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TitleGr\"obner bases in difference-differential modules and difference-differential dimension polynomials.
Author(s) Franz Winkler, Meng Zhou
TypeArticle in Journal
AbstractIn this paper we extend the theory of Gröbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for constructing these Gröbner bases counterparts. To this aim we introduce the concept of “generalized term order” on ℕ m ×ℤ n and on difference-differential modules. Using Gröbner bases on difference-differential modules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.
KeywordsGröbner basis, generalized term order, difference-differential module
ISSN1006-9283; 1862-2763/e
URL http://link.springer.com/article/10.1007%2Fs11425-008-0081-4
JournalSci. China, Ser. A
PublisherScience in China Press, Beijing; Springer, Heidelberg
Translation No
Refereed No