Finding First Integrals Using Normal Forms Modulo Differential Regular Chains

François Boulier (1) , François Lemaire (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

This paper introduces a definition of polynomial first inte-grals in the differential algebra context and an algorithm for computing them. The method has been coded in the Maple computer algebra system and is illustrated on the pendulum and the Lotka-Volterra equations. Our algorithm amounts to finding linear dependences of rational fractions, which is solved by evaluation techniques.

Mots clés: First integral; linear algebra; differential algebra; nonlinear system

Domaines: Calcul formel [cs.SC]

François Boulier, François Lemaire. Finding First Integrals Using Normal Forms Modulo Differential Regular Chains. Computer Algebra in Scientific Computing 2015, Sep 2015, Aachen, Germany. pp.101-118. ⟨hal-01234982⟩