Details:
Title  Gr\"obner bases with respect to several orderings on differencedifferential modules and multivariate dimension polynomials.  Author(s)  Lanlan Liu, Meng Zhou  Type  Article in Journal  Abstract  We present a new algorithmic approach for computing the Gröbner bases with respect to several generalized term orders on m × n and on differencedifferential modules. We define a special type of reduction for several generalized term orders in a free left module over a ring of differencedifferential operators. This reduction is different from the reduction of A. B. Levin [J. Symb. Comput. 42, No. 5, 561–578 (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 differencedifferential dimension polynomials in several variables in the case of that the difference operators are inversive.  Keywords  Gröbner bases; generalized term orders; differencedifferential dimension polynomials  ISSN  10000577 
Language  English  Journal  J. Syst. Sci. Math. Sci.  Volume  32  Number  8  Pages  964975  Publisher  Science Press, Beijing  Year  2012  Edition  0  Translation 
No  Refereed 
No 
