On Computing Groebner Basis in the Rings of Differential Operators

Abstract

Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Groebner basis more efficiently by this new criterion