Numerical Irreducible Decomposition using PHCpack

Abstract:

Homotopy continuation methods have proven to be reliable and efficient to approximate all isolated solutions of a polynomial system. A recent development is the application of these methods to deal with components of solutions. In the developing field of numerical algebraic geometry we strive to develop numerically stable algorithms to compute an irreducible decomposition of the solution set of a polynomial system. This task involves elimination and factorization into irreducible components. We show how to use the software PHC in conjunction with Maple and how to call routines from PHCpack within a C program. This is ongoing joint work with Andrew Sommese (University of Notre Dame) and Charles Wampler (General Motors Research Laboratories).

Dagstuhl-Seminar 01421, Integration of Algebra and Geometry Software Systems, 18 October 2001.