / 895 \\
27.4: Decimal floating-point input / 895 \\
27.5: Based-number input / 899 \\
27.6: General floating-point input / 900 \\
27.7: The {\tt scanf} family / 901 \\
27.8: Summary / 910 \\
A: Ada interface / 911 \\
A.1: Building the Ada interface / 911 \\
A.2: Programming the Ada interface / 912 \\
A.3: Using the Ada interface / 915 \\
B: C\# interface / 917 \\
B.1: C\# on the CLI virtual machine / 917 \\
B.2: Building the C\# interface / 918 \\
B.3: Programming the C\# interface / 920 \\
B.4: Using the C\# interface / 922 \\
C: C++ interface / 923 \\
C.1: Building the C++ interface / 923 \\
C.2: Programming the C++ interface / 924 \\
C.3: Using the C++ interface / 925 \\
D: Decimal arithmetic / 927 \\
D.1: Why we need decimal floating-point arithmetic /
927 \\
D.2: Decimal floating-point arithmetic design issues /
928 \\
D.3: How decimal and binary arithmetic differ / 931 \\
D.4: Initialization of decimal floating-point storage /
935 \\
D.5: The {\tt <decfloat.h>} header file / 936 \\
D.6: Rounding in decimal arithmetic / 936 \\
D.7: Exact scaling in decimal arithmetic / 937 \\
E: Errata in the Cody\slash Waite book / 939 \\
F: Fortran interface / 941 \\
F.1: Building the Fortran interface / 943 \\
F.2: Programming the Fortran interface / 944 \\
F.3: Using the Fortran interface / 945 \\
H: Historical floating-point architectures / 947 \\
H.1: CDC family / 949 \\
H.2: Cray family / 952 \\
H.3: DEC PDP-10 / 953 \\
H.4: DEC PDP-11 and VAX / 956 \\
H.5: General Electric 600 series / 958 \\
H.6: IBM family / 959 \\
H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
H.8: Unusual floating-point systems / 966 \\
H.9: Historical retrospective / 967 \\
I: Integer arithmetic / 969 \\
I.1: Memory addressing and integers / 971 \\
I.2: Representations of signed integers / 971 \\
I.3: Parity testing / 975 \\
I.4: Sign testing / 975 \\
I.5: Arithmetic exceptions / 975 \\
I.6: Notations for binary numbers / 977 \\
I.7: Summary / 978 \\
J: Java interface / 979 \\
J.1: Building the Java interface / 979 \\
J.2: Programming the Java MathCW class / 980 \\
J.3: Programming the Java C interface / 982 \\
J.4: Using the Java interface / 985 \\
L: Letter notation / 987 \\
P: Pascal interface / 989 \\
P.1: Building the Pascal interface / 989 \\
P.2: Programming the Pascal MathCW module / 990 \\
P.3: Using the Pascal module interface / 993 \\
P.4: Pascal and numeric programming / 994 \\
Bibliography / 995 \\
Author/editor index / 1039 \\
Function and macro index / 1049 \\
Subject index / 1065 \\
Colophon / 1115",
}
@Book{Brackx:1992:CAL,
author = "F. Brackx and D. Constales",
title = "Computer algebra with {LISP} and {REDUCE}: an
introduction to computer-aided pure mathematics",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xi + 264",
year = "1992",
ISBN = "0-7923-1441-7",
ISBN-13 = "978-0-7923-1441-7",
LCCN = "QA155.7.E4 B72 199",
bibdate = "Wed Feb 15 14:23:35 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Davenport:1988:CAS,
author = "J. H. Davenport and Y. Siret and E. Tournier",
title = "Computer Algebra, Systems and Algorithms for Algebraic
Computation",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xix + 267",
year = "1988",
ISBN = "0-12-204230-1",
ISBN-13 = "978-0-12-204230-0",
LCCN = "QA155.7.E4 D39 1988",
bibdate = "Wed Feb 15 14:27:34 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
}
@Book{Davenport:1993:CAS,
author = "J. H. Davenport and Y. Siret and E. Tournier",
title = "Computer Algebra, Systems and Algorithms for Algebraic
Computation",
publisher = pub-AP,
address = pub-AP:adr,
edition = "Second",
pages = "??",
year = "1993",
ISBN = "0-12-204230-1",
ISBN-13 = "978-0-12-204230-0",
bibdate = "Wed Feb 15 14:25:34 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "Translated from the French by A. Davenport and J. H.
