Quick start

On this short page you will learn the simple ways to use Hom4PS-3 on Linux/Unix (please make sure you have already installed Hom4PS-3 on your system). All the examples below are shown with the very simple example file:

/usr/share/doc/hom4ps/testcases/simple.sym

Please replace those parts of the commands with the name of your own input file.

Solving a polynomial system, the easy way

Though Hom4PS-3 is a highly customizable software package with hundreds of options with which you can control the way it runs, you may still use it as a "blak box solver". You can use ask Hom4PS-3 to solve a polynomial system simply with the command:

hom4ps-easy /usr/share/doc/hom4ps/testcases/simple.sym

The program find the best algorithms to solve this system. It will then display the solutions (at least those isolated ones).

Solving a polynomial system, the fast way

The above command performs extra steps to improve numerical stability and refine solutions using multi-precision floating point arithmetic. These steps may not be necessary in many cases, yet they may consume a significant amount of time. To skip these steps and perform a much faster computation, simply use the command:

hom4ps-fast /usr/share/doc/hom4ps/testcases/simple.sym

Solving a small polynomial system

Both hom4ps-easy and hom4ps-fast shown above are optimized for medium to large sized polynomial systems. For smaller sized polynomial systems, however, the two may carry too much overhead.

hom4ps-small /usr/share/doc/hom4ps/testcases/simple.sym

The answers should appear almost instantly.

Finding real solutions

All the above commands find complex solutions. But in many situations, only the real solutions are needed. You can find the real solutions only via the command:

hom4ps-real /usr/share/doc/hom4ps/testcases/simple.sym

However, please note that this command is only doing a simple filtering according to the relative magnitude of the imaginary part of the solutions: a solution is discarded if its imaginary part is considered to be big. This is a rather crude process, and it is not guaranteed to work correctly. Indeed, to distinguish real and nonreal solutions is a rather difficult problem. You can find more information in more detailed documentation.