112 citations · 425 across the 52 of their papers we have counts for
9 papers · 1 filter
On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz
Lorenzo Baldi, Bernard Mourrain, Adam Parusinski
The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answer…
On the Effective Putinar's Positivstellensatz and Moment Approximation
Lorenzo Baldi, Bernard Mourrain
We analyse the representation of positive polynomials in terms of Sums of Squares. We provide a quantitative version of Putinar's Positivstellensatz over a compact basic semialgebr…
Computing real radicals by moment optimization
Lorenzo Baldi, Bernard Mourrain
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generi…
Exact Moment Representation in Polynomial Optimization
Lorenzo Baldi, Bernard Mourrain
We investigate the problem of representing moment sequences by measures in the context ofPolynomial Optimization Problems, that consist in finding the infimum of a real polynomial…
Curve valuations and mixed volumes in the implicitization of rational varieties
Alicia Dickenstein, Maria Isabel Herrero, Bernard Mourrain
We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend resu…
Punctual Hilbert Schemes and Certified Approximate Singularities
Angelos Mantzaflaris, Bernard Mourrain, Agnes Szanto
In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a poly…