Calculation of Homology of Quandles, Racks, Biquandles and Biracks.
This document describes the installation and usage of the code in this repository, both for the calculation of homology as well as for the S test.
Installation
the easiest way to install this package is by first installing the package devtools via install.package(devtools) followed by library(devtools) There might be a warning about missing Rtools. This can be ignored (for the purposes of this package) as they are unneccessary. Then, to install the package quhomology proper, run install_github("ansgarwenzel/quhomology") .
Usage
First, load the package via library(quhomology) The main calculations are done by running homology(degree,k,quandle) and degenerate_homology(degree,k), where k is the order of the rack/birack, degree is the degree of the homology group (that is, degree=2 for H_2) and quandle is a boolean variable as follows: TRUE calculates the quandle homology whereas FALSE calculates the rack homology. Finally, degenerate_homology calculates the degenerate homology group.
The package is set up to calculate the homology of the dihedral quandle. Should another quandle'S homology be calculated, the up_action and down_action functions have to be changed. For details, run ?up_action and ?down_action
S_test the second function of the package is a test whether a set of order k with a given up_action and down_action (change as required, see help pages for details) for this, change the actions as required and then run S_test(k)
Question/Problems? Send an email to ansgar.wenzel+quhomology(at)gmail.com.