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Team : PolSys - Polynomial Systems

Axes : SSR (👥👥), TMC (👥👥).

Team leader :

Mohab Safey El Din Campus Pierre et Marie Curie 26-00/321

No event planned at present.

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Short presentation

Dessin Bulles HAL Staff directory 3 software

The PolSys team activity is centered on the design of algorithms based on computer algebra and symbolic computation to solve systems of polynomial constraints, the implementation of these algorithms and their applications.
The fundamental problem of solving systems of polynomial constraints arises in a wide range of areas such as cryptology, computational geometry, program verification in computer science, mathematical conjectures of geometric or combinatorial nature, and in engineering sciences such as robotics, biology, chemistry to cite a few.
The nonlinear nature of these problems and the requirements on exactness and exhaustiveness which arise in some applications make the use of local numerical and approximation methods difficult. Hence, the algorithmic challenges for solving polynomial systems are numerous, especially when considering that this problem is NP-hard. By using methods from computer algebra such as Gröbner bases computations, the PolSys team designs algorithms which allow:

In order to solve this wide range of algorithmic problems, the PolSys team develops several dedicated software. In particular, the msolve C library is already used in several computer algebra systems such as SageMath and OSCAR (see also other software developed by the team).
Also, the team has a regular activity in several application areas such as cryptology and robotics.

Staff directory

Computer Algebra. Polynomial System Solving. Gröbner Bases. Complexity. Real roots. Parametric systems. Cryptology. Algebraic Cryptanalysis. Algebraic Computational Geometry. Applications. Symbolic/Numeric Interaction. Software. High performance Linear Algebra.

http://www-polsys.lip6.fr

Selected publications

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Contact

mohab.safey (at) nulllip6.fr