Gröbner bases in difference-differential modules

This is joint work with M. Zhou of Beihang University in Beijing. The work has been supported by the Austrian FWF project P16357-N04 and by th

Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules

AbstractIn this paper we present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural double filtration. The approach is based on a method of special Gröbner bases with respect to “generalized term orders” on Nm×Zn and on difference-differential modules. We define a special type of reduction for two generalized term orders in a free left module over a ring of difference-differential operators. Then the concept of relative Gröbner bases w.r.t. two generalized term orders is defined. An algorithm for constructing these relative Gröbner bases is presented and verified. Using relative Gröbner bases, we are able to compute difference-differential dimension polynomials in two variables