Software for polynomial continuation
Charles Wampler homepage.
Other people's software
by Daniel Bates, Jon Hauenstein, Andrew Sommese, and Charles Wampler, is a C program
for solving polynomial systems.
- Finds isolated solutions by total degree or multihomogeneous degree homotopies.
- Implements the latest method, called "regeneration," which efficiently finds isolated
solutions by introducing the equations one-by-one.
- Finds positive dimensional solution sets and breaks them into irreducible components.
- Has adaptive multiprecision arithmetic for maintaining accuracy in larger problems.
- Endgames for fast, accurate treatment of singular roots.
- Simple input file format.
- Provides parameter homotopy, useful for efficiently solving multiple examples in a parameterized family of systems.
- Allows user-defined homotopies.
- Supports parallel computing.
- A detailed users manual is available from SIAM Books. See my publications.
by Charles Wampler, is a suite of MatLab routines for learning about
polynomial continuation. Although created for use with the book by Sommese and Wampler,
HomLab is a general-purpose solver, fast enough for moderately-sized systems. If you are
concerned about speed, numerical accuracy, and user-friendliness, try Bertini.
If you want to learn the techniques of polynomial continuation from the inside, HomLab
is your entry point.
is a code written
in Ada, by Jan Verschelde.
- Treatment of isolated solutions includes polyhedral homotopy (also known as
the BKK approach, mixed volume, or polytope method).
- Treatment of positive-dimensional solutions includes irreducible decomposition
and diagonal homotopy.
- The PHC pages also include a large collection of interesting examples.
by T.-Y. Li, T.-L. Lee, T. Chen and N. Ovenhouse. Code for polyhedral homotopy (serial and parallel versions).
- Very fast polyhedral homotopy method.
- You can also look for HomPack, POLSYS_PLP, and POLSYS_GLP by Layne Watson and his collaborators.