We consider the problem of computing minimal real or complex deformations to the
coefficients in a list of relatively prime real or complex multivariate polynomials such that the …

We develop a new symbolic-numeric algorithm for the certification of singular isolated
points, using their associated local ring structure and certified numerical computations. An …

We present an m-adic Newton iteration with quadratic convergence for lexicographic
Gröbner basis of zero dimensional ideals in two variables. We rely on a structural result …

This paper presents two new constructions related to singular solutions of polynomial
systems. The first is a new deflation method for an isolated singular root. This construction …

This paper presents two new constructions related to singular solutions of polynomial
systems. The first is a new deflation method for an isolated singular root. This con-struction …

We consider polynomial systems of Prony type, appearing in many areas of mathematics.
Their robust numerical solution is considered to be difficult, especially in “near-colliding” …

We present an explicit algorithm to compute a closed basis of the local dual space of
I=(f1,…, ft) at a given isolated singular solution xˆ=(xˆ1,…, xˆs) when the Jacobian matrix J …

We give an algorithm for the symbolic solution of polynomial systems in Z [X, Y]. Following
previous work with Lebreton, we use a combination of lifting and modular composition …

A new algorithm is proposed in this paper for computing the nearest polynomial to multiple
given polynomials with a given zero in the real case, where the distance between …

Singular zeros of systems of polynomial equations constitute a bottleneck when it comes to
computing, since several methods relying on the regularity of the Jacobian matrix of the …