The goal of the subproject is to develop mathematical theories, algorithms, and software for efficiently proving/disproving algebraic statements and solving algebraic constraints over the real numbers. The statement/conditions may contain inequalities and quantifiers. The importance of the goal comes from the observation that many difficult problems in mathematics, scientific, engineering and industrial computation can be reduced to that of solving algebraic constraints.

• Parametrization: Some equational constraints can be solved by giving an "algebraic" parametrization of the solution set, i.e. a parametrization by rational functions. We are developing algorithms for finding parametrizations of algebraic surfaces, and for simplifying given parametrizations.
• Singularity Analysis: A solution set of algebraic constraints does in general have singularities, which are obstacles for identifying its topology or for visualizing. Resolution is a standard way to analyze these singularities. We are developing algorithms for singularity resolution and studying applications (e.g. for the parametrization problem).
• Box Approximation: Algebraic solution sets may be approximated by rectangular floating point boxes.

List of Publications.