Software for Numerical Algebraic Geometry

Abstract:

In collaboration with Andrew Sommese and Charles Wampler, new homotopies have been proposed to deal with positive dimensional solution sets of polynomial systems. Applications come from the design of mechanical devices (such as parallel robots) which permit motion. In such situations one wishes to know whether a positive solution set decomposes into several irreducible components. A special case of this problem is the factorization of multivariate polynomials with complex approximate coefficients. This talk will outline the modular design of PHCpack, with an emphasis on those features which deal with positive dimensional solution components.

Session on Numerical Polynomial Algebra at the First Joint Meeting of CAIMS & SIAM, 24th Annual Meeting of CAIMS/SCMAI, 16-20 June 2003, Montreal, Canada.