Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time - Université Toulouse 1 Capitole Accéder directement au contenu
Article Dans Une Revue Journal of Complexity Année : 2011

Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time

Résumé

In this paper we study planar polynomial differential systems of this form: dX/dt=A(X, Y ), dY/dt= B(X, Y ), where A,B belongs to Z[X, Y ], degA ≤ d, degB ≤ d, and the height of A and B is smaller than H. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: D =A(X, Y )dX + B(X, Y )dY . Darboux polynomials are usually computed with the method of undetermined coefficients. With this method we have to solve a polynomial system. We show that this approach can give rise to the computation of an exponential number of reducible Darboux polynomials. Here we show that the Lagutinskii-Pereira's algorithm computes irreducible Darboux polynomials with degree smaller than N, with a polynomial number, relatively to d, log(H) and N, binary operations. We also give a polynomial-time method to compute, if it exists, a rational first integral with bounded degree.
Fichier principal
Vignette du fichier
cheze_darboux_web.pdf (271.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00517694 , version 1 (15-09-2010)

Identifiants

Citer

Guillaume Chèze. Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time. Journal of Complexity, 2011, 27 (2), pp.246-262. ⟨10.1016/j.jco.2010.10.004⟩. ⟨hal-00517694⟩
141 Consultations
253 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More