On Computing Groebner Basis in the Rings of Differential Operators
Xiaodong Ma, Yao Sun, Dingkang Wang
TL;DR
This paper introduces a new criterion for computing Groebner bases in rings of differential operators, improving efficiency and generalizing previous criteria by Insa and Pauer.
Contribution
A novel criterion for Groebner basis computation in differential operator rings that encompasses previous methods and enhances computational efficiency.
Findings
New criterion generalizes Insa and Pauer's method
Allows more efficient Groebner basis computation
Unifies previous criteria as special cases
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.
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