Davenport. Also available in French and Russian.",
acknowledgement = ack-nhfb,
}
@TechReport{Flatau:1988:SAA,
author = "Piotr J. Flatau and John P. Boyd and William R.
Cotton",
title = "Symbolic Algebra in Applied Mathematics and
Geophysical Fluid Dynamics\emdash {REDUCE} Examples",
number = "Version 1.1",
institution = "Department of Atmospheric Science, Colorado State
University",
address = "Fort Collins, CO 80521, USA",
year = "1988",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
}
@Book{Grozin:1997:URH,
author = "A. G. Grozin",
title = "Using {REDUCE} in high energy physics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiv + 384",
year = "1997",
DOI = "https://doi.org/10.1017/CBO9780511524400",
ISBN = "0-521-01952-4, 0-521-56002-0 (hardcover)",
ISBN-13 = "978-0-521-01952-1, 978-0-521-56002-3 (hardcover)",
LCCN = "QC793.3.H5 G76 1997",
MRclass = "81-04",
MRnumber = "1437601 (98j:81002)",
MRreviewer = "T. C. Mohan",
bibdate = "Sat Sep 13 16:02:50 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "English translation of an original Russian edition.",
URL = "http://www.inp.nsk.su/persons/A_G_Grozin/book/",
acknowledgement = ack-nhfb,
keywords = "Reduce computer-algebra system",
tableofcontents = "\\
Preface \\
Part I. REDUCE Language \\
1. Welcome to REDUCE \\
2. Functions and substitutions \\
3. REDUCE as a programming language \\
4. Additional facilities \\
5. Matrices, vectors, tensors, operators \\
6. Input-output \\
7. Examples \\
Part II. Selected Problems In Classical Physics \\
1. The classical nonlinear operator \\
2. Nonlinear water waves \\
3. Calculation of the curvature tensor \\
4. Examples \\
Part III. Quantum Mechanics \\
1. Adding angular momenta \\
2. The quantum nonlinear oscillator \\
3. A rotator in a weak field \\
4. Radiative transitions in charmonium \\
5. Examples \\
Part IV. Quantum Electrodynamics \\
1. Kinematics \\
2. Fields \\
3. Feynman diagrams \\
4. Scattering in an external field \\
5. Charged particle scattering \\
6. Photon-electron scattering \\
7. Positronium annihilation \\
Part V. Weak Interactions \\
1. Electroweak interaction \\
2. W and Z decays \\
3. Weak decays \\
4. W production \\
Part VI. Quantum Chromodynamics \\
1. Feynman diagrams in QCD \\
2. e+e- annihilation into hadrons \\
3. Charmonium decays \\
4. Quark and gluon scattering \\
Part VII. Radiative Corrections \\
1. Dimensional regularization and renormalization \\
2. Radiative corrections in quantum electrodynamics \\
3. Radiative corrections in quantum chromodynamics \\
References \\
Index",
}
@Book{Grozin:2005:URH,
author = "A. G. Grozin",
title = "Using {REDUCE} in high energy physics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 384",
year = "2005",
ISBN = "0-521-01952-4 (paperback)",
ISBN-13 = "978-0-521-01952-1 (paperback)",
LCCN = "QC793.3.H5 G76 2005",
bibdate = "Mon Sep 4 10:47:00 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/redextra.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0632/2006272924-d.html;
http://www.loc.gov/catdir/enhancements/fy0632/2006272924-t.html",
acknowledgement = ack-nhfb,
remark = "Originally published in \cite{Grozin:1997:URH}.",
subject = "Particles (Nuclear physics); Data processing; REDUCE",
}
@TechReport{Hearn:1987:RUM,
author = "Anthony C. Hearn",
title = "{REDUCE User's Manual, Version 3.3}",
number = "CP 78",
institution = "Rand Corporation",
address = "Santa Monica, CA, USA",
month = jul,
year = "1987",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "Also available in a Japanese translation by Hiroshi
Toshima from McGraw Hill Japan, 1988.",
}
@TechReport{Hearn:1993:RUM,
author = "Anthony C. Hearn",
title = "{REDUCE User's Manual, Version 3.5}",
number = "CP 78",
institution = "Rand Corporation",
address = "Santa Monica, CA, USA",
month = oct,
year = "1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "Also available in a Japanese translation by Hiroshi
Toshima from McGraw Hill Japan, 1988.",
}
@Book{Hehl:1992:CAK,
author = "F. W. Hehl and V. Winkelmann and H. Meyer",
title = "{Computer-Algebra. Ein Kompaktkurs {\"u}ber die
Anwendung von REDUCE}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??",
year = "1992",
ISBN = "3-540-55724-5",
ISBN-13 = "978-3-540-55724-1",
bibdate = "Wed Feb 15 14:28:42 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Hehl:1993:RKA,
author = "Friedrich W. Hehl and Volker Winkelmann and Hartmut
Meyer",
title = "{Reduce: Ein Kompaktkurs {\"u}ber die Anwendung von
Computer-Algebra}. ({German}) [{Reduce}: a compact
course on the use of computer algebra]",
language = "German",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
year = "1993",
ISBN = "3-642-78227-2, 3-540-56705-4 (print)",
ISBN-13 = "978-3-642-78227-5, 978-3-540-56705-9 (print)",
LCCN = "QD39.3.E46",
bibdate = "Mon Sep 4 10:48:18 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
URL = "http://link.springer.com/openurl?genre=book\%26isbn=978-3-540-56705-9;
http://link.springer.com/10.1007/978-3-642-78227-5",
acknowledgement = ack-nhfb,
language = "German",
subject = "Chemistry; Algebra; Data processing; Mathematical
physics; Engineering mathematics; Computer Applications
in Chemistry; Mathematical Methods in Physics;
Numerical and Computational Physics; Appl.
