A Maple Package for Computing Groebner Bases for Linear Recurrence Relations
Vladimir P. Gerdt, Daniel Robertz
TL;DR
This paper introduces a Maple software package that computes Groebner bases for linear recurrence relations, facilitating automatic generation of difference schemes and reduction of Feynman integrals.
Contribution
It presents a novel Maple package utilizing Janet and Janet-like divisions for efficient computation of Groebner bases in linear difference ideals.
Findings
Successfully computes Groebner bases for linear difference ideals
Demonstrates applications in generating difference schemes for PDEs
Shows reduction techniques for multiloop Feynman integrals
Abstract
A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type
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