Gröbner basis structure and decomposition of polynomial systems

Thursday, September 21, 2006 - 10:50am - 11:40am
EE/CS 3-180
Shuhong Gao (Clemson University)
A Gröbner basis for an ideal under an elimination order reflects much of the
geometric structure of the variety defined by the ideal. We discuss how this
relationship can be used in decomposing polynomial systems (with or without
parameters) and in primary decomposition of ideals. As an application, we show
how this technique can be used in designing deterministic algorithms for
factoring univariate polynomials over finite fields, which aims to reduce the
factoring problem to a combinatorial one. The talk is based on joint work
with Genhua Guan, Raymond Heindl, Jand-Woo Park, Virginia Rodrigues, and
Jeff Stroomer.
MSC Code: