Computing solutions of linear Mahler equations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematics of Computation Year : 2018

Computing solutions of linear Mahler equations

Abstract

Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently, the problem of solving Mahler equations in closed form has occurred in connection with number-theoretic questions. A difficulty in the manipulation of Mahler equations is the exponential blow-up of degrees when applying a Mahler operator to a polynomial. In this work, we present algorithms for solving linear Mahler equations for series, polynomials, and rational functions, and get polynomial-time complexity under a mild assumption. Incidentally, we develop an algorithm for computing the gcrd of a family of linear Mahler operators.
Fichier principal
Vignette du fichier
mahlersols.pdf (688.04 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01418653 , version 1 (16-12-2016)
hal-01418653 , version 2 (10-04-2018)

Identifiers

Cite

Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, Marc Mezzarobba. Computing solutions of linear Mahler equations. Mathematics of Computation, 2018, 87, pp.2977-3021. ⟨10.1090/mcom/3359⟩. ⟨hal-01418653v2⟩
467 View
596 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More