Signature-based algorithms for Gröbner bases over Tate algebras - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2020

Signature-based algorithms for Gröbner bases over Tate algebras

Abstract

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.
Fichier principal
Vignette du fichier
F5.pdf (243.64 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02473665 , version 1 (10-02-2020)
hal-02473665 , version 2 (10-05-2021)

Identifiers

Cite

Xavier Caruso, Tristan Vaccon, Thibaut Verron. Signature-based algorithms for Gröbner bases over Tate algebras. ISSAC 2021 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata / Virtual, Greece. ⟨10.1145/3373207.3404035⟩. ⟨hal-02473665v2⟩
161 View
307 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More