Gr{ö}bner bases over polytopal affinoid algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913821405216768 |
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| author | Barkatou, Moulay A. Legrand, Lucas Vaccon, Tristan |
| author_facet | Barkatou, Moulay A. Legrand, Lucas Vaccon, Tristan |
| contents | Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry. In this article, we present a theory of Gr{ö}bner bases for polytopal affinoid algebras that extends both Caruso et al.'s theory of Gr{ö}bner bases on Tate algebras and Pauer et al.'s theory of Gr{ö}bner bases on Laurent polynomials. We provide effective algorithms to compute Gr{ö}bner bases for both ideals of Laurent polynomials and ideals in polytopal affinoid algebras. Experiments with a Sagemath implementation are provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_13382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gr{ö}bner bases over polytopal affinoid algebras Barkatou, Moulay A. Legrand, Lucas Vaccon, Tristan Symbolic Computation Commutative Algebra Number Theory Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry. In this article, we present a theory of Gr{ö}bner bases for polytopal affinoid algebras that extends both Caruso et al.'s theory of Gr{ö}bner bases on Tate algebras and Pauer et al.'s theory of Gr{ö}bner bases on Laurent polynomials. We provide effective algorithms to compute Gr{ö}bner bases for both ideals of Laurent polynomials and ideals in polytopal affinoid algebras. Experiments with a Sagemath implementation are provided. |
| title | Gr{ö}bner bases over polytopal affinoid algebras |
| topic | Symbolic Computation Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2403.13382 |