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TitleGr\"obner bases with respect to several orderings on difference-differential modules and multivariate dimension polynomials.
Author(s) Lanlan Liu, Meng Zhou
TypeArticle in Journal
AbstractWe present a new algorithmic approach for computing the Gröbner bases with respect to several generalized term orders on m × n and on difference-differential modules. We define a special type of reduction for several generalized term orders in a free left module over a ring of difference-differential operators. This reduction is different from the reduction of A. B. Levin [J. Symb. Comput. 42, No. 5, 561578 (2007; Zbl 1144.13013)]. Then the concept of Gröbner bases with respect to several generalized
term orders is defined. An algorithm for constructing these Gröbner bases is presented and verified. Using the Gröbner bases, we are able to compute difference-differential dimension polynomials in several variables in the case of that the difference operators are inversive.
KeywordsGröbner bases; generalized term orders; difference-differential dimension polynomials
JournalJ. Syst. Sci. Math. Sci.
PublisherScience Press, Beijing
Translation No
Refereed No