Gr{\'o}bner bases over Tate algebras
| Autor: | Xavier Caruso, Thibaut Verron, Tristan Vaccon |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Lithe and fast algorithmic number theory (LFANT), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathématiques & Sécurité de l'information (XLIM-MATHIS), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Johannes Kepler University Linz [Linz] (JKU), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Power series
Computer Science - Symbolic Computation GeneralLiterature_INTRODUCTORYANDSURVEY Mathematics::Number Theory p-adic precision 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Mathematics - Algebraic Geometry Analytic geometry ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Computer Science::Symbolic Computation 0101 mathematics Tate algebra Mathematics [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] Mathematics::Commutative Algebra Mathematics - Number Theory 010102 general mathematics [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Algebra Formalism (philosophy of mathematics) Gröbner bases [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] F4 algorithm |
| Zdroj: | ISSAC 2019-International Symposium on Symbolic and Algebraic Computation ISSAC 2019-International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326257⟩ ISSAC |
| DOI: | 10.1145/3326229.3326257⟩ |
| Popis: | International audience; Tate algebras are fundamental objects in the context of analytic geometry over the p-adics. Roughly speaking, they play the same role as polynomial algebras play in classical algebraic geometry. In the present article, we develop the formalism of Gröbner bases for Tate algebras. We prove an analogue of the Buchberger criterion in our framework and design a Buchberger-like and a F4-like algorithm for computing Gröbner bases over Tate algebras. An implementation in SM is also discussed. |
| Databáze: | OpenAIRE |
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