On Computation of Groebner Bases for Linear Difference Systems

TL;DR

This paper introduces an algorithm for computing Groebner bases of linear difference ideals, adapting Janet-like reductions from polynomial algorithms to difference polynomial rings over a difference field.

Contribution

It presents a novel algorithm specifically designed for linear difference ideals, extending polynomial Groebner basis techniques to the difference algebra context.

Findings

Algorithm successfully computes Groebner bases for linear difference ideals

Adapts Janet-like reductions to difference polynomial rings

Applicable over ground difference fields

Abstract

In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.