LE Huu Phuoc

PhD student (ATER, Sorbonne Université)
Team : PolSys
Arrival date : 09/08/2018
    Sorbonne Université - LIP6
    Boîte courrier 169
    Couloir 26-00, Étage 3, Bureau 338
    4 place Jussieu
    75252 PARIS CEDEX 05
    FRANCE

Tel: +33 1 44 27 71 30, Huu-Phuoc.Le (at) nulllip6.fr
https://lip6.fr/Huu-Phuoc.Le

Supervision : Mohab SAFEY EL DIN

On solving parametric polynomial systems and quantifier elimination over the reals : algorithms, complexity and implementations

Solving polynomial systems is an active research area located between computer sciences and mathematics. It finds many applications in various fields of engineering and sciences (robotics, biology, cryptography, imaging, optimal control). In symbolic computation, one study and design-efficient algorithms that compute exact solutions to those applications, which could be very delicate for numerical methods because of the non-linearity of the given systems.
Most applications in engineering are interested in the real solutions to the system. The development of algorithms to deal with polynomial systems over the reals is based on the concepts of effective real algebraic geometry in which the class of semi-algebraic sets constitutes the main objects.
This thesis focuses on three problems below, which appear in many applications and are widely studied in computer algebra and effective real algebraic geometry:

  • Classify the real solutions of a parametric polynomial system according to the values of the parameters;
  • One-block quantifier elimination, which is also the computation of the projection of a semi-algebraic set
  • Computation of the isolated points of a semi-algebraic set.
We designed new symbolic algorithms with better complexity than the state-of-the-art. In practice, our efficient implementations of these algorithms are capable of solving applications beyond the reach of the state-of-the-art software.

2020-2022 Publications