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.
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal.inria.fr/inria-00138206
Contributor : Bruno Salvy <>
Submitted on : Friday, September 14, 2007 - 2:10:58 PM
Last modification on : Thursday, February 7, 2019 - 2:24:43 PM
Long-term archiving on : Tuesday, September 21, 2010 - 1:08:04 PM

Files

BoChLeSaSc07-hal.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Alin Bostan, Frédéric Chyzak, Bruno Salvy, Grégoire Lecerf, Éric Schost. Differential Equations for Algebraic Functions. ISSAC, Jul 2007, Waterloo, Canada. pp.8, ⟨10.1145/1277548.1277553⟩. ⟨inria-00138206v2⟩

Share

Metrics

Record views

336

Files downloads

330