24 citations · 60 across the 22 of their papers we have counts for
24 papers
On semidefinite-representable sets over valued fields
Corentin Cornou, Simone Naldi, Tristan Vaccon
Polyhedra and spectrahedra over the real numbers, or more generally their images under linear maps, are respectively the feasible sets of linear and semidefinite programming, and f…
Geometric Generality of Transformer-Based Gröbner Basis Computation
Yuta Kambe, Yota Maeda, Tristan Vaccon
The intersection of deep learning and symbolic mathematics has seen rapid progress in recent years, exemplified by the work of Lample and Charton. They demonstrated that effective…
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…
Learning to Compute Gröbner Bases
Hiroshi Kera, Yuki Ishihara, Yuta Kambe +2
Solving a polynomial system, or computing an associated Gröbner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly expo…
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Victor Magron, Przemysław Koprowski, Tristan Vaccon
Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for co…
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…
Signature-based algorithms for Gr{ö}bner bases over Tate algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
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…
Gr{ö}bner bases over Tate algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
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 algeb…
On Affine Tropical F5 Algorithms
Tristan Vaccon, Thibaut Verron, Kazuhiro Yokoyama
Let be a field equipped with a valuation. Tropical varieties over can be defined with a theory of Gr{ö}bner bases taking into account the valuation of .Because of the us…
ZpL: a p-adic precision package
Xavier Caruso, David Roe, Tristan Vaccon
We present a new package ZpL for the mathematical software system SM. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision i…
A Tropical F5 algorithm
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. While generalizing the…
Characteristic polynomials of p-adic matrices
Xavier Caruso, David Roe, Tristan Vaccon
We analyze the precision of the characteristic polynomial of an p-adic matrix A using differential precision methods developed previously. When A is integral with preci…
On the p-adic stability of the FGLM algorithm
Guénaël Renault, Tristan Vaccon
Nowadays, many strategies to solve polynomial systems use the computation of a Gr{ö}bner basis for the graded reverse lexicographical ordering, followed by a change of ordering alg…
On p-adic differential equations with separation of variables
Pierre Lairez, Tristan Vaccon
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted…
p-Adic Stability In Linear Algebra
Xavier Caruso, David Roe, Tristan Vaccon
Using the differential precision methods developed previously by the same authors, we study the p-adic stability of standard operations on matrices and vector spaces. We demonstrat…
Matrix-F5 algorithms over finite-precision complete discrete valuation fields
Tristan Vaccon
Let be a sequence of homogeneous polynomials with -adic coefficients. Such system may happen, for example, in arithme…
Tracking p-adic precision
Xavier Caruso, David Roe, Tristan Vaccon
We present a new method to propagate -adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy applicat…
Matrix-F5 algorithms and tropical Gröbner bases computation
Tristan Vaccon
Let be a field equipped with a valuation. Tropical varieties over can be defined with a theory of Gröbner bases taking into account the valuation of . Because of the use…