• 论文 •

### 循环差分-微分模上双变元维数多项式的Gr\"obner基算法

1. 北京电子科技职业学院, 北京 100176
• 出版日期:2017-07-25 发布日期:2017-09-30

HUANG Guanli,L¨U Jiangyi,ZHANG Hualei. Computing Bivariate Dimension Polynomials in Cyclic Difference-Differential Modules via Gr\"obner Bases[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(7): 1722-1728.

### Computing Bivariate Dimension Polynomials in Cyclic Difference-Differential Modules via Gr\"obner Bases

HUANG Guanli ,L¨U Jiangyi ,ZHANG Hualei

1. Beijing Polytechnic, Beijing 100176
• Online:2017-07-25 Published:2017-09-30

Gr\"obner基算法是在计算机辅助设计和机器人学、信息安全等领域广泛应用的重要工具.文章在周梦 和Winkler (2008)给出的差分-微分模上Gr\"obner基算法和差分-微分维数多项式算法基础上,进一步研究了分别差分部分和微分部分的双变元维数多项式算法. 在循环差分-微分模情形,构造和证明了利用差分-微分模上Gr\"obner基计算双变元维数多项式的算法.

Groebner basis theory and its computer algorithms have numerous applications inside computer aided design, robotics, cryptosystems and other engineering technique. In this paper we use the difference-differential Gr\"obner bases introduced by Zhou and Winkler (2008) to compute bivariate difference-differential dimension polynomials of difference-differential modules. In cyclic module case, an algorithm for computing bivariate dimension polynomials in difference-differential modules is constructed and verified via the Gr\"obner bases.

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