PHC is a general-purpose solver for polynomial systems that features recent research advances in root-counting methods. The software package is portable via the gnu-ada compiler. Practical evidence for the performance of its black-box solver has been given on a large set of applications.
A recent new exciting development concerns homotopies that solve problems in enumerative geometry, see [Sottile 1997] and [Huber, Sottile and Sturmfels 1998].