Software for numerical irreducible decomposition

Abstract:

This talk is on the design and organization of software for solving polynomial systems numerically. In the last century, this numerical solving was confined to approximating all isolated solutions. Recent homotopy methods developed in collaboration with Andrew Sommese and Charles Wampler decompose positive dimensional solution sets into irreducible components. This numerical irreducible decomposition is one of fundamental tools in numerical algebraic geometry. The satisfactory performance of the algorithms on a wide class of practical applications justifies our efforts to make the software publicly available both as toolbox and blackbox.

Computational Algebraic Geometry workshop, 8-10 August 2002, Foundations on Computational Mathematics, Minneapolis.