Software for certifying numerical solutions to polynomial equations

Jonathan Hauenstein and Frank Sottile

Algorithm 921: alphaCertified: certifying solutions to polynomial systems ACM Transactions on Mathematical Software, 48, No. 4 (2012) 21 pages.

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.

Version 1.3 (October 2013)   Download alphaCertified and documentation. A short FAQ.

Stewart platform with 40 real positions.
Four-bar linkages.
Shapiro conjecture.

Research supported by the National Science Foundation under grant DMS-0915211.
Last modified: Fri Oct 25 03:15:47 CDT 2013