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TitleComputing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules
Author(s) Franz Winkler, Meng Zhou
TypeArticle in Journal
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 N m × Z n 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.
KeywordsRelative Gröbner basis, Generalized term order, Difference-differential module, Difference-differential dimension polynomial
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717108000230
LanguageEnglish
JournalJournal of Symbolic Computation
Volume43
Number10
Pages726 - 745
Year2008
Edition0
Translation No
Refereed No
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