CARUSO, Xavier; VACCON, Tristan; VERRON, Thibaut

doi:10.1145/3476446.3535491

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CARUSO, Xavier
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

VACCON, Tristan
XLIM [XLIM]

VERRON, Thibaut
University of Linz - Johannes Kepler Universität Linz [JKU]

Langue

Communication dans un congrès

Ce document a été publié dans

International Symposium On Symbolic And Algebraic Computation, 2022-07-04, Lille.

ACM

Résumé en anglais

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.< Réduire

Mots clés en anglais

Algorithms

Gröbner bases

Tate algebra

Mora's algorithm

Universal Gröbner basis

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190695

DOI

http://dx.doi.org/10.1145/3476446.3535491

Project ANR

Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251