## 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.