centerfocus Documentation

Experimental results for the Poincaré center problem

We implement a fast version of Frommers algorithm to calculate the focal values of a plane autonomous system over a finite field.

This is a improved version of

For the implementation we followed Kay Moritzen and André Höhn
See for the Frommer algorithm over finite fields also the Appendix A of our article "Experimental results for the Poincaré center problem", in NoDEA, Volume 14, Numbers 5-6, 671-698, DOI: 10.1007/s00030-007-5036-x arXiv:math/0505547v2
Authors and contributors: Hans-Christian Graf von Bothmer, Martin Cremer and Jakob Kroeker
License: LGPL

Get stable source code revision from SourceForge :

svn co --revision 440 DESTFOLDER 

Get development source code from SourceForge :


View project directory structure




Maybe you have to edit the LinuxSrc/ -file and change the used compiler (CC, CXX) ans set appropriate OPTFLAGS

Implementation check:

To view interface definitions or implementation details, switch to the Modules-Tab.

Compile :


Precondition :

Installed Basic Linear Algebra Library (for example ATLAS)

Steps :

1. provide a environment variable, which contains the correct location of a Basic Linear Algebra Library .
In a bash shell, for example you would add something like

export BLASLAPACK_LIBS=/usr/lib64/ 	

in your ~/.bash_profile file.

2a. Change to the folder LinuxSrc and type:

make centerfocus 

2b. Generate an optimized version for a defined characteristic:


Binary files are written to folder 'c-program/bin'

Run compiled centerfocus program (and redirect stderr):

%executable% inputfile outputfile 2>/dev/null 


%executable% - outputfile 2>/dev/null 

to read parameters from stdin

If no output file is specified, a default output file name is used.

output file format:

See centerfocusResultFileFormat.pdf


The default configuration ('make centerfocus') deals only with small characteristics(<100)

Greater values are possible (for characteristic and epsPrecision), but currently not supported.

All external Library dependencies:


Input file example 1

The first example is related to our article "Focal Values of Plane Cubic Centers" published in "Qualitative Theory of Dynamical Systems", DOI 10.1007/s12346-010-0031-8
The input file contails the autonomous system for which the first eleven focal values vanishes, but the 12th does not.
The corresponding Jacobian matrix of s_1,..,s_11 has also full rank. The generated result file will contain the focal values s_j for the example and the Jacobian matrix of s_1,..,s_11.

Input file example 2

The input file contails the autonomous system for which the first twelve focal values vanishes, but the 13th does not.
The corresponding Jacobian matrix of s_1,..,s_12 has also full rank.

A third, more advanced input file example

  To perform random search replace polynomial coeffitients with '?'

'--': comments (Macaulay style)

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