Mathematics/Computational Methods of Engineering;
Theoretical and Computational Chemistry; Symbolic and
Algebraic Manipulation; Data processing.; Chemistry.;
Engineering mathematics.; Mathematical physics.",
tableofcontents = "1 Erste Vorlesung \\
1.1 Eine erste interaktive Reduce-Sitzung \\
1.2 Was kann CA f{\"u}r Sie tun? \\
1.3 Der Reduce-Zeichensatz \\
1.4 Ganze, rationale und reelle Zahlen \\
1.5 Variablen und ihre Bezeichner \\
1.6 Ein Reduce-Programm \\
eine Abfolge von Befehlen \\
1.7 Ergebnisse auf Variablen zuweisen \\
1.8 Zugriff auf alte Ein- und Ausgaben \\
1.9 Hausaufgaben \\
2 Zweite Vorlesung \\
2.1 In Reduce eingebaute Operatoren \\
2.2 Reduce-Ausdr{\"u}cke \\
2.3 Wie Reduce Ausdr{\"u}cke auswertet \\
2.4 Schleifen f{\"u}r wiederholte Anweisungen \\
2.5 Schleifen und Listen \\
2.6 Mehrdimensionale Objekte: Felder \\
2.7 Hausaufgaben \\
3 Dritte Vorlesung \\
3.1 Die IF-Anweisung \\
3.2 Mehrere Anweisungen zusammenfassen: I.
Gruppenanweisung \\
3.3 Mehrere Anweisungen zusammenfassen: IL
Blockanweisung \\
3.4 Elementare mathematische Punktionen \\
3.5 Differentiation mit dem DF-Operator \\
3.6 Integration mit dem INT-Operator \\
3.7 Substitution mit SUB und Regel-Listen \\
3.8 Hausaufgaben \\
4 Vierte Vorlesung \\
4.1 Operatoren, die auf Listen wirken \\
4.2 Jede Gleichung hat zwei Seiten \\
4.3 L{\"o}sen von (nicht- )linearen Gleichungen \\
4.4 Zerlegen von Polynomen und rationalen Punktionen
\\
4.5 Den Programmablauf mit logischen Operatoren steuern
\\
4.6 Mitteilungen schreiben \\
4.7 Wie Sie Ihre eigenen Operatoren definieren \\
4.8 Regel-Listen und LET-Anweisung \\
4.9 Hausaufgaben \\
5 F{\"u}nfte Vorlesung \\
5.1 Regel-Listen aktivieren und deaktivieren \\
5.2 Mehr {\"u}ber Regel-Listen \\
5.3 Beispiele: Fakult{\"a}t und Binomialkoeffizienten
\\
5.4 L{\"o}schen selbstdefinierter Regeln \\
5.5 Kommutative, nichtkommutative, symmetrische und
antisymmetrische Operatoren \\
5.6 Prozeduren f{\"u}r wiederholten Gebrauch von
Befehlen \\
5.7 Eine Prozedur f{\"u}r die l'Hospital-Regel und ein
Wort der Vorsicht \\
5.8 Hausaufgaben \\
6 Sechste Vorlesung \\
6.1 Rechnen mit Matrizen \\
6.2 Schalter ein- und ausschalten \\
6.3 Ausdr{\"u}cke umordnen \\
6.4 Ein- und Ausgaben in Reduce \\
6.5 Fortran-Programme erzeugen \\
6.6 Abschlie{\ss}ende Bemerkungen \\
6.7 Hausaufgaben \\
7 Siebte Vorlesung \\
7.1 Vektor- und Tensorrechnung \\
7.2 Pakete f{\"u}r 3-dimensionale Vektoralgebra und
Vektoranalysis \\
7.3 Tensoranalysis, Christoffel-Symbole, Allgemeine
Relativit{\"a}t \\
7.4 Das EXCALC-Paket f{\"u}r {\"a}u{\ss}ere
Differentialformen \\
7.5 Grafikausgabe mit Gnuplot \\
7.6 Hausaufgaben \\
A Einige zus{\"a}tzliche {\"U}bungsaufgaben \\
B Unterschiede zwischen Reduce 3.3 und Reduce 3.4 \\
C Weitere Informationen zu Reduce \\
C.1 Wo k{\"o}nnen Sie Reduce kaufen? \\
C.2 Ausf{\"u}hrungszeiten f{\"u}r den
Reduce-Standardtest \\
D Literatur",
}
@Book{Hirota:1989:IRD,
author = "Ryogo Hirota and Masaaki Ito",
title = "Introduction to {REDUCE} --- Doing Symbolic
Computation on {PC}",
publisher = "Science sha",
