A New Approach to Primary Decomposition

The rst 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 p I to an intersection of prime ideals P i , then the determination of ideals I i whose the radical is prime (equal to P i), and lastly, the extraction of the possible embedded components included in I i. The second is to give an implementation of this algorithm via a new software comm ponent, called The Central Control y , in which we implemented distributed algorithms performing the basic operations of algebraic geometry.