HAL : inria-00138206, version 2

arXiv : cs/0703121

DOI : 10.1145/1277548.1277553

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ISSAC, Waterloo : Canada (2007)

Versions disponibles

v1 (23-03-2007)

v2 (14-09-2007)

Differential Equations for Algebraic Functions

Alin Bostan 1, Frédéric Chyzak 1, Bruno Salvy 1, Grégoire Lecerf 2, Éric Schost 3

(2007)

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.

1 :	ALGO (INRIA Rocquencourt)
	INRIA
2 :	Laboratoire de Mathématiques de Versailles (LM-Versailles)
	CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines
3 :	Department of Computer Science
	University of Western Ontario

Domaine

:

Informatique/Calcul formel Mathématiques/Analyse classique

Mots-clés : Computer algebra – algebraic series – differential resolvents – creative telescoping – complexity

inria-00138206, version 2

http://hal.inria.fr/inria-00138206

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Contributeur : Bruno Salvy <>

Soumis le : Vendredi 14 Septembre 2007, 14:10:58

Dernière modification le : Vendredi 14 Septembre 2007, 15:44:16