address = "Tokyo, Japan",
month = jun,
year = "1989",
bibdate = "Wed Feb 15 14:30:44 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "In Japanese.",
}
@Proceedings{MacCallum:1991:ACR,
editor = "Malcolm A. H. MacCallum and Francis J. Wright",
booktitle = "{Algebraic computing with REDUCE: lecture notes from
the First Brazilian School on Computer Algebra}",
title = "{Algebraic computing with REDUCE: lecture notes from
the First Brazilian School on Computer Algebra}",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xx + 294",
year = "1991",
ISBN = "0-19-853444-2 (hardcover), 0-19-853443-4 (paperback)",
ISBN-13 = "978-0-19-853444-0 (hardcover), 978-0-19-853443-3
(paperback)",
LCCN = "QA155.7.E4 B73 1989",
bibdate = "Wed Feb 15 14:31:51 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
abstract = "REDUCE is one of the most widely available and simple
to use computer algebra systems. It enables users to
manipulate complex algebraic expressions and equations
symbolically just as mathematicians and scientists do
traditionally on paper, and its capabilities include
differentiation and exact symbolic integration. This
book provides a comprehensive introduction to REDUCE
from starting to run it through to using some of the
user-contributed REDUCE packages written for specific
applications. The authors' aim is to enable all
students using REDUCE for the first time to gain a
familiarity with the full range of REDUCE commands
while at the same time learning something of the
internal workings of REDUCE. Throughout, numerous
exercises are provided to illustrate themes covered in
the text as well as to encourage ``hands on'' working
with REDUCE. Both authors are expert users of REDUCE
and the text is based on their many years of teaching
the system to undergraduate and graduate students. As a
result, all those coming to use REDUCE for the first
time will find this an invaluable tutor and guide. For
more advanced users, it covers a number of aspects not
included in the REDUCE manual.",
acknowledgement = ack-nhfb,
tableofcontents = "1. REDUCE as an Algebraic Calculator \\
2. Controlling REDUCE; Operators and Matrices \\
3. REDUCE as an Algebraic Programming Language \\
4. Algebraic Procedures, Operators and Algorithms \\
5. A Look Inside REDUCE \\
6. Programming in (R) Lisp \\
7. Factorization and Integration in REDUCE \\
8. The User-Contributed REDUCE Packages \\
9. Advanced Topics",
}
@Book{Marti:1993:REA,
author = "Jed B. Marti",
title = "{RLISP} '88: An Evolutionary Approach to Program
Design and Reuse",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xiii + 254",
year = "1993",
ISBN = "981-02-1479-0",
ISBN-13 = "978-981-02-1479-1",
LCCN = "QA76.3.L23 M3 1993",
bibdate = "Wed Feb 15 16:06:09 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Nakamura:1989:SCS,
author = "Hideharu Nakamura and Shouichi Matsui",
title = "Symbolic Computation in Structural Mechanics using
{REDUCE}",
publisher = "Gihodo Shuppan",
address = "Tokyo, Japan",
year = "1989",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "In Japanese.",
