Looking for the order of a system of arbitrary ordinary differential equations. De investigando ordine systematis aequationum differentialium vulgarium cujuscunque

Carl Gustav Jacob Jacques Simon Jacobi , François Ollivier (1)

1 MAX, Laboratoire d'Informatique de l'X

This paper was edited by S. Cohn and C.W. Borchardt from posthumous manuscripts of C.G.J. Jacobi. The various canonical forms that a given system ordinary differential equations may take are considered. Looking for the order of the system, without using a normal form, is reduced to a problem of inequalities: the affectation problem. A new type of formulas, the truncated determinants, is introduced. The non vanishing of this quantity means that the order will be equal to the value H , solution of this in- equalities problem, which is obtained by an algorithm similar to Harold Kuhn's Hungarian method

Mots clés: Differential algebra; Order of a differential system; Jacobi's bound; Assignment problem

Domaines: Calcul formel [cs.SC]; Histoire et perspectives sur les mathématiques [math.HO]; Recherche opérationnelle [math.OC]

Carl Gustav Jacob Jacques Simon Jacobi, François Ollivier. Looking for the order of a system of arbitrary ordinary differential equations. De investigando ordine systematis aequationum differentialium vulgarium cujuscunque. Applicable Algebra in Engineering, Communication and Computing, 2009, 20 (1), pp.7-32. ⟨10.1007/s00200-009-0087-3⟩. ⟨hal-00820908⟩