|Title||Gr\"obner bases with respect to several orderings on difference-differential 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 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, 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 difference-differential dimension polynomials in several variables in the case of that the difference operators are inversive.
|Keywords||Gröbner bases; generalized term orders; difference-differential dimension polynomials|
|Journal||J. Syst. Sci. Math. Sci.|
|Publisher||Science Press, Beijing|