Gröbner Bases with Respect to Generalized Term Orders and their Application to the Modelling Problem

We present an algorithm to decide whether a homogeneous linear partial difference equation with constant coefficients provides an unfalsified model for a finite set of observations, which consist in multiindexed signals, known on a finite subset ofNn. To this aim we introduce the concept of “generalized term order” and extend the theory of Gröbner bases accordingly.