Signature-based standard basis algorithm under the framework of GVW algorithm (Q6615411)
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scientific article; zbMATH DE number 7923140
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Signature-based standard basis algorithm under the framework of GVW algorithm |
scientific article; zbMATH DE number 7923140 |
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Signature-based standard basis algorithm under the framework of GVW algorithm (English)
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8 October 2024
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This paper focuses on the improvement of computing Gröbner bases. The starting point is the papers [\textit{S. Gao} et al., ISSAC 2010, 13--19 (2010; Zbl 1321.68531); \textit{S. Gao} et al., Math. Comput. 85, No. 297, 449--465 (2016; Zbl 1331.13018)], usually referred as GVM algorithm. In this paper, based on the famous Mora normal form algorithm, the authors extend the cover theorem to any semigroup order, which can be either global, local or even mixed. As a consequence, an algorithm for signature-based standard bases is presented for any semigroup order under the framework of the GVW algorithm is presented.
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signature-based algorithms
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standard bases
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semigroup orders
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Mora normal form algorithm
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cover theorem
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