32 citations · 100 across the 24 of their papers we have counts for
4 papers · 1 filter
Valuative lattices and spectra
Henri Lombardi, Assia Mahboubi
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical m…
Virtual Roots of Real Polynomials
Laureano Gonzalez--Vega, Henri Lombardi, Louis Mahé
The fact that a real univariate polynomial misses some real roots is usually overcame by considering complex roots, but the price to pay for, is a complete lost of the sign structu…
Dynamical method in algebra: Effective Nullstellensätze
Michel Coste, Henri Lombardi, Marie-Françoise Roy
We give a general method for producing various effective Null and Positivstellensätze, and getting new Positivstellensätze in algebraically closed valued fields and ordered groups.…
An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem
Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy
We prove elementary recursive bounds in the degrees for Positivstellensatz and Hilbert 17-th problem, which is the expression of a nonnegative polynomial as a sum of squares of rat…