@techreport{8117edd1d4a24cbeadc8152ac1e2e26e,
title = "Bivariate difference-differential dimension polynomials and their computation in Maple",
abstract = "We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gr{\"o}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{\"o}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.",
author = "D{\"o}nch, {Christian Eckhardt Karl-H}",
year = "2009",
language = "English",
series = "RISC Report Series",
publisher = "RISC, JKU Linz",
number = "09-19",
type = "WorkingPaper",
institution = "RISC, JKU Linz",
}