6 citations · 6 across the 7 of their papers we have counts for
7 papers
A decisive Theorem (Un théorème décisif)
Henri Lombardi
We give an elementary proof of the theorem which states that a finite unramified algebra over a discrete field is tracically étale. -- Nous donnons une démonstration élémentaire du…
Algebraic identities to prove that a neat finite free algebra is tracically étale
Claude Quitté, Henri Lombardi
The central objective of this article is to provide an elementary proof of the following theorem, of which we are unaware of any trace in the existing literature. If is a net f…
Cyclotomic polynomials without using the zeros of
Gema M. Diaz-Toca, Henri Lombardi, Claude Quitté
This note aims to construct an ``intrinsic'' splitting field for the polynomial over the rational field , in a way that Gauss, Kummer, Kronecker and Bishop would hav…
Rationally presented metric spaces and complexity, the case of the space of uniformly continuous real functions on a compact interval
Henri Lombardi, Salah Labhalla, E. Moutai
We define the notion of {\em rational presentation of a complete metric space} in order to study metric spaces from the algorithmic complexity point of view. In this setting, we st…
Geometric theories for real number algebra without sign test or dependent choice axiom
Henri Lombardi, Assia Mahboubi
In this memoir, we seek to construct a constructive theory that is as complete as possible to describe the algebraic properties of the real number field in constructive mathematics…
Dynamic computations inside the algebraic closure of a valued field
Franz-Viktor Kuhlmann, Henri Lombardi, Hervé Perdry
We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the \NPAz. They are made in the same spirit as the dynamic algebraic closur…
Spectral spaces versus distributive lattices: a dictionary
Henri Lombardi
The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and a short dictionary for this an…