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
http://www.centerfocus.de/strudel_programs.html
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 https://centerfocus.svn.sourceforge.net/svnroot/centerfocus/strudel/trunk/c-program --revision 440 DESTFOLDER
Get development source code from SourceForge :
svn co https://centerfocus.svn.sourceforge.net/svnroot/centerfocus/strudel/trunk/c-program DESTFOLDER
View project directory structure
Requirements
=============
- C++ Compiler
- Basic Linear Algebra Subroutines Library (BLAS) installed and eventually
- Boost ,
- popt ,
- libtool and
- autoconf
Configuration:
============
Maybe you have to edit the LinuxSrc/common.mk -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/libblas.so
in your ~/.bash_profile file.
2a. Change to the folder LinuxSrc and type:
2b. Generate an optimized version for a defined characteristic:
make dcenterfocus FIELDCHAR=%%NUM% EPSPRECISION=1 MAXMONOMDEGREE=3
Binary files are written to folder 'c-program/bin'
|
Run compiled centerfocus program (and redirect stderr):
.============================================
| %executable% inputfile outputfile 2>/dev/null
or
%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
Limitations:
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:
- Library implementing the BLAS Interface (not included). License: vendor-dependend
- FFPACK-FFLAS is included, Lesser General Public License
- Boost Library development files (not included), License : Boost Software License
- cxxtest (included), Lesser General Public License,
- popt (included version 1.14), License: MIT/X Consortium
- DMTCP (Distributed MultiThreaded Checkpointing), included, license: Lesser General Public (version 3 or later)
Examples:
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.
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.
| To perform random search replace polynomial coeffitients with '?'
'--': comments (Macaulay style)
|