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Degree Bounds to Find Polynomial Solutions of Parameterized Linear Difference Equations in ΠΣ-Fields

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

An important application of solving parameterized linear difference equations in ΠΣ-fields, a very general class of difference fields, is simplifying and proving of nested multisum expressions and identities. Together with other reduction techniques described elsewhere, the algorithms considered in this article can be used to search for all solutions of such difference equations. More precisely, within a typical reduction step one often is faced with subproblems to find all solutions of linear difference equations where the solutions live in a polynomial ring. The algorithms under consideration deliver degree bounds for these polynomial solutions.

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Authors and Affiliations

  1. Research Institute for Symbolic Computation, J. Kepler University Linz, 4040, Linz, Austria

    Carsten Schneider

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  1. Carsten Schneider
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Correspondence to Carsten Schneider.

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Supported by the SFB-grant F1305 and the grant P16613-N12 of the Austrian FWF.

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Schneider, C. Degree Bounds to Find Polynomial Solutions of Parameterized Linear Difference Equations in ΠΣ-Fields. AAECC 16, 1–32 (2005). https://doi.org/10.1007/s00200-004-0167-3

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  • DOI: https://doi.org/10.1007/s00200-004-0167-3

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