A New Approach to Primary Decomposition

✍ Scribed by Alain Sausse

• Book ID: 102600835
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 332 KB
• Volume: 31
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.2000.1017

✦ Synopsis

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 P i , then the determination of ideals I i whose radical is prime (equal to P i ), and finally, 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 component, called The Central Control † , in which we implemented distributed algorithms performing the basic operations of algebraic geometry.