Hom4PS-3 is a parallel numerical solver for polynomial systems developed based on the polyhedral homotopy continuation method.
libtropicana: A library designed to find regular simplicial subdivision of lattice convex polytopes and also compute normalized volume as a byproduct. It is written completely in C++ with optional interface for leveraging spBLAS (Sparse BLAS) routines. It is open source software. Users may freely distribute its source under the terms of the LGPLv3 license.
MixedVol-3 is a software package for computing mixed volume and mixed cells of polytopes in any dimension. It is now an integral part of Hom4PS-3, but I plan to make it an independent software program.
Skywalker (under active development) is a parallel program for finding real solutions to nonlinear systems of equations that implements Newton homotopy, fixed point homotopy, d-homotopy, and many other real homotopy constructions. It is used in my collaborative work with Dhagash Mehta, Jonathan Hauenstein, and David Wales that studies the configuration of chemical clusters.
Akimbo (under active development) in an OpenCL-based library for evaluating multi-variate systems of polynomials together with their Jacobian matrices on GPU.