Prime Decomposition of Ideals in Polynomial Rings
Stephen Melczer, Department of Mathematics, Simon Fraser University.Wednesday June 23rd in K9509 at 3:30pm.
Abstract. Given an ideal I in a polynomial ring, two fundamental questions that arise in algebraic geometry are to determine the radical of I and to represent the radical as the intersection of prime ideals. In the case where I has Hilbert Dimension 0 there are well known and efficient algorithms for solving these problems. We will give an overview of these algorithms and discuss how, through a suitable decomposition, they can be used in the case of positive dimensional ideals. Finally, we discuss how pre-processing a positive dimensional ideal using certain splitting techniques can result in a large increase in performance. Results comparing these algorithms with and without pre-processing in Maple will be shown.