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IMI/Publicaţii/CSJM/Ediţii/CSJM v.20, n.2 (59), 2012/

Computation of Difference Gröbner Bases

Authors: V. P. Gerdt, D. Robertz

Abstract

This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Gröbner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the package LDA (Linear Difference Algebra) and we describe the main features of the package. Its applications are illustrated by generation of finite difference approximations to linear partial differential equations and by reduction of Feynman integrals. We also present the algorithm for an ideal generated by a finite set of nonlinear difference polynomials. If the algorithm terminates, then it constructs a Gröbner basis of the ideal.

Vladimir P. Gerdt
Laboratory of Information Technologies
Joint Institute for Nuclear Research
141980 Dubna, Russia
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Daniel Robertz
Lehrstuhl B für Mathematik
RWTH Aachen
52062 Aachen, Germany
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