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

A Signature-Based Algorithm for Computing Gröbner Bases over Principal Ideal Domains

Autor: Thibaut Verron, Maria Francis

Publikováno v: Mathematics in Computer Science. 14:515-530

Signature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in general rings is not yet as well understood. In this paper, we presen

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74f2239fd2a2c875dbda86e17446b9cc
https://doi.org/10.1007/s11786-019-00432-5

Integral bases for p-recursive sequences

Autor: Manuel Kauers, Shaoshi Chen, Thibaut Verron, Lixin Du

Publikováno v: ISSAC

In an earlier paper, the notion of integrality known for algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5893d0146f079ad0ab5a67061d865cb0
https://doi.org/10.1145/3373207.3404004

Time minimal saturation of a pair of spins and application in magnetic resonance imaging

Autor: Jérémy Rouot, Thibaut Verron, Bernard Bonnard, Olivier Cots

Publikováno v: Mathematical Control and Related Fields
Mathematical Control and Related Fields, AIMS, 2020, 10 (1), pp.47-88. ⟨10.3934/mcrf.2019029⟩
Mathematical Control and Related Fields, 2020, 10 (1), pp.47-88. ⟨10.3934/mcrf.2019029⟩

In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e3e15aecb79050638a4165d398ec06e8
https://hal.inria.fr/hal-01779377

On the complexity of computing Gröbner bases for weighted homogeneous systems

Autor: Thibaut Verron, Jean-Charles Faugère, Mohab Safey El Din

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, 2016, 76, pp.107-141. ⟨10.1016/j.jsc.2015.12.001⟩
Journal of Symbolic Computation, Elsevier, 2016, 76, pp.107-141. ⟨10.1016/j.jsc.2015.12.001⟩

International audience; Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights $W=(w_{1

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5fb4157ede00052acbd45e2bd6638d1
https://doi.org/10.1016/j.jsc.2015.12.001