Parametric Polynomial Systems

Overview:

Parametric polynomial system solving is a challenge coming from many applications, such as biology, control theory, robotics, deformation of hypersurface singularities, etc. When a problem can be modelled by a parametric system, the main issue is not only to return its solutions, but also to describe them. The design of algorithms to solve parametric systems has recently become an active and expanding research field. Manipulating parametric systems is at the heart of computer algebra. It calls upon a wide range of methods, such as comprehensive Gröbner bases, Cylindrical Algebraic Decomposition, Quantifier Elimination, Comprehensive Triangular Sets, Comprehensive Involutive Systems, Parametric Local Cohomology System, etc.

This session is focused on the art of parametric system solving, for general class of systems or dedicated to specific application problems, including the following topics:

• comprehensive Gröbner bases (systems)
• quantifier elimination
• comprehensive triangular sets
• deformation of hypersurface singularities
• modelisation of parametric problems
• optimization of parametric systems
• resolution of sparse parametric systems
• low-level computation with multivariate polynomial coefficients
• resolution of polynomial systems with boolean parameters
• description of the real solutions of a parametric system
• description of the parameter space of a polynomial system
• extension of algorithms from non parametric to parametric systems

Call for Contributions: