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Grbner bases in difference-differential modules and difference-differential dimension polynomials
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作者 franz winkler 《Science China Mathematics》 SCIE 2008年第9期1732-1752,共21页
In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module eq... In this paper we extend the theory of Grbner bases to difference-differential 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 construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules 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. 展开更多
关键词 Grbner basis generalized TERM order difference-differential module difference-differential DIMENSION POLYNOMIAL
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