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

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

Gr{\'o}bner bases over Tate algebras

Autor: Xavier Caruso, Thibaut Verron, Tristan Vaccon

Publikováno v: ISSAC 2019-International Symposium on Symbolic and Algebraic Computation
ISSAC 2019-International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326257⟩
ISSAC

International audience; Tate algebras are fundamental objects in the context of analytic geometry over the p-adics. Roughly speaking, they play the same role as polynomial algebras play in classical algebraic geometry. In the present article, we deve

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::572524ca9ecde30c7afc62d950f748a3
http://arxiv.org/abs/1901.09574

On Affine Tropical F5 Algorithms

Autor: Tristan Vaccon, Kazuhiro Yokoyama, Thibaut Verron

Publikováno v: ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation
ISSAC '18: 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018, ⟨10.1145/3208976.3209012⟩
Journal of Symbolic Computation
Journal of Symbolic Computation, Elsevier, 2021, 102, pp.132-152. ⟨10.1016/j.jsc.2019.10.012⟩
ISSAC

This article is an extended version of: https://hal.archives-ouvertes.fr/hal-01792165; 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 th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d6e2d3b81fe2846358d10c2411e5a26
http://arxiv.org/abs/1805.06183

Characteristic polynomials of p-adic matrices

Autor: Tristan Vaccon, David Roe, Xavier Caruso

Publikováno v: 2017-17. 2017
ISSAC
ISSAC'17-Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation
The International Symposium on Symbolic and Algebraic Computation (ISSAC)
The International Symposium on Symbolic and Algebraic Computation (ISSAC), University of Kaisersiautern, Jul 2017, Kaiserslautern, Germany. pp.389-396

We analyze the precision of the characteristic polynomial XM of an nxnp-adic matrix M using differential precision methods developed previously. When M is an integral matrix whose entries are all given at the same precision O(pN), we give a criterion

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d65389a2a0b6e70d4f08ebb905defd5
https://hal.archives-ouvertes.fr/hal-01458027/file/charpoly.pdf