Acyclic Subspace Homology Algorithm
AsHomMD is my implementation of the
Acyclic Subspace Homology Algorithm
for cubical sets in dimension 2, 3 and 4.
This software 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
AsHomMD 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
Since Acyclic Subspace Homology Algorithm is designed for full cubical sets, every cubical
set which is not a full cubical set is blown up to a full cubical set
(with the same homology) before the algorithm is applied.
(a cubical circle blown up to a full cubical circle)
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 (default)
- 2 - Betti and torsion numbers
- 3 - Betti and torsion numbers with some details of the computation process
Engines
You may also control the version of the algorithm
To do so add option
engine=xx
where xx may be
- AS - acyclic subspace construction based on simple intersection
- ASR - acyclic subspace construction based on simple intersection and recursion
- ASH - acyclic subspace construction based on independent homology computation
- ASLT - acyclic subspace construction based on lookup talbes (only in dimension 3)
(c) Marian Mrozek, Kraków, 2006