差分-微分模上多个序的Grbner基及多变量维数多项式  

GROBNER BASES WITH RESPECT TO SEVERAL ORDERINGS ON DIFFERENCE-DIFFERENTIAL MODULES AND MULTIVAPIATE DIMENSION POLYNOMIALS

作　　者：刘兰兰[1,2] 周梦[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191 [2]贵州民族大学理学院,贵阳550025

出　　处：《系统科学与数学》2012年第8期964-975,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10871017);北京市自然科学基金(1102026)资助项目

摘　　要：基于2008年Zhou和Winkler给出的计算有限生成的差分-微分双滤模的希尔伯特多项式的算法,文章构造了差分-微分模上相对多个序的的Grbner基,并给出和证明了计算这种Grbner基的算法.作为其应用,给出了计算差分-微分模的多变量维数多项式的新算法.推广了Zhou和Winkler(2008)所得结果,也推进了Levin(2007)所得结果.In this paper we present a new algorithmic approach for computing the Grobner bases with respect to several generalized term orders on N^m × Z^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 Levin （2007）. Then the concept of GrSbner bases with respect to several generalized term orders is defined. An algorithm for constructing these GrSbner bases is presented and verified. Using the GrSbner bases, we are able to compute difference-differential dimension polynomials in several variables in the case of that the difference operators are inversive. So our results have developed the theorem of Levin （2007） to Laurent-Ore polynomial ring, while Levin considered difference-differential dimension polynomials in several variables for modules over Ore polynomial rings with non-inversive difference operators. Moreover, the result is a generalization of theories of Zhou and Winkler （2008）.

关 键 词：Grbner基 广义项序 差分-微分模 维数多项式 

分 类 号：O174.14[理学—数学]