Differential Equations for Algebraic Functions

Abstract : It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove the existence of recurrences of order and degree close to optimal. We study the complexity of computing these differential equations and recurrences. We deduce a fast algorithm for the expansion of algebraic series.
Type de document :
Communication dans un congrès
C. W. Brown. ISSAC, Jul 2007, Waterloo, Canada. ACM Press, pp.8, 2007, International Conference on Symbolic and Algebraic Computation. 〈10.1145/1277548.1277553〉
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00138206
Contributeur : Bruno Salvy <>
Soumis le : vendredi 14 septembre 2007 - 14:10:58
Dernière modification le : vendredi 25 mai 2018 - 12:02:02
Document(s) archivé(s) le : mardi 21 septembre 2010 - 13:08:04

Fichiers

BoChLeSaSc07-hal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Alin Bostan, Frédéric Chyzak, Bruno Salvy, Grégoire Lecerf, Éric Schost. Differential Equations for Algebraic Functions. C. W. Brown. ISSAC, Jul 2007, Waterloo, Canada. ACM Press, pp.8, 2007, International Conference on Symbolic and Algebraic Computation. 〈10.1145/1277548.1277553〉. 〈inria-00138206v2〉

Partager

Métriques

Consultations de la notice

300

Téléchargements de fichiers

183