112 citations · 425 across the 52 of their papers we have counts for
5 papers · 1 filter
The Hilbert scheme of points and its link with border basis
Mariemi Alonso, Jérome Brachat, Bernard Mourrain
In this paper, we give new explicit representations of the Hilbert scheme of points in $\PP^{r}$ as a projective subvariety of a Grassmanniann variety. This new explicit descri…
Continued Fraction Expansion of Real Roots of Polynomial Systems
Angelos Mantzaflaris, Bernard Mourrain, Elias P. P. Tsigaridas
We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the…
Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials
Houssam Khalil, Bernard Mourrain, Michelle Schatzman
In this paper, we re-investigate the resolution of Toeplitz systems , from a new point of view, by correlating the solution of such problems with syzygies of polynomials or…
Symmetric tensor decomposition
Jerome Brachat, Pierre Comon, Bernard Mourrain +1
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 fo…
On the Computation of Matrices of Traces and Radicals of Ideals
Itnuit Janovitz-Freireich, Bernard Mourrain, Lajos Ronayi +1
Let be a system of polynomials generating a zero-dimensional ideal $\I$, where is an arbitrary algebraically closed field. We…