What ? Solving systems of polynomial equations and inequalities by mean of exact/certified algorithms.
For example, for systems with a finite number of complex solutions, a main goal is to compute an accurate approximation (up to an arbitrary precision set by the end-user) of all the real roots (they are certified to be real , not « complex with a small imaginary part »).
Solutions are proposed for univariate polynomials, zero-dimensional, general and parametric systems.
How ? Specific components for SALSA software.
RS (zero-dimensional systems), DV (parametric systems) coupled with a fast Gröbner engine (FGb) and using specific low-level libraries such as MPFI (multiprécision interval arithmetic).
What for ? Systems of polynomial equations (and inequalities) appear naturally in numerous applications :
