Hom4PS-3 has its own project website now. Please visit here.
Solving systems of polynomial equations is an important problem in mathematics. It has a wide range of applications in many fields of mathematics, sciences, and engineering. By the Abel’s impossibility theorem and Galois theory, explicit formulae for solutions to such systems by radicals are unlikely to exist, as a result, numerical computation arises naturally in the solution to such systems. Homotopy continuation methods represent a major class of numerical methods for solving systems of polynomial equations. Hom4PS-3 is a software package that implements many homotopy continuation algorithms with which it could numerically approximate, identify, and classify solutions to systems of polynomial equations.
Hom4PS-3 is an ongoing project currently under active development. For the more stable version, you are encouraged to try out Hom4PS-2.0 which is more mature and stable.
The Hom4PS-3 team
The Hom4PS-3 team is led by Professor Tien-Yien Li.
- Tianran Chen, Michigan State University
- Tien-Yien Li, Michigan State University
- Tsung-Lin Lee, National Sun Yat-sen University
We are supported by our research assistants
- Nick Ovenhouse
Hom4PS-3 is has many new features.
There are many different homotopy constructions for solving systems of polynomial equations each with its own strength. Hom4PS-3 currently supports the following homotopy constructions:
- Total degree homotopy
- Cheater’s homotopy
- Polyhedral homotopy
- Complex Newton’s homotopy
Other homotopy constructions are still under development.
Hom4PS-3 is capable of performing computation in parallel on a wide range of parallel computer architectures, including:
- Multi-core and Many-core architecture
- Computer clusters
- Distributed computation environments
Features that improve numerical robustness
- Automatic multi-precision
- Projective path tracking
- Singular end game
Hom4PS-3 is directly related to earlier software packages in the Hom4PS family.
There are other software packages that also implement numerical homotopy continuation algorithms for solving systems of polynomial equations: