Title: Solving Polynomial Equations

Hamid Rahkooy,
Research Institute for Symbolic Computation, Hagenberg, Austria
Centre de Recerce Matematica, Barcelona, Spain
date December 4, 2013


How do you find the solutions of a system of linear equation?
We learn the answer in the high school: Gassian elimination.
What if we have polynomial equations?
Classically Resultant were used to give a partial answer to this
question. A complete answer has been given via Groebner Bases which
was introduced in 1965 by Buchberger. First part of this talk will
contain a fast review to Groebner bases, its complexity and
applications on solving polynomial equations and graph coloring.
Second part of the talk will be on the resultant and their use to solve
polynomial equations. We will quote on our ongoing work on the
relations and the differences  between  resultant and Groebner bases.