To indicate related software dedicated to solving polynomial systems by homotopy continuation, four different packages that are publicly available are briefly mentioned. We also refer to a program for computing mixed volumes. In closing this section we indicate some large-scale related software projects.
HOMPACK [Morgan, Sommese, and Watson 1989] [Watson, Billups, and Morgan 1987] and CONSOL [Morgan 1987] are written in Fortran 77. HOMPACK is a general package for homotopy continuation with a polynomial driver. It has been parallelized [Allison, Chakraborty, and Watson 1989], [Harimoto and Watson 1989], and extended with an end game [Sosonkina, Watson, and Stewart 1996]. A Fortran 90 version appeared recently [Watson, Sosonkina, Melville, Morgan, and Walker 1997]. The package POLSYS_PLP [Wise, Sommese, and Watson 1998] for constructing partitioned linear-product start systems is intended to be used in conjunction with HOMPACK90. The code for CONSOL is contained in [Morgan 1987, Appendix 6]. Morgan, Sommese and Wampler [1991, 1992a, 1992b] developed techniques to handle end-point singularities.
Malajovitch created pss to apply homotopy continuation with verification by -theory. The program contains facilities for parallel continuation. Originally written in C, the newest version [Malajovich 1996] is programmed in C++. Pelican [Huber 1995,Huber 1996] implements in C the polyhedral methods of [Huber and Sturmfels 1995]. Gao has created Fortran software for polyhedral continuation, with facilities to compute the affine roots [Gao, Li, and Wang 1997].
The computation of mixed volumes is a crucial step in the resolution of sparse polynomial systems. The C program mvlp [Emiris 1994,Emiris and Canny 1995] computes mixed volumes, see [Giordano 1996] for a distributed version. For a general resultant-based polynomial-system solver, we refer to [Wallack, Emiris, and Manocha 1998].
In recent years, the attention to software for solving polynomial systems increased largely. FRISCO [The FRISCO Consortium] is a three-year project funded by the European Commission under the Esprit Reactive LTR Scheme (project no. 21.024). A demo of the software produced by the predecessor project PoSSo is available at [The Pisa Team of PoSSo].