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

download the compiled 32 bit executable for MS Windows 9x/2k/Me/XP
or download the compiled 32 bit executable for Linux on a PC
or download the compiled 64 bit executable for Linux on a PC
or download source code and follow the compilation instructions

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

A list of comma separated cube coordinates enclosed in parentheses: fullCubicalCircle.cub
A list of blank separated cube coordinates: fullCubicalCircle.txt

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