Computing representations for radicals of finitely generated differential ideals

François Boulier (1, 2) , Daniel Lazard (3) , François Ollivier (4) , Michel Petitot (1)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 CALFOR - Calcul Formel
3 SALSA - Solvers for Algebraic Systems and Applications
4 MAX, Laboratoire d'Informatique de l'X

This paper deals with systems of polynomial di erential equations, ordinary or with partial derivatives. The embedding theory is the di erential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld-Gröbner, which computes a representation for the radical p of the diff erential ideal generated by any such sys- tem . The computed representation constitutes a normal simpli er for the equivalence relation modulo p (it permits to test embership in p). It permits also to compute Taylor expansions of solutions of . The algorithm is implemented within a package in MAPLE.

Mots clés: Computer algebra; Differential algebra

Domaines: Calcul formel [cs.SC]

François Boulier, Daniel Lazard, François Ollivier, Michel Petitot. Computing representations for radicals of finitely generated differential ideals. Applicable Algebra in Engineering, Communication and Computing, 2009, 20 (1), pp.73-121. ⟨10.1007/s00200-009-0091-7⟩. ⟨hal-00820902⟩