Representation for the radical of a finitely generated differential ideal

Abstract

International audienceWe give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for testing membership in J. This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been programmed. We also give a method to obtain a obtain a characteristic set of J, if the ideal is prime

Computing representations for radicals of finitely generated differential ideals

“…The Rosenfeld-Gröbner algorithm was first described by Boulier [1994] and improved by Boulier et al [1995]. This paper contains new results.…”

“…The book of [Becker and Weispfenning, 1991, pages 230-232] furnished us many important informations on that subject. It is much more efficient than the ones given by Boulier [1994] or Boulier et al [1995].…”

“…It was first published in [Boulier et al, 1995, Lemma 2, page 161] with a proof relying on basic arguments. During the Special Year in Differential Algebra and Algebraic Geometry organized in 1995 at the City College of New York by Prof. Hoobler and Sit, a weakness in the proof was pointed out 2 : there was a claim which was true but not proved.…”

“…The knowledge of Morrison's proof helped us to fix ours. Section 2.2 contains the argument [Ollivier, 1998] missing in [Boulier et al, 1995].…”

“…This was the choice in Boulier et al [1995]. This representation is not only heavy but also non canonical for different regular differential systems may define the same regular differential ideal.…”