The reduction to normal form of a non-normal system of differential equations

De æquationum differentialium systemate non normali ad formam normalem revocando

DOI: 10.1007/s00200-009-0088-2

Cite this article as:
Ollivier, F. AAECC (2009) 20: 33. doi:10.1007/s00200-009-0088-2


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 m2 numbers by adding minimal numbers 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 the system: the equations ui = 0 must be respectively differentiated i times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.


Differential algebraOrder of a differential systemJacobi’s boundAssignment problemDifferential resolventShortest reduction in normal form

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.LIX UMR CNRS 7161, CNRS, École polytechniquePalaiseau CedexFrance