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Computing Sampling Points on a Singular Real Hypersurface using Lagrange's Sy...
Let $f$ be a polynomial in $\mathbbQ[X_1, ..., X_n]$ of degree bounded by $D$ and, for $t\in\mathbbQ$, $\mathcalH_t\subset\mathbbC^n$ the hypersurface defined by... -
Solving Parametric Polynomial Systems
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0,... -
Representations of polynomials, algorithms and lower bounds
Computational complexity is the study of the resources — time, memory, …— needed to algorithmically solve a problem. Within these settings, algebraic complexity theory... -
Occupation measures and semidefinite relaxations for optimal control
This thesis details a global method for optimal control of open-loop systems. This is done by relaxing the control problem as a generalized moment problem, which can... -
Polynomial systems solving and elliptic curve cryptography
Since the last decade, attacks on the elliptic curve discrete logarithm problem (ECDLP) which requires to solve polynomial systems have been quite successful. This... -
Algebraic Geometry & Computer Vision: Polynomial Systems, Real & Complex Roots
Article dans revue scientifique avec comité de lecture. -
Solving Zero-Dimensional Systems through the Rational Univariate Representation
Article dans revue scientifique avec comité de lecture. -
Polar varieties and computation of one point in each connected component of a...
Colloque avec actes et comité de lecture. internationale. -
Résolution de systèmes d'égalités et d'inégalités polynomiales
Stage ENS. Rapport de stage. -
Properness defects of projections and computation of at least one point in ea...
Article dans revue scientifique avec comité de lecture. internationale.
