- Calculate simplicial homology of finite simplicial complexes (with integer coefficients)
- Apply classical constructors and modifiers from algebraic topology to simplicial complexes
- Construct and modify order complexes of finite partially ordred sets. Important classes of partially ordred sets from combinatorics and finite group theory are implemented.
- Calculate the Smith-Normal-form of a sparse integer matrix (this is part of the homology computations but can be applied to any matrix of interest). Four algorithms (deterministic and probabilitic) are implemented.
Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms.
Jean-Guillaume Dumas, Frank Heckenbach, B. David Saunders and Volkmar Welker.
In Algebra, Geometry and Software Systems, Michael Joswig and Nobuki Takayama, editors. Springer, March 2003, pp 177--206.
The package may be tried out by submitting gap/homology commands via this form SimplicialHomologyForm.html and receiving results via the web or email. This facility is in beta test.
As the compilation process requires a lot of new GNU features, some binaries are available and these architectures are currently supported:
- i686-pc-linux-gnu, version 1.4.3 (797 Kb),
- i686-pc-cygwin-gcc, version 1.4.3 (1349 Kb),
- i686-pc-linux-gnu, version 1.4.2 (780 Kb),
- i686-pc-linux-gnu, version 1.4.1 (716 Kb),
- i686-pc-linux-gnu, version 1.1 beta (805 Kb),
- i686-pc-linux-gnu (775 Kb),
- SGI_IRIX6.5, version 1.1 beta (1500 Kb, thanks to Malcolm Tobias),
- UltraSparc (694 Kb).
Sources for this GAP package are also available:
homology-1.4.5.tgz
( 263 Kb,
Last update: Thursday, December 8th 2011
). - homology-1.4.4.tgz ( 258 Kb, Final update: Tuesday, November 16th 2010 ).
- homology-1.4.3.tgz ( 254 Kb, Final update: Wednesday, November 4th 2009 ).
- homology-1.4.2.tgz ( 254 Kb, Final update: Thursday October 21, 2004 ).
- homology-1.4.1.tgz ( 284 Kb, Final update: Monday July 7, 2003 ).
- homology-1.0.tgz ( 157 Kb, Final update: Saturday August 4, 2001 ).
This package requires GAP, the GNU C++ and Pascal (G++, GPC) compilers, the GNU Multi-Precision Library (GMP) and GNU make (make). The required versions are GAP 4, G++ 2.95, GPC 19990118 (beta), GMP 2.0.2, and any fairly recent version of make. They can be obtained e.g. from the following web sites:
| : http://www-gap.dcs.st-and.ac.uk/~gap | |
| : http://gcc.gnu.org | |
| : http://www.gnu-pascal.de | |
| : http://gmplib.org | |
| : http://www.gnu.org/software/make |
After extracting the binary archive file to GAP home directory, check that the binaries are in the correct "bin" directory: it should be "$gaphome/pkg/homology/bin/`cat "$gaphome/sysinfo.gap" | sed 's/GAParch=//'`. If they are not, change the bin directory to $gaphome/pkg/homology/bin/xxx, where "xxx" is given in "$gaphome/sysinfo.gap". Then run GAP and execute this gap command:
| RequirePackage("homology"); |
To install this share package (after extracting the package's source archive file to the GAP home directory) go to the directory `pkg/homology' (the directory containing this README file) and call
| /bin/sh ./configure |
| /bin/sh ./configure --help |
If you want to use GMP only for compiling this package you should first install it, for instance in the default path searched by 'configure': `pkg/homology/src/Gmp/gmp-2.0.2'.
Afterwards call `make' (or 'gmake' GNU make) to compile the binary.
| make all |
Copyright 1999 J.-G. Dumas, F.
Heckenbach, B. D. Saunders, V. Welker.