Software for polynomial continuation

Our software
• Bertini
  by Daniel Bates, Jon Hauenstein, Andrew Sommese, and Charles Wampler, is a C program for solving polynomial systems.
  Key features:
  • 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.
• HomLab
  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.
  
Other people's software
• PHC
  is a code written in Ada, by Jan Verschelde.
  Key features:
  • 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.
• HOM4PS
  by T.-Y. Li, T.-L. Lee, T. Chen and N. Ovenhouse. Code for polyhedral homotopy (serial and parallel versions).
  Key features:
  • Very fast polyhedral homotopy method.
• You can also look for HomPack, POLSYS_PLP, and POLSYS_GLP by Layne Watson and his collaborators.