On Polynomial Ideals and Overconvergence in Tate Algebras
| Autor: | Caruso, Xavier, Vaccon, Tristan, Verron, Thibaut |
|---|---|
| Přispěvatelé: | Lithe and fast algorithmic number theory (LFANT), 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)-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), 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), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Johannes Kepler Universität Linz (JKU) |
| Rok vydání: | 2022 |
| Předmět: |
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Computer Science - Symbolic Computation FOS: Computer and information sciences Mathematics - Number Theory Mathematics::Commutative Algebra Mathematics::Number Theory Symbolic Computation (cs.SC) [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Mathematics - Algebraic Geometry ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Mora's algorithm Universal Gröbner basis Gröbner bases [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Number Theory (math.NT) Tate algebra Algebraic Geometry (math.AG) Algorithms |
| Zdroj: | International Symposium On Symbolic And Algebraic Computation International Symposium On Symbolic And Algebraic Computation, Jul 2022, Lille, France. ⟨10.1145/3476446.3535491⟩ |
| DOI: | 10.1145/3476446.3535491 |
| Popis: | International audience; In this paper, we study ideals spanned by polynomials or overconvergent series in a Tate algebra. With state-of-the-art algorithms for computing Tate Gröbner bases, even if the input is polynomials, the size of the output grows with the required precision, both in terms of the size of the coefficients and the size of the support of the series. We prove that ideals which are spanned by polynomials admit a Tate Gröbner basis made of polynomials, and we propose an algorithm, leveraging Mora's weak normal form algorithm, for computing it. As a result, the size of the output of this algorithm grows linearly with the precision. Following the same ideas, we propose an algorithm which computes an overconvergent basis for an ideal spanned by overconvergent series. Finally, we prove the existence of a universal analytic Gröbner basis for polynomial ideals in Tate algebras, compatible with all convergence radii. |
| Databáze: | OpenAIRE |
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