On solutions of Linear Ordinary Difference Equations in their Coefficient Field

Manuel Bronstein 1
1 CAFE - Computer algebra and functional equations
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We extend the notion of monomial extensions of differential fields, i.e. simp- le transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q-difference equations with polynomial coefficients.
Type de document :
Rapport
RR-3797, INRIA. 1999
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https://hal.inria.fr/inria-00072862
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Soumis le : mercredi 24 mai 2006 - 11:07:26
Dernière modification le : jeudi 11 janvier 2018 - 16:31:50
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:25:27

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Manuel Bronstein. On solutions of Linear Ordinary Difference Equations in their Coefficient Field. RR-3797, INRIA. 1999. 〈inria-00072862〉

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