Representation for the radical of a finitely generated differential ideal

François Boulier (1) , Daniel Lazard (2) , François Ollivier (3) , Michel Petitot (1)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 LIP6 - Laboratoire d'Informatique de Paris 6
3 GAGE - Groupe Aleph et Géode

We 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.

Mots clés: differential algebra; Rosenfeld; Rosenfeld-Gröbner; computer algebra

Domaines: Equations aux dérivées partielles [math.AP]; Algèbre commutative [math.AC]; Calcul formel [cs.SC]

François Boulier, Daniel Lazard, François Ollivier, Michel Petitot. Representation for the radical of a finitely generated differential ideal. Jul 1995, pp.158-166. ⟨hal-00138020v1⟩