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On computing Gröbner bases in rings of differential operators

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Abstract

Insa and Pauer presented a basic theory of Gröbner 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 Gröbner 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 Gröbner basis more efficiently by this new criterion.

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Authors and Affiliations

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    XiaoDong Ma, Yao Sun & DingKang Wang

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  1. XiaoDong Ma
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  2. Yao Sun
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  3. DingKang Wang
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Correspondence to DingKang Wang.

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Ma, X., Sun, Y. & Wang, D. On computing Gröbner bases in rings of differential operators. Sci. China Math. 54, 1077–1087 (2011). https://doi.org/10.1007/s11425-011-4176-y

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  • DOI: https://doi.org/10.1007/s11425-011-4176-y

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