}
@Book{Ochiai:1990:LAU,
author = "Mitsuyuki Ochiai and Kiyokazu Nagatomo",
title = "Linear Algebra using {REDUCE}",
publisher = "Kindai Kagaku sha",
month = jan,
year = "1990",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "In Japanese.",
}
@Book{Rayna:1987:RSA,
author = "Gerhard Rayna",
title = "{REDUCE}\emdash Software for Algebraic Computation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 329",
year = "1987",
ISBN = "0-387-96598-X (New York), 3-540-96598-X (Berlin)",
ISBN-13 = "978-0-387-96598-7 (New York), 978-3-540-96598-5
(Berlin)",
LCCN = "QA155.7.E4 R39 1987",
bibdate = "Wed Feb 15 15:34:33 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Steeb:1992:CFA,
author = "Willi-Hans Steeb and Michael Antonie van Wyk",
title = "Chaos and Fractals: Algorithms and Computations",
publisher = "BI-Wissenschaftsverlag",
address = "Mannheim, Germany",
pages = "177",
year = "1992",
ISBN = "3-411-15961-8",
ISBN-13 = "978-3-411-15961-1",
LCCN = "QA614.86 .S73 1992",
bibdate = "Wed Feb 15 15:34:54 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "This book includes 26 Turbo C and C++, 47 Turbo
PASCAL, and 23 REDUCE programs.",
acknowledgement = ack-nhfb,
}
@Book{Steeb:1992:ACR,
author = "Willi-Hans Steeb and Dirk Lewien",
title = "Algorithms and Computation with {REDUCE}",
publisher = "BI-Wissenschaftsverlag",
address = "Mannheim, Germany",
pages = "153",
year = "1992",
ISBN = "3-411-15651-1",
ISBN-13 = "978-3-411-15651-1",
bibdate = "Wed Feb 15 16:00:31 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
note = "This book gives a collection of 75 standard methods in
mathematics, physics and engineering together with
their programs in REDUCE 3.4. Each item consists of a
one page mathematical description and one page REDUCE
algebraic source text (in most cases a few lines only).
The book is an introduction by example to algebraic
programming in REDUCE and a collection of ready to use
solutions for many mathematical subtasks.",
acknowledgement = ack-nhfb,
}
@Book{Steeb:1994:QMU,
author = "Willi-Hans Steeb",
title = "Quantum mechanics using computer algebra: includes
sample programs for {REDUCE}, {MAPLE}, {MATHEMATICA}
and {C++}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "viii + 189",
year = "1994",
ISBN = "981-02-1770-6",
ISBN-13 = "978-981-02-1770-9",
LCCN = "QC174.17.D37 S74 1994",
bibdate = "Wed Feb 15 15:58:54 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Ueberberg:1992:ECR,
author = "Johannes Ueberberg",
title = "{Einf{\"u}hrung in die Computeralgebra mit REDUCE}.
({German}) [{Introduction} to computer algebra with
{REDUCE}]",
publisher = "BI-Wissenschaftsverlag",
address = "Mannheim, Germany",
pages = "331",
year = "1992",
ISBN = "3-411-15781-X",
ISBN-13 = "978-3-411-15781-5",
LCCN = "",
MRclass = "68-01, 68W30",
bibdate = "Wed Feb 15 16:02:34 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Winkelmann:1988:RBS,
author = "Volker Winkelmann and Friedrich W. Hehl",
editor = "D. Stauffer and F. W. Hehl and V. Winkelmann and J. G.
