Some improvements for the algorithm of Gröbner bases over dual valuation domain

Licui Zheng; Dongmei Li; Jinwang Liu; Licui Zheng; Dongmei Li; Jinwang Liu

doi:10.3934/era.2023203

Electronic Research Archive

2023, Volume 31, Issue 7: 3999-4010. doi: 10.3934/era.2023203

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Research article

Some improvements for the algorithm of Gröbner bases over dual valuation domain

Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China

Received: 20 January 2023 Revised: 28 April 2023 Accepted: 08 May 2023 Published: 22 May 2023

As a special ring with zero divisors, the dual noetherian valuation domain has attracted much attention from scholars. This article aims at to improve the Buchberger's algorithm over the dual noetherian valuation domain. We present some criterions that can be applied in the algorithm for computing Gröbner bases, and the criterions may drastically reduce the number of S-polynomials in the course of the algorithm. In addition, we clearly demonstrate the improvement with an example.
- Gröbner bases,
- dual noetherian valuation domain,
- S-polynomials
Citation: Licui Zheng, Dongmei Li, Jinwang Liu. Some improvements for the algorithm of Gröbner bases over dual valuation domain[J]. Electronic Research Archive, 2023, 31(7): 3999-4010. doi: 10.3934/era.2023203

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Abstract

As a special ring with zero divisors, the dual noetherian valuation domain has attracted much attention from scholars. This article aims at to improve the Buchberger's algorithm over the dual noetherian valuation domain. We present some criterions that can be applied in the algorithm for computing Gröbner bases, and the criterions may drastically reduce the number of S-polynomials in the course of the algorithm. In addition, we clearly demonstrate the improvement with an example.

References

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