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Computing representations for radicals of finitely generated differential ideals

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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.

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Authors and Affiliations

  1. Université Lille I, LIFL, 59655, Villeneuve d’Ascq, France

    François Boulier & Michel Petitot

  2. Université Paris VI, LIP6, 75252, Paris, France

    Daniel Lazard

  3. École Polytechnique, LIX, 91128, Palaiseau Cedex, France

    François Ollivier

Authors
  1. François Boulier
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  2. Daniel Lazard
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  3. François Ollivier
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  4. Michel Petitot
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Corresponding author

Correspondence to François Boulier.

Additional information

A part of this work (in particular the MAPLE diffalg package) was realized while the first author was a postdoctoral fellow at the Symbolic Computation Group of the University of Waterloo, N2L 3G6 ON, Canada.

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Boulier, F., Lazard, D., Ollivier, F. et al. Computing representations for radicals of finitely generated differential ideals. AAECC 20, 73–121 (2009). https://doi.org/10.1007/s00200-009-0091-7

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  • DOI: https://doi.org/10.1007/s00200-009-0091-7

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