592 citations
- Université de LimogesFR138 papers
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14 papers · 1 filter
Solving generic parametric linear matrix inequalities
Simone Naldi, Mohab Safey El Din, Adrien Taylor +1
We consider linear matrix inequalities (LMIs) with the 's being symmetric matrices, with entries in a ring $\mathcal…
Gr{ö}bner bases over polytopal affinoid algebras
Moulay A. Barkatou, Lucas Legrand, Tristan Vaccon
Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical g…
Universal Analytic Gr{ö}bner Bases and Tropical Geometry
Tristan Vaccon, Thibaut Verron
A universal analytic Gr{ö}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{ö}bner basis for all suitable convergence radii. In a previous article, the…
Fast evaluation of some p-adic transcendental functions
Xavier Caruso, Marc Mezzarobba, Nobuki Takayama +1
We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our…
On FGLM Algorithms with Tate Algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
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 g…
Computing syzygies in finite dimension using fast linear algebra
Vincent Neiger, Éric Schost
We consider the computation of syzygies of multivariate polynomials in a finite-dimensional setting: for a -module of finite dimension …