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02/04/2023
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Pourchet proved in 1971 that every nonnegative univariate polynomial wit...
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02/15/2022
On Polynomial Ideals And Overconvergence In Tate Algebras
In this paper, we study ideals spanned by polynomials or overconvergent ...
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06/17/2021
Fast evaluation of some p-adic transcendental functions
We design algorithms for computing values of many p-adic elementary and ...
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02/10/2021
On FGLM Algorithms with Tate Algebras
Tate introduced in [Ta71] the notion of Tate algebras to serve, in the c...
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09/04/2020
On FGLM Algorithms with Tropical Gröbner bases
Let K be a field equipped with a valuation. Tropical varieties over K ca...
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09/03/2020
On a non-archimedean broyden method
Newton's method is an ubiquitous tool to solve equations, both in the ar...
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08/31/2020
Super-linear convergence in the p-adic QR-algorithm
The QR-algorithm is one of the most important algorithms in linear algeb...
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02/11/2020
Signature-based algorithms for Gröbner bases over Tate algebras
Introduced by Tate in [Ta71], Tate algebras play a major role in the con...
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01/28/2019
Gröbner bases over Tate algebras
Tate algebras are fundamental objects in the context of analytic geometr...
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05/16/2018
On Affine Tropical F5 Algorithms
Let K be a field equipped with a valuation. Tropical varieties over K ca...
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02/23/2018
ZpL: a p-adic precision package
We present a new package ZpL for the mathematical software system SM. It...
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05/16/2017
A Tropical F5 algorithm
Let K be a field equipped with a valuation. Tropical varieties over K ca...
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02/06/2017
Characteristic polynomials of p-adic matrices
We analyze the precision of the characteristic polynomial of an n× n p-a...
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02/03/2016
Division and Slope Factorization of p-Adic Polynomials
We study two important operations on polynomials defined over complete d...
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02/02/2016
On the p-adic stability of the FGLM algorithm
Nowadays, many strategies to solve polynomial systems use the computatio...
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01/31/2016