**
DESCRIPTION OF P4**

P4 stands for Polynomial Planar Phase Portraits. P4 is a program which studies a specific Polynomial Planar Vector Field (or Differential System) of any degree.

It determines all the singular points (finite and infinite ones) of the Vector Field, including those with linear part identically zero giving an explicit description of the neighbourhood of the singular points.

In particular cases of Polynomial Planar Vector Fields where it is possible to determine if a point is surrounded by a continuous of periodic orbits, P4 also detects it.

The program also locates the singular points which own separatrices and finds and draws them giving a complete vision of the global phase portrait.

P4 is able to look for limit cycles in specific regions determined by the user up to a certain degree of precision.

**AUTHORS OF P4**

Chris
Herssens, Dept. of Mathematics, Limburg Universitair Centrum,
Diepenbeek,
Limburg, Belgium. E-mail: herssens@luc.ac.be

Peter de Maesschalck, Dept. of Mathematics, Limburg Universitair Centrum, Diepenbeek, Limburg, Belgium. E-mail: peter.demaesschalck@uhasselt.be

Joan
C. Artés, Dept. de Matemàtiques,
Universitat
Autònoma
de Barcelona, Cerdanyola, Barcelona, Catalunya, Spain. E-mail: artes@mat.uab.cat

Freddy Dumortier, Dept. of Mathematics, Limburg Universitair Centrum, Diepenbeek, Limburg, Belgium. E-mail: fdumorti@uhasselt.be

Jaume
Llibre, Dept. de Matemàtiques, Universitat Autònoma
de Barcelona, Cerdanyola, Barcelona, Catalunya, Spain. E-mail: jllibre@mat.uab.cat

**CONDITIONS TO RUN P4**

P4 works in C under any UNIX enviroment and also in C++ under WINDOWS or MacOSX enviroment.

You also need to own either REDUCE (only for UNIX enviroment) or MAPLE (under any enviroment). These are algebraic compilers that you must purchase for your specific computer. You may contact REDUCE to get a copy of first. MAPLE can be adquired on specialized shops or contact MAPLE.

You
may already look to the introduction of the book at Intro.

**HELP FOR RUNNING P4**

Meanwhile
you may like to visit the help file
we are preparing. This will give you a better look of what P4 may do.

**INSTALLING P4 IN WINDOWS
**

Download P4.

1) Simply unzip this file in any folder (avoid folders whose name contains a blank).

2) Put a shortcut to /p4/bin/p4.exe on the desktop.

3) A temporary directory is needed. Maybe c:/TEMP.

4) Execute it and go to the "About P4.." - "Main Settings".

5) Specify the paths, that is, add the name of the directory where you have put P4, and the name of the temporary directory.

6) We suggest you to create a P4files directory where to put the examples you work with.

7) With right-click on the P4 icon you can force the start in the P4files directory to get closer to your files.

NOTE: P4 runs perfectly with MAPLE 9.X versions, but somehow it
does not yet with the new MAPLE 10.