HomLab Home Page
HomLab: Homotopy Continuation Lab
Software for solving polynomial systems
Status: HomLab dates from 2005 and is no longer actively maintained. It may still be useful for learning the techniques described in the text by Sommese and Wampler. Otherwise, see Bertini for up-to-date software.
Facts in brief:
- Purpose: The numerical solution of systems of polynomial equations
- Approach: Homotopy continuation.
- Author: Charles Wampler
- Background: HomLab was created for learning about polynomial continuation. It is a suite of Matlab routines created for use with the book
The Numerical Solution of Systems
of Polynomials Arising in Engineering and Science
The HomLab distribution includes codes to be used in working the exercises at the end of each chapter.
by Andrew J. Sommese and Charles W. Wampler, II,
World Scientific, 2005.
In addition, HomLab is a general-purpose solver, fast enough for moderately-sized systems.
If you are interested in serious computation, you should consider using Bertini instead.
- Cost: Free, but please buy the book. See the official license policy.
- Finds isolated solutions by total-degree, multihomogeneous-degree, or linear-product homotopy.
- Implements parameter continuation for families of systems, such as the inverse
kinematics of six-revolute serial-link arms, or the forward kinematics of Stewart-Gough
- Treats positive-dimensional solutions by computing witness sets.
- Provides two ways of specifying a system
- "tableau" style for easy representation of simple systems,
- straight-line functions written as Matlab m-files, for greater efficiency.
- Uses homogenization to accurately compute solutions "at infinity."
- Provides a fractional power-series endgame to accurately compute singular roots
(up to multiplicity approximately 4).
Charles Wampler homepage.
Maintained by Charles Wampler/ charles.w.wampler(at)gm.com /revised
March 31, 2005