Coreduction Homology Algorithm
CrHomMD is my implementation of the
Coreduction Homology Algorithm
for general and full cubical sets in dimensions from 2 to 12.
The Coreduction Homology Algorithm for dimesions 2,3 and 4 is also available as a part of the
CAPD
and
CHOMP software libraries.
Download
To use it you need to
Usage
The basic usage is
CrHomMD filename
where filename denotes the name of a file containing a cubical set
in one of the admissible formats described below.
File Formats
A cubical set is stored in a text file as a comma seperated set of elementary cubes
enclosed in braces. For instance
{
[0,1]x[0],
[0,1]x[1],
[0]x[0,1],
[1]x[0,1]
}
is the representation of a cubical circle.
File Formats for Full Cubical Sets
Coreduction Homology Algorithm may be applied for general cubical sets
as well as full cubical sets.
For full cubical sets there are two other text formats available
Binary File Formats
Additionally, the input may be a black and white two dimensional bitmap
(*.bmp file) or an extension of this binary format to higher dimension
(*.bmd file).
Output
The amount of information provided may be controlled with
verbose=n
where n may be
- 0 - only Betti numbers
- 1 - Betti numbers and computation time
- 2 - Betti and torsion numbers (default)
- 3 - Betti and torsion numbers with some details of the computation process
(c) Marian Mrozek, Kraków, 2007