Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Vaccon, Tristan"'
Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry.In this article, we present a theory of Gr{\"o}bner bases for
Externí odkaz:
http://arxiv.org/abs/2403.13382
Autor:
Vaccon, Tristan, Verron, Thibaut
Publikováno v:
ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023, Jul 2023, Troms{{\o}}, Norway. pp.517-525
A universal analytic Gr{\"o}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{\"o}bner basis for all suitable convergence radii. In a previous article, the authors proved the existence of finite UAGB's for polynomial idea
Externí odkaz:
http://arxiv.org/abs/2401.05759
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the worst case
Externí odkaz:
http://arxiv.org/abs/2311.12904
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
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 constructing such a decomposition. The sole purpose of the present paper
Externí odkaz:
http://arxiv.org/abs/2302.02202
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{\"o}bner bases, even if the input is polynomials, the size of the output grows with the required
Externí odkaz:
http://arxiv.org/abs/2202.07509
We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect to the targ
Externí odkaz:
http://arxiv.org/abs/2106.09315
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{\"o}bner bases over Tat
Externí odkaz:
http://arxiv.org/abs/2102.05324
Publikováno v:
ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata Greece, France. pp.257-264
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:
http://arxiv.org/abs/2009.02067
Autor:
Dahan, Xavier, Vaccon, Tristan
Publikováno v:
ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata Greece, France. pp.114-121
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 methods use an iteration
Externí odkaz:
http://arxiv.org/abs/2009.01511
Autor:
Kulkarni, Avinash, Vaccon, Tristan
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 real or complex matrix, even when the dimensions of the matrix are enorm
Externí odkaz:
http://arxiv.org/abs/2009.00129