by Daniel Bates, Jon Hauenstein, Andrew Sommese, and Charles Wampler
Bertini is a suite of algorithms for solving systems of polynomial equations, including methods for isolated solutions and for irreducible decomposition. It has versions for both serial and parallel computing, and provides multiprecision arithmetic for greater reliability.
Bertini is open-source, written in C, and has executable downloads for Linux, MacOS, and Windows.
The following book describes the algorithms and contains a full users manual
Numerically Solving Polynomial Systems with Bertini
by Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
SIAM Books, 2011.
by Charles Wampler
This legacy code is no longer supported, but it is still available in support of the book:
The Numerical Solution of Systems
of Polynomials Arising in Engineering and Science
by Andrew J. Sommese and Charles W. Wampler, World Scientific, 2005.
HomLab is a suite of MatLab scripts and functions.
A HomLab users guide appears in Appendix C of the aforementioned book..
bertini_real, by silviana amethyst, uses Bertini to compute cell decompositions of algebraic curves and surfaces.
paramatopy, by silviana amethyst, uses Bertini in parallel mode to efficiently compute solutions to many examples sampled from a parameterized family of polynomial systems.
Wrappers for calling Bertini have been implemented in:
Some other software packages for polynomial continuation are: