Toric Generalized Characteristic Polynomials

Abstract: We illustrate an efficient new method for handling polynomial systems with degenerate solution sets. In particular, a corollary of our techniques is a new algorithm to find an isolated point in every excess component of the zero set (over an algebraically closed field) of any

n

by

n

system of polynomial equations. Since we use the sparse resultant, we thus obtain complexity bounds (for converting any input polynomial system into a multilinear factorization problem) which are close to cubic in the degree of the underlying variety -- significantly better than previous bounds which were pseudo-polynomial in the classical B'ezout bound. By carefully taking into account the underlying toric geometry, we are also able to improve the reliability of certain sparse resultant based algorithms for polynomial system solving.

This page was built for publication: Toric Generalized Characteristic Polynomials

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6502453)