CARUSO, Xavier; VACCON, Tristan; VERRON, Thibaut

Métadonnées

Licence d’utilisation du document

CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]

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 — ISSAC 2021, 2021-07-18, Virtual event.

ACM

Résumé en anglais

Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism of Gröbner bases over Tate algebras has been introduced and advanced signature-based algorithms have been proposed. In the present article, we extend the FGLM algorithm of [FGLM93] to Tate algebras. Beyond allowing for fast change of ordering, this strategy has two other important benefits. First, it provides an efficient algorithm for changing the radii of convergence which, in particular, makes effective the bridge between the polynomial setting and the Tate setting and may help in speeding up the computation of Gröbner basis over Tate algebras. Second, it gives the foundations for designing a fast algorithm for interreduction, which could serve as basic primitive in our previous algorithms and accelerate them significantly.< Réduire

Mots clés en anglais

Algorithms

Gröbner bases

Tate algebra

FGLM algorithm

p-adic precision

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191638

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