author = {Christian Doench},
title = {{Bivariate difference-differential dimension polynomials and their computation in Maple}},
language = {english},
abstract = {We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gr�bner basis of a finitely generated difference-differential module and we use this to compute the bivariate difference-differential dimension polyomial of the module with respect to the natural bifiltration of the ring of difference-differential operators. An overview regarding affine Hilbert polynomials, Kolchin�s differential dimension polynomials and difference-differential dimension polynomials is given. Then the notion of relative Gr�bner basis and its use for computing bivariate difference-differential dimension polynomials is explained. After this the implementations of the two algorithms are illustrated by a couple of examples.},
number = {09-19},
year = {2009},
keywords = {Groebner basis; Differential ring; Differential module; Differencedifferential module; Difference differential dimension polynomial.},
sponsor = {This work has been supported by the Austrian FWF project P20336-N18.},
length = {29},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}