The reduction to normal form of a non-normal system of differential equations. De aequationum differentialium systemate non normali ad formam normalem revocando

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

1 MAX, Laboratoire d'Informatique de l'X

This paper was edited by Sigismund Cohn, C.W. Borchardt and A. Clebsch from posthumous manuscripts of C.G.J. Jacobi. The solution of the following problem: "to transform a square table of m^2 numbers by adding minimal numbers l_i to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of he system: the equations u_i = 0 must be respectively diff erentiated l_i times. One also determines the number of di fferentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.

Mots clés: Differential algebra; Order of a differential system; Jacobi's bound; Assignment problem; Differential resolvent; Shortest reduction in normal form

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. The reduction to normal form of a non-normal system of differential equations. De aequationum differentialium systemate non normali ad formam normalem revocando. Applicable Algebra in Engineering, Communication and Computing, 2009, 20 (1), pp.33-64. ⟨10.1007/s00200-009-0088-2⟩. ⟨hal-00821064⟩