New documentation
Examples and usage documentation is here (under construction).Usage guide
After compiling the library, several executables will be placed incapd/capdRedHom/bin
subdirectory. The main executables are:
- redHom - computes Betti numbers and torsion coefficients of cubical sets, simplicial complexes and general, regular CW complexes using geometric reductions/coreductions and discrete Morse theory
- cubRedHom - a version of redHom specialized for cubical sets. Uses reductions via aycyclic subspace construction as well as geometric reductions/coreductions. Slightly faster than redHom in low dimensions.
- CrbHomMD - computes homology generators of cubical sets using geometric reductions/coreductions
- CrbMapHomMD - computes homology of acyclic valued, upper semicontinuous cubical maps
redHom
The simplest use is
redHom fileName
where fileName is the name of the input file containing
a cubical set or simplicial complex in one of the acceptable formats.
This will execute in turn: shaving, coreduction algorithm, discrete Morse theory
reduction and finally algebraic reductions. Output will contain homology groups
(Betti numbers and torsion coefficients).
Command line options
cubRedHom
The simplest use is
cubRedHom fileName
where fileName is the name of the input file containing
a cubical set in one of the acceptable formats.
This will execute reductions via acyclic subspace for 2 or 3 dimensional full cubical sets
or coreductions for other inputs followed by algebraic reductions.
Output will contain homology groups (Betti numbers and torsion coefficients).
Command line options
CrbHomMD
The simplest use is
CrbHomMD fileName
where fileName is the name of the input file containing
a cubical set in one of the acceptable formats.
CrbMapHomMD
The simplest use is
CrbMapHomMD fileName
where fileName is the name of the input file containing
an acyclic valued, upper semicontinuous cubical map
in the prescribed format.
This will execute in turn
- the construction of the graph
- the coreductions of the domain, range and graph
- the construction of the chain maps of the projections of the reduced graph onto reduced domain and range
- the algebraic reductions of the domain, range, graph and the projections.