Efficient algorithms for abelian varieties and their moduli spaces Page 1 HAL Id: tel-03498268
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …

We improve significantly the Nart-Montes algorithm for factoring polynomials over a
complete discrete valuation ring A. Our first contribution is to extend the Hensel lemma in the …

We provide an irreducibility test in the ring K [[x]][y] whose complexity is quasi-linear with
respect to the discriminant valuation, assuming the input polynomial F is square-free and K …

Tate introduced in [18] the notion of Tate algebras to serve, in the context of analytic
geometry over the p-adics, as a counterpart of polynomial algebras in classical algebraic …

Solving polynomials is a fundamental computational problem in mathematics. In the real
setting, we can use Descartes' rule of signs to efficiently isolate the real roots of a square …

We present a new package ZpL for the mathematical software system SageMath. It
implements a sharp tracking of precision on p-adic numbers, following the theory of …

We provide an irreducibility test in the ring K [[x]][y] whose complexity is quasi-linear with
respect to the valuation of the discriminant, assuming the input polynomial F square-free and …

Rédiger un mémoire d'habilitation n'est certes pas écrire un livre, mais c'est l'occasion
d'inscrire l'ensemble de ses contributions dans un contexte mathématique cohérent plus …

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 …

1.1 Secret sharing and cryptography 1 1.2 Purpose of this document and a brief description
of my research 3 1.2. 1 Overview 3 1.2. 2 Algorithms for abelian varieties 4 1.2. 3 Algorithms …