Exact symbolic-numeric computation of planar algebraic curves

We have implemented our algorithms as prototypical contributions to the C++-project Cgal. We exploit graphics hardware to expedite the remaining symbolic computations. We have also compared our implementation with the current reference implementations, that is, Lgp and Maple's Isolate for polynomial system solving, and Cgal's bivariate algebraic kernel for analyses and arrangement computations of algebraic curves. For various series of challenging instances, our exhaustive experiments show that the new implementations outperform the existing ones.