Zabolitzky",
booktitle = "Computer Simulation and Computer Algebra. Lectures for
Beginners",
title = "{REDUCE for Beginners, Six Lectures on the Application
of Computer Algebra}",
publisher = pub-SV,
address = pub-SV:adr,
year = "1988",
ISBN = "0-387-96598-X (New York), 3-540-96598-X (Berlin)",
ISBN-13 = "978-0-387-96598-7 (New York), 978-3-540-96598-5
(Berlin)",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
}
@InProceedings{Winkelmann:1993:RBS,
author = "Volker Winkelmann and Friedrich W. Hehl",
title = "{REDUCE for Beginners, Six Lectures on the Application
of Computer Algebra}",
crossref = "Stauffer:1993:CSC",
pages = "??--??",
year = "1993",
bibdate = "Wed Feb 15 16:05:40 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
@Book{Grabmeier:2003:CAH,
editor = "Johannes Grabmeier and Erich Kaltofen and Volker
Weispfenning",
title = "Computer algebra handbook: foundations, applications,
systems",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xx + 637",
year = "2003",
ISBN = "3-540-65466-6",
ISBN-13 = "978-3-540-65466-7",
LCCN = "QA155.7.E4 C64954 2003",
MRclass = "68W30, 00B15, 68-06",
bibdate = "Tue Nov 22 06:00:25 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
z3950.loc.gov:7090/Voyager",
note = "Includes CD-ROM.",
URL = "http://www.springer.com/sgw/cda/frontpage/0,11855,1-102-22-1477871-0,00.html",
acknowledgement = ack-nhfb,
keywords = "Aldor; AXIOM; Derive; exact arithmetic; Macsyma;
Magma; Maple Mathematica; MuPAD; REDUCE; TI-92",
subject = "Algebra; Data processing",
}
@Book{Roberts:2015:MED,
author = "A. J. (Anthony John) Roberts",
title = "Model Emergent Dynamics in Complex Systems",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 748",
year = "2015",
ISBN = "1-61197-355-4",
ISBN-13 = "978-1-61197-355-6",
LCCN = "QA845 .R62 2015",
bibdate = "Wed Sep 16 10:09:42 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical modeling and computation",
URL = "http://www.loc.gov/catdir/enhancements/fy1503/2014024843-b.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014024843-d.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014024843-t.html",
acknowledgement = ack-nhfb,
author-dates = "1957--",
remark = "From a posting by the book's author to the
Reduce-algebra-developers mailing list on 16 September
2015: ``Reduce is used throughout, and is fundamental
to the achievements in, my recent book [this one]''.",
subject = "Dynamics; Mathematical models; Computational
complexity; Differential equations; Asymptotic theory",
tableofcontents = "Preface \\
Part I. Asymptotic Methods Solve Algebraic and
Differential Equations: \\
1. Perturbed algebraic equations solved iteratively \\
2. Power series solve ordinary differential equations
\\
3. A normal form of oscillations illuminate their
character \\
Part I summary \\
Part II. Center Manifolds Underpin Accurate Modeling:
4. The center manifold emerges \\
5. Construct slow center manifolds iteratively \\
Part II summary \\
Part III. Macroscale Spatial Variations Emerge from
Microscale Dynamics \\
6. Conservation underlies mathematical modeling of
fluids \\
7. Cross-stream mixing causes longitudinal dispersion
along pipes \\
8. Thin fluid films evolve slowly over space and time
\\
9. Resolve inertia in thicker faster fluid films \\
Part III summary \\
Part IV. Normal Forms Illuminate Many Modeling Issues:
10. Normal-form transformations simplify evolution \\
11. Separating fast and slow dynamics proves modeling
\\
12. Appropriate initial conditions empower accurate
forecasts \\
13. Subcenter slow manifolds are useful but do not
emerge \\
Part IV summary \\
Part V. High Fidelity Discrete Models Use Slow
Manifolds: \\
14. Introduce holistic discretization on just two
elements \\
15. Holistic discretization in one space dimension \\
Part V summary \\
Part VI. Hopf Bifurcation: Oscillations Within the
Center Manifold: \\
16. Directly model oscillations in Cartesian-like
variables \\
17. Model the modulation of oscillations \\
Part VI summary \\
Part VII. Avoid Memory in Modeling Nonautonomous
Systems, Including Stochastic: \\
18. Averaging is often a good first modeling
approximation \\
19. Coordinate transforms separate slow from fast in
nonautonomous dynamics \\
20. Introducing basic stochastic calculus \\
21. Strong and weak models of stochastic dynamics \\
Part VII summary \\
Bibliography \\
Index",
}
@Proceedings{Stauffer:1993:CSC,
editor = "D. Stauffer and F. W. Hehl and V. Winkelmann and J. G.
Zabolitzky",
booktitle = "Computer Simulation and Computer Algebra. Lectures for
Beginners",
title = "Computer Simulation and Computer Algebra. Lectures for
Beginners",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "x + 287",
year = "1993",
ISBN = "0-387-56530-2 (New York), 3-540-56530-2 (Berlin)",
ISBN-13 = "978-0-387-56530-9 (New York), 978-3-540-56530-7
(Berlin)",
LCCN = "QA76.9.C65 C656 1993",
bibdate = "Wed Feb 15 17:13:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/redbooks.bib",
acknowledgement = ack-nhfb,
}
