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CompHom

comphom is a simple C++ program for computing simplicial homology groups of triangulated simplicial complexes.

Dependencies

comphom requires a C++ compiler and CMake for building. Alternatively, a simple Makefile is supplied.

How do I install comphom?

If you have CMake installed:

$ mkdir build
$ cd build
$ cmake ../
$ make

If you want to try out the Makefile instead:

$ make

The Makefile should work for any POSIX-compatible operating system.

What does comphom do?

Given a triangulation (or a whole bunch of them), comphom computes homology groups and writes the results to a file. One line is used per triangulation and if read from left to right, they descend in order. In other words: the highest dimension is the first group from the left, the lowest dimension is on the very right side of the line.

First, the rank of the free part of the group is printed. Afterwards the torsion parts are printed in the form Z_n. The torsion parts will be concatenated via '+'.

How do I use comphom…

…when using F. Lutz' triangulations?

F. Lutz has some nice triangulations on his website. These have been used to test the program. If you want to use them, please visit the Manifold Page at http://www.math.tu-berlin.de/diskregeom/stellar.

To feed them into comphom, follow these three steps:

  1. Download all triangulations you are interested in.
  2. Use the Perl script lex_convert.pl to convert the files into the format comphom understands: perl lex_convert.pl --input <file>
  3. Start comphom: comphom --input <file>.ct [--output <file>.out]

…when using my own triangulations?

If you have your own triangulations, the process is even simpler:

  1. Convert the triangulation so that comphom can process it. This is very easy: each simplex is entered in one line. After all simplices have been entered, add one line reading 'EOT' (end of triangulation).
  2. Start comphon: comphom --input <file> [--output <file>.out]