alphaCertified:
Software for certifying numerical solutions to polynomial equations

Jonathan Hauenstein and Frank Sottile

alphaCertified: certifying solutions to polynomial systems with Jonathan Hauenstein. 21 pages, 2010.

Smale's α-theory uses estimates related to Newton's method to certify solutions to polynomial systems. The program alphaCertified implements algorithms based on α-theory to certify solutions to polynomial systems using both exact rational arithmetic and arbitrary precision floating point arithmetic. It also implements an algorithm to certify whether a given point corresponds to a real solution of a real polynomial system, as well as algorithms to heuristically validate solutions to overdetermined systems. Examples are presented to demonstrate the algorithms.
Download alphaCertified and documentation. A short FAQ.

Examples
Stewart platform with 40 real positions.
Four-bar linkages.
Conics.
Shapiro conjecture.
Last modified: Mon Nov 22 12:08:09 CDT 2010