User's Guide for SymPol

INTRODUCTION:

SymPol is a C++ tool to work with symmetric polyhedra. It helps to compute restricted automorphisms (parts of the linear symmetry group) of polyhedra and performs polyhedral description conversion up to a given or computed symmetry group. You may download the complete SymPol package (version 0.1.8) and then follow the instructions below. Additional background information can be found in [BDS09] and in the Diploma thesis of the author Thomas Rehn.

DOWNLOAD:

Version 0.1.8(309 KB, Sep 27 2012)
Version 0.1.7(304 KB, Apr 02 2012)
Version 0.1.6(304 KB, Mar 14 2012)
Version 0.1.5a(302 KB, Oct 17 2011)
Version 0.1.4(282 KB, May 10 2011)
Version 0.1.3(282 KB, Feb 03 2011)
Version 0.1.2(281 KB, Nov 17 2010)
Version 0.1.1(275 KB, Sep 06 2010)
Version 0.1(276 KB, Jun 28 2010)
SymPol manual 0.1(177 KB, Jun 28 2010)

INSTALLATION:

After you have extracted a SymPol distribution package, you will find the following directories:

contrib contains scripts to manipulate .ine/.ext files.
data contains various example polyhedra in .ine/.ext files.
external contains all third-party software used by SymPol: cdd, lrs, PermLib
sympol contains the source code of the SymPol application.

SymPol requires

Boost in version 1.34.1 or higher
GMP with both C and C++ bindings
CMake in version 2.6 or higher

If CMake, GMP and Boostare correctly installed the SymPol applications can be built with:

~/sympol$ mkdir build && cd build
~/sympol/build$ cmake -DCMAKE_BUILD_TYPE=Release  ..
~/sympol/build$ make
# as root or in su/sudo shell
~/sympol/build$ make install

Then the SymPol binary will be installed in /usr/local/bin. On Linux systems you may have to call ldconfig as root afterwards so that the system knows about the new shared libraries (cddgmp and lrsgmp).

EXAMPLE USAGE:

Compute the restricted automorphism group

 sympol --automorphisms-only input-file.ine

Estimate the difficulty of a representation conversion

 sympol -e input-file.ine

Do a representation conversion

For “easy” input, try direct conversion:

 sympol -d input-file.ine

For “difficult” input, try one level of Adjacency Decomposition Method:

 sympol -a input-file.ine

If you want a combination of Incidence and Adjacency Decomposition Method, try

 sympol --idm-adm-level 1 2 -i input-file.ine

and adjust the recursion levels as needed.

Representation conversion and adjacency graph

 sympol -a --adjacencies -i input-file

performs a representation conversion up to symmetries with non-recursive ADM and prints the adjacency graph of the result in a format for use with Graphviz.

LICENSE:

As both cdd and lrs are published under GPL2, SymPol is also available under GPL2. Parts of the source code come with a more liberal license: The author's PermLib is BSD licensed.

REFERENCES:

[BDS09]: David Bremner, Mathieu Dutour Sikiric, and Achill Schürmann. Polyhedral representation conversion up to symmetries. In David Avis, David Bremner, and Antoine Deza, editors, Polyhedral computation, CRM Proceedings & Lecture Notes, pages 45–72. American Mathematical Society, 2009. [http]
[Reh10]: Thomas Rehn. Polyhedral Description Conversion up to Symmetries. Diploma thesis (mathematics), Otto von Guericke University Magdeburg, November 2010. [PDF]

CONTACT:

If you have any kind of question about SymPol, it's usage or you have additions, remarks, comments, etc. please feel free to contact its authors Thomas Rehn and/or Achill Schürmann

Last update: Sep 27 2012