Computational Algebra Seminar: Gao -- Grobner bases and fibre structures of points

Speaker: Shuhong Gao (Clemson University)
Title: Grobner bases and fibre structures of points
Time & Place: 3:05-4pm, Thursday 26 July 2007, Carslaw 535

Abstract:
Classical elimination theory deals mainly with the question when partial
solutions can be extended to complete solutions for a polynomial system.
We ask whether it is possible to predict the exact number solutions
of a system without actually solving it. In this talk, we present
some a relationship between certain Grobner bases and the fibre
structures of the solution variety for a polynomial system (that defines a
$0$-dimensional radical ideal).  We show that from a Grobner basis one can
easily read out information about the numbers of extensions of partial
solutions, and one can decompose the system into smaller systems that are
easier to solve.

Joint work with Virginia M. Rodrigues (PUCRS, Brazil)
and Jeffrey Stroomer (Xilinx, Inc.).