Gr(o)bner bases in difference-differential modules and difference-differential dimension polynomials

• 来源期刊: 中国科学A辑(英文版)
• 年，卷（期）: 2008,（9）
• 页码范围: 1732-1752
• 页数: 21页
• 语种: 英文
• DOI: 10.1007/s11425-008-0081-4

摘要

In this paper we extend the theory of Gr(o)bner bases to difierence-difierential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration.We present and verify algorithms for constructing these Gr(o)bner bases counterparts.To this aim we introduce the concept of"generalized term order"on Nm×Zn and on difierence-difierential modules.Using Gr(o)bner bases on difierence-difierential modules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.