Computing representations for radicals of finitely generated differential ideals

Authors:
François Boulier;Daniel Lazard;François Ollivier;Michel Petitot
Affiliations:
Université Lille I, LIFL, 59655, Villeneuve d’Ascq, France;Université Paris VI, LIP6, 75252, Paris, France;École Polytechnique, LIX, 91128, Palaiseau Cedex, France;Université Lille I, LIFL, 59655, Villeneuve d’Ascq, France
Venue:
Applicable Algebra in Engineering, Communication and Computing - Special Issue: Jacobi's Legacy
Year:
2009

Citing 0
Cited 8

Computing differential characteristic sets by change of ordering

Journal of Symbolic Computation
Thomas decomposition of algebraic and differential systems

CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
On the regularity property of differential polynomials modulo regular differential chains

CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Chemical reaction systems, computer algebra and systems biology

CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
A general procedure for accurate parameter estimation in dynamic systems using new estimation errors

ANB'10 Proceedings of the 4th international conference on Algebraic and Numeric Biology
Algorithmic Thomas decomposition of algebraic and differential systems

Journal of Symbolic Computation
A new algorithmic scheme for computing characteristic sets

Journal of Symbolic Computation
The input-output relationship approach to structural identifiability analysis

Computer Methods and Programs in Biomedicine

Quantified Score

Hi-index	0.00

Visualization

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 of the differential ideal generated by any such system Σ. The computed representation constitutes a normal simplifier for the equivalence relation modulo (it permits to test membership in ). 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.