Mixcell: A parallel mixed cell computation software package

Mixcell computes the mixed cells as well as the mixed volume of a set of convex polytopes in any dimension. The mixed volume is a functional arose in the study of linear combinations of multiple convex bodies. It has important applications in the study of system of polynomial equations as, by the Berstein’s theorem, the number of isolated solutions a system of polynomial equations has, counting multiplicity, is bounded by the mixed volume of Newton polytopes of the system. This bound is usually much tighter than another well studied bound, the Bezout number.

Mixcell is a software package that computes mixed volume and mixed cells using fast numerical algorithms. Mixcell is capable of performing computation in parallel on many parallel computer architectures.

Hom4PS-3: A parallel polynomial system solver

Hom4PS-3 is a software package for solving systems of polynomial equations based on the approach of homotopy continuation methods. It supports a wide range of parallel computer architectures.

See the its project website for detail.