Installation instructions on programs performing proofs described in paper
T. Kapela, C. Simo, Computer assisted proofs for non-symmetric planar choreographies and for stability of the Eight
This document describes how to compile and run programs which perform computer assisted proofs of choreographies existence and linear stability of the Eight. For more details see paper T. Kapela, C. Simo, Computer assisted proofs for non-symmetric planar choreographies and for stability of the Eight. Here we give only technical details about
Programs make intensive use of CAPD library which provide various tools for rigorous computations e.g.
interval arithmetics, rigorous integration of ODEs,
several methods of set representation, computation of Newton/Krawczyk operators.
For more details see http://capd.wsb-nlu.edu.pl
In distribution we include only that part of CAPD package which is being used.
The program has been tested under:
Mandriva 2007 with gcc 4.1.1,
Fedora Core 4 with gcc 3.4.2,
MS Windows XP Home Edition with gcc gcc 3.4.2 compiler. We use the MinGW compiler (Minimalist GNU for Windows - http://www.mingw.org) distributed with Dev-C++.
For a proof of the stability of the Eight we need very good estimates therefore we use multiple precision interval
arithmetics based on GMP and MPFR packages. To be able to compile that part you need to have those packages installed
in your Linux system.
In fact those packages are still under development and they can change in the future.
Pogramm was compiled sucessufully with
GMP 4.1.4 and 4.2.1,
If you do not have those packages or if you compile under Windows then program will be compiled with double floting points arithmetics but obtained estimated will not be good enough to complete proof.
Choreographies Existence Proofs
unzip file choreo.zip with options that preserve directories structure
Change directory to 'choreo'
- Invoke command:
- make for linux systems without GMP or MPFR
- make target=X11-gmp for linux systems with GMP and MPFR packages
- make target=win for Windows
After succesfull compilation executable files, which perform proofs, are placed in directory bin:
- 3bodies - existence of Eight,
- 5bodies - existence of choreography with 5 bodies,
- 6bodies - existence of non symmetric choreography wich 6 bodies,
- 7bodies - existence of non symmetric choreography wich 7 bodies,
- 3stability - linear stability of the Eight restricted to the plane and zero angular momentum motions.
Change directory to 'bin' and run selected programs
e.g../3bodies under Linux or 3bodies under Windows.
Important: You need to run them from directory bin.
Results of computations are placed in directory 'bin/reports' in files report?.txt where ? is the number of bodies.
ConsoleOutput.txt is the log file for the most recent run programm.
Sometimes changes in makefile's are needed depending on your system installation.
For more details see documentation of CAPD package.