Some improvements for the algorithm of Gröbner bases over dual valuation domain
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 comput...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-05-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023203?viewType=HTML |
| _version_ | 1797690980813504512 |
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| author | Licui Zheng Dongmei Li Jinwang Liu |
| author_facet | Licui Zheng Dongmei Li Jinwang Liu |
| author_sort | Licui Zheng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T02:07:01Z |
| format | Article |
| id | doaj.art-33ded9fafb894caabe13b168cd0b7338 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-12T02:07:01Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-33ded9fafb894caabe13b168cd0b73382023-09-07T02:13:47ZengAIMS PressElectronic Research Archive2688-15942023-05-013173999401010.3934/era.2023203Some improvements for the algorithm of Gröbner bases over dual valuation domainLicui Zheng0Dongmei Li 1Jinwang Liu2Department of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, ChinaDepartment of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, ChinaDepartment of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, ChinaAs 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.https://www.aimspress.com/article/doi/10.3934/era.2023203?viewType=HTMLgröbner basesdual noetherian valuation domains-polynomials |
| spellingShingle | Licui Zheng Dongmei Li Jinwang Liu Some improvements for the algorithm of Gröbner bases over dual valuation domain Electronic Research Archive gröbner bases dual noetherian valuation domain s-polynomials |
| title | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| title_full | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| title_fullStr | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| title_full_unstemmed | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| title_short | Some improvements for the algorithm of Gröbner bases over dual valuation domain |
| title_sort | some improvements for the algorithm of grobner bases over dual valuation domain |
| topic | gröbner bases dual noetherian valuation domain s-polynomials |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023203?viewType=HTML |
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