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

On a non-archimedean broyden method

Autor: Tristan Vaccon, Xavier Dahan

Publikováno v: ISSAC '20: International Symposium on Symbolic and Algebraic Computation
ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata Greece, France. pp.114-121, ⟨10.1145/3373207.3404045⟩
ISSAC

International audience; Newton's method is an ubiquitous tool to solve equations, both in the archimedean and non-archimedean settings --- for which it does not really differ. Broyden was the instigator of what is called "quasi-Newton methods". These

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98b5b9f8d8cdb62afe8d8ab91c3cb7a9

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

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

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