Signature-based algorithms for Gröbner bases over Tate algebras
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | CARUSO, Xavier | |
| hal.structure.identifier | Mathématiques & Sécurité de l'information [XLIM-MATHIS] | |
| dc.contributor.author | VACCON, Tristan | |
| hal.structure.identifier | University of Linz - Johannes Kepler Universität Linz [JKU] | |
| dc.contributor.author | VERRON, Thibaut | |
| dc.date.accessioned | 2024-04-04T02:46:33Z | |
| dc.date.available | 2024-04-04T02:46:33Z | |
| dc.date.created | 2020 | |
| dc.date.conference | 2020-07-20 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191562 | |
| dc.description.abstractEn | Introduced by Tate in [Ta71], Tate algebras play a major role in the context of analytic geometry over the-adics, where they act as a counterpart to the use of polynomial algebras in classical algebraic geometry. In [CVV19] the formalism of Gröbner bases over Tate algebras has been introduced and effectively implemented. One of the bottleneck in the algorithms was the time spent on reduction , which are significantly costlier than over polynomials. In the present article, we introduce two signature-based Gröbner bases algorithms for Tate algebras, in order to avoid many reductions. They have been implemented in SageMath. We discuss their superiority based on numerical evidences. | |
| dc.language.iso | en | |
| dc.subject.en | F5 algorithm | |
| dc.subject.en | Gröbner bases | |
| dc.subject.en | Algorithms | |
| dc.subject.en | Tate algebra | |
| dc.subject.en | Power series | |
| dc.subject.en | P-adic precision | |
| dc.subject.en | F5 algorithm | |
| dc.title.en | Signature-based algorithms for Gröbner bases over Tate algebras | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.1145/3373207.3404035 | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| dc.identifier.arxiv | 2002.04491 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | ISSAC 2021 - International Symposium on Symbolic and Algebraic Computation | |
| bordeaux.country | GR | |
| bordeaux.conference.city | Kalamata / Virtual | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02473665 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02473665v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=CARUSO,%20Xavier&VACCON,%20Tristan&VERRON,%20Thibaut&rft.genre=unknown |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||