A New Approach to Primary Decomposition

The first purpose of this paper is to describe a new mathematical approach for the computation of an irredundant primary decomposition of a given polynomial ideal I. This presentation will be formed of three parts: a decomposition of the associated radical ideal I to an intersection of prime ideals Pi, then the determination of ideals Iiwhose radical is prime (equal to Pi), and finally, the extraction of the possible embedded components included in Ii. The second is to give an implementation of this algorithm via a new software component, called The Central Control2, in which we implemented distributed algorithms performing the basic operations of algebraic geometry.