Gröbner bases in difference-differential modules with coefficients in a commutative ring

Abstract

Insa and Pauer presented a basic theory of Grobner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al. In this paper, we present an algorithmic approach for computing Grobner bases in difference-differential modules with coefficients in a commutative ring. We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem. Our result is a generalization of theories of Insa and Pauer, Ma et al., Zhou and Winkler and includes them as special cases.