Experimental results for the Poincaré center problem
Improved version of
http://www-ifm.math.uni-hannover.de/~bothmer/strudel
For the implementation we followed
Kay Moritzen and
André Höhn
Get development source code from SourceForge :
svn co https://centerfocus.svn.sourceforge.net/svnroot/centerfocus/strudel/trunk DESTFOLDER
or
Get stable version:
Centerfocus on Sourceforge
or
Get precompiled executables: (right mouse click)
Linux 32Bit executable
Requirements
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Configuration:
============
Maybe you have to edit te common.mk -file and change the used compiler (CC, CXX) ans set appropriate OPTFLAGS
Implementation check:
=================
To view interface definitions or implementationdetails, switch to the Modules-Tab.
Compile :
========
| | Change to folder c-program/LinuxSrc and type:
Generate an optimized version for a defined characteristic:
make dcenterfocus FIELDCHAR=%%NUM% EPSPRECISION=1
Pleas note: binary files are written to '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.
Limitations:
--------------
The default configuration (make centerfocus) deals only with small characteristics<100 and epsPrecision=1.
or characteristic<10.000 and epsPrecision=0.
Greater values are possible(for characteristic and epsPrecision), but this option is not finally implemented.
input file example:
================
| | To perform random search replace polynomial coeffitients with '?'
'--': comments (Macaulay style)
|
| |
| p | = 29; | -- field characteristic |
| maxStrudel | = 13; | -- number of max focal values to compute |
| minNullen | = 9; | -- search for examples where first 'minNullen' focal values vanishes |
| minRank | = 9; | -- search for examples where jacobian matrix has a rank greater or equal to 'minRank' |
| jacobi | = true; | -- perform jacobi matrix rank check (true/false) |
| jacobiUnterMatrix | = false; | -- |
| anzZufall | = 2000000; | -- number of random trials for each experiment |
| grad | = 3; | -- maximal polynomial degree of p,q |
| epsilon | = true; | -- compute with epsilon |
| epsPrecision | = 1; | -- epsilon precision size (currenly only 0 and 1 supported) |
| zufallInit | = -30; | -- starting random seed, see 'zeitAlsZufall' |
| rechneBisMaxStrudel | = false; | -- 'false': abort focal values computation of a example if a value does not vanish; 'true': compute all 'maxStrudel' focal values |
| benutzeFormel1 | = true; | -- compute q(3,0) in a kind that first focal value vanish |
| benutzeFormel2 | = true; | -- compute p(3,0) in a kind that second focal value vanish |
| hamilton | = true; | -- true: don't filter Hamilton components |
| zeitAlsZufall | = false; | -- false: use inital seed for random function given in 'zufallInit'; true: use timer as initial seed |
L = {
|
| -- first Experiment |
| { |
| { |
| {27, 9, 22}, | | -- Polymomial P coefficients with monomial degree = 2 |
| {3, 8, 5}, | | -- Polymomial Q coefficients with monomial degree = 2 |
| {11, 20, 4, 3}, | | -- Polymomial P coefficients with monomial degree = 3 |
| {3, 25, 20, 18} | | -- Polymomial Q coefficients with monomial degree = 3 |
| } |
| }, |
| -- second Experiment |
| { |
| { |
| {?, ?, ?}, | | -- Random polymomial P coefficients with monomial degree = 2 |
| {?, ?, ?}, | | -- Random polymomial Q coefficients with monomial degree = 2 |
| {?, ?, ?, ?}, | | -- Random polymomial P coefficients with monomial degree = 3 |
| {?, ?, ?, ?} | | -- Random polymomial Q coefficients with monomial degree = 3 |
| } |
| } |
| } |
|
|
