112 citations · 425 across the 52 of their papers we have counts for
59 papers
ON THE DISTANCE TO DISCRIMINANTS AND OSCULATING VARIETIES
Khazhgali Kozhasov, Bernard Mourrain, Adam Parusi{ń}ski
We study the problem of finding the closest singular hypersurface to a given nonsingular one from algebro-geometric point of view. The set of singular hypersurfaces of a given…
Symmetric tensor decomposition on rational varieties
Matteo Bechere, Salma Kuhlmann, Bernard Mourrain
We study the Waring decomposition of symmetric tensors with nodes on a rational variety. We provide an explicit characterisation of the existence of such a decomposition under some…
An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets
Lorenzo Baldi, Teresa Krick, Bernard Mourrain
We study the problem of representing multivariate polynomials with rational coefficients, which are nonnegative and strictly positive on finite semialgebraic sets, using rational s…
An algebraic framework for geometrically continuous splines
Angelos Mantzaflaris, Bernard Mourrain, Nelly Villamizar +1
Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called -…
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…
Univariate Rational Sums of Squares
Teresa Krick, Bernard Mourrain, Agnes Szanto
Given rational univariate polynomials f and g such that gcd(f, g) and f / gcd(f, g) are relatively prime, we show that g is non-negative on all the real roots of f if and only if g…