A computer scientist point of view on Hilbert's differential theorem of zeros

François Boulier (1, 2) , François Lemaire (1, 2)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 CALFOR - Calcul Formel

What is a solution of a system of polynomial differential equations ? This paper provides an original presentation of well-known theorems, with a computer scientist flavor, relying on an improved normal form algorithm.

Mots clés: computer algebra; differential algebra; theorem of zeros; normal form; Rosenfeld-Gröbner

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

François Boulier, François Lemaire. A computer scientist point of view on Hilbert's differential theorem of zeros. 2007. ⟨hal-00170091v2⟩