9 citations · 9 across the 8 of their papers we have counts for
11 papers
On Polynomial Ideals And Overconvergence In Tate Algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
In this paper, we study ideals spanned by polynomials or overconvergent series in a Tate algebra. With state-of-the-art algorithms for computing Tate Gr{ö}bner bases, even if the i…
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…
On FGLM Algorithms with Tropical Gröbner bases
Yuki Ishihara, Tristan Vaccon, Kazuhiro Yokoyama
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{ö}bner bases taking into account the valuation of K. Because of the use of…
On a non-archimedean broyden method
Xavier Dahan, Tristan Vaccon
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…
Super-linear convergence in the p-adic QR-algorithm
Avinash Kulkarni, Tristan Vaccon
The QR-algorithm is one of the most important algorithms in linear algebra. Its several variants make feasible the computation of the eigenvalues and eigenvectors of a numerical re…