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 with nonzero constant terms.
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Pré-publication, Document de travail
2016
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  • HAL Id : hal-01418653, version 1

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Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, Marc Mezzarobba. Computing solutions of linear Mahler equations . 2016. 〈hal-01418653〉

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