Termination of algorithm for computing relative Gr?bner bases and difference differential dimension polynomials

Abstract

We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produced, if the term orders ‘\prec’ and ‘{\prec }^{\prime }’ are difference-differential degree compatibility. So we present a condition on the generalized orders and prove that under the condition the algorithm for computing relative Gröbner bases will terminate. Also the relative Gröbner bases exist under the condition. Finally, we prove the algorithm for computation of the bivariate dimension polynomials in difference-differential modules terminates.

Keywords

Relative Gröbner basis / difference-differential module / bivariate dimension polynomial / termination of algorithm

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