  In this paper we consider systems of partial (multidimensional) linear
difference equations. Specifically, such systems arise in scientific computing
under discretization of linear partial differential equations and in
computational high energy physics as recurrence relations for multiloop Feynman
integrals. The most universal algorithmic tool for investigation of linear
difference systems is based on their transformation into an equivalent Groebner
basis form. We present an algorithm for this transformation implemented in
Maple. The algorithm and its implementation can be applied to automatic
generation of difference schemes for linear partial differential equations and
to reduction of Feynman integrals. Some illustrative examples are given.
