Výsledky vyhledávání - "p-adic precision"

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Autor: Caruso, Xavier, Roe, David, Vaccon, Tristan

We present a new package ZpL for the mathematical software system SM. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in [4]. The underlying algorithms are mostly based on automa

Externí odkaz: http://arxiv.org/abs/1802.08532

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Report

Tracking p-adic precision

Autor: Caruso, Xavier, Roe, David, Vaccon, Tristan

We present a new method to propagate $p$-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stable computation of the SOMOS 4 sequence.

Externí odkaz: http://arxiv.org/abs/1402.7142

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ZpL: a p-adic precision package

Autor: Xavier Caruso, David Roe, Tristan Vaccon

Publikováno v: ISSAC 2018
ISSAC 2018, Jul 2018, New York, United States. ⟨10.1145/3208976.3208995⟩
ISSAC

International audience; We present a new package ZpL for the mathematical software system SageMath. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in previous papers by the same

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3988cd88fcbe35e5ceeb37f1baa66744
https://hal.archives-ouvertes.fr/hal-01715800

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Dissertation/ Thesis

Précision p-adique

Autor: Vaccon, Tristan

Les nombres p-adiques sont un analogue des nombres réels plus proche de l’arithmétique. L’avènement ces dernières décennies de la géométrie arithmétique a engendré la création de nombreux algorithmes utilisant ces nombres. Ces derniers

Externí odkaz: http://www.theses.fr/2015REN1S032/document

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Akademický článek

Tracking $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$-adic precision.

Autor: Caruso, Xavier, Roe, David, Vaccon, Tristan

Publikováno v: LMS Journal of Computation & Mathematics; Jul2014, Vol. 17 Issue A, p274-294, 21p

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On FGLM Algorithms with Tate Algebras

Autor: Xavier Caruso, Tristan Vaccon, Thibaut Verron

Publikováno v: ISSAC
International Symposium on Symbolic and Algebraic Computation — ISSAC 2021
International Symposium on Symbolic and Algebraic Computation — ISSAC 2021, Jul 2021, Virtual event, Russia

International audience; 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 Gr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45fc5ed71d8056b44dee760cb2d94fda
https://doi.org/10.1145/3452143.3465521

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On FGLM Algorithms with Tropical Gröbner bases

Autor: Yuki Ishihara, Kazuhiro Yokoyama, Tristan Vaccon

Publikováno v: ISSAC '20: International Symposium on Symbolic and Algebraic Computation
ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. pp.257-264, ⟨10.1145/3373207.3404037⟩
ISSAC

Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases has proved t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14101c3df560d2ea12044147a44c5313
https://hal.archives-ouvertes.fr/hal-02928709/document

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Signature-based algorithms for Gröbner bases over Tate algebras

Autor: Tristan Vaccon, Xavier Caruso, Thibaut Verron

Publikováno v: ISSAC
ISSAC 2021-International Symposium on Symbolic and Algebraic Computation
ISSAC 2021-International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata / Virtual, Greece. ⟨10.1145/3373207.3404035⟩

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 Gr{\"o}bn

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::24d4e9182a67519f05b75c530fbdd2cc
https://hal.archives-ouvertes.fr/hal-02473665/file/F5.pdf

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Matrix-F5 algorithms and tropical Gröbner bases computation

Autor: Tristan Vaccon

Publikováno v: International Symposium on Symbolic and Algebraic Computation, ISSAC 2015
International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Jul 2015, Bath, United Kingdom. 〈10.1145/2755996.2756665〉
International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Jul 2015, Bath, United Kingdom. ⟨10.1145/2755996.2756665⟩

International audience; Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gröbner bases taking into account the valuation of $K$. Because of the use of the valuation, this theory is promising f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d856b759281da007f69544e2b5d0da0
https://doi.org/10.1016/j.jsc.2017.11.014

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