Deformation techniques for sparse polynomial systems

GUILLERMO MATERA

Colonia del Sacramento

Congreso; XVI Coloquio Latinoamericano de Álgebra; 2005

Universidad de la República

We discuss an efficient deformation technique which allows us to solve zero-dimensional "sparse" polynomial systems. The deformation consists in a flat morphism of affine varieties with a fiber representing the original system, and a "distinguished" fiber from which we know its infinitesimal structure. The algorithm computes a complete description of the generic fiber of the morphism under consideration, by a Hensel lifting of infinitesimal structure of the distinguished fiber, and solves the original system by specialization of the generic fiber