Differential Equations for Algebraic Functions

Simple item page
dc.creatorBostan, Alin
dc.creatorChyzak, Frédéric
dc.creatorSalvy, Bruno
dc.creatorLecerf, Grégoire
dc.creatorSchost, Éric
dc.date2007-03-23
dc.date2007-09-14
dc.date.accessioned2026-07-07T09:29:55Z
dc.date.available2026-07-07T09:29:55Z
dc.descriptionIt 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.
dc.identifierhttps://arxiv.org/abs/cs/0703121
dc.identifierhttp://arxiv.org/abs/cs/0703121
dc.identifierISSAC'07, pages 25--32, ACM Press, 2007.
dc.identifierdoi:10.1145/1277548.1277553
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157967
dc.subjectSymbolic Computation
dc.subjectClassical Analysis and ODEs
dc.titleDifferential Equations for Algebraic Functions
dc.typetext

Files

Collections

arXiv