Applicable Algebra in Engineering, Communication and Computing

, Volume 13, Issue 5, pp 395–425

Resolvent Representation for Regular Differential Ideals

Authors

  • Thomas Cluzeau
    • LACO, Université de Limoges, 123 avenue Albert Thomas, 87060 Limoges (e-mail: Thomas.Cluzeau@unilim.fr)
  • Evelyne Hubert
    • INRIA – CAFE, 2004 route des Lucioles, 06902 Sophia Antipolis (e-mail: Evelyne.Hubert@inria.fr)

DOI: 10.1007/s00200-002-0110-4

Cite this article as:
Cluzeau, T. & Hubert, E. AAECC (2003) 13: 395. doi:10.1007/s00200-002-0110-4

Abstract

 We show that the generic zeros of a differential ideal [A]:HA defined by a differential chain A are birationally equivalent to the general zeros of a single regular differential polynomial. This provides a generalization of both the cyclic vector construction for system of linear differential equations and the rational univariate representation of algebraic zero dimensional radical ideals. In order to achieve generality, we prove new results on differential dimension and relative orders which are of independent interest.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003