fast-semigroup-homology 0.0.2

Compute homology of finite semigroups and monoids

Fast Semigroup Homology

This is a package for computing the integral homology of finite semigroups. It is very fast in most cases:

$ python -m fast_semigroup_homology -i "010100;010100;232322;232322;010100;010100" -d 12
H_0: Z
H_1: trivial
H_2: Z
H_3: Z^2
H_4: Z^4
H_5: Z^8
H_6: Z^16
H_7: Z^32
H_8: Z^64
H_9: Z^128
H_10: Z^256
H_11: Z^512
H_12: Z^1024
Elapsed (wall) time: 0:00:00.001716

Installation: pip install fast_semigroup_homology

Usage

To compute the homology of an individual semigroup with the command line, run python -m fast_semigroup_homology -i "01;10" -d 10 as above, replacing the string that follows -i with the multiplication table for some semigroup. Such a multiplication table must be entered as strings of digits separated by semicolons, all wrapped in quotes. Letters (as in hexadecimal) are also supported to allow semigroups of size at most 10+26=36 to be passed in quotes after -i. The integer following -d indicates the maximum dimension to compute to.

Alternatively, you can use this library from python code:

>>> from fast_semigroup_homology import fast_integral_semigroup_homology as h
>>> h([[0,1],[1,0]], 10) # Homology of C2
[{0: 1}, {2: 1}, {}, {2: 1}, {}, {2: 1}, {}, {2: 1}, {}, {2: 1}, {}]

If you have a folder of HDF5 files like those produced by Semisearch, you can instead run:

python -m fast_semigroup_homology -f /PATH/TO/FOLDER -o MAXORDER -d MAXDIM -c NUM_CORES

This will make a folder called results in the current working directory with .hdf5 files containing the homology groups [H_0, ... H_MAXDIM] of the semigroups from the files order1.hdf5 through orderMAXORDER.hdf5 in the folder passed after -f. If NUM_CORES is specified, that many processes will compute in parallel. Beware that some calculations can require a lot of memory, so making NUM_CORES too high can make the program crash. If you are running out of memory, you can also try adding swap space.

My results folder is also stored in this repository, which you can browse and download. This is not included when pip installs this package.