Prime Decomposition of Ideals in Polynomial Rings

Stephen Melczer, Department of Mathematics, Simon Fraser University.

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.