Computing representations for radicals of finitely generated differential ideals

  • François Boulier
  • Daniel Lazard
  • François Ollivier
  • Michel Petitot
Article

Abstract

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld–Gröbner, which computes a representation for the radical \({\mathfrak p}\) of the differential ideal generated by any such system Σ. The computed representation constitutes a normal simplifier for the equivalence relation modulo \({\mathfrak p}\) (it permits to test membership in \({\mathfrak p}\)). It permits also to compute Taylor expansions of solutions of Σ. The algorithm is implemented within a package (the package (diffalg) is available in MAPLE standard library since MAPLE VR5) in MAPLE.

Keywords

Computer algebra Differential algebra 

Mathematics Subject Classification (2000)

12H05 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • François Boulier
    • 1
  • Daniel Lazard
    • 2
  • François Ollivier
    • 3
  • Michel Petitot
    • 1
  1. 1.Université Lille I, LIFLVilleneuve d’AscqFrance
  2. 2.Université Paris VI, LIP6ParisFrance
  3. 3.École Polytechnique, LIXPalaiseau CedexFrance

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