Calculates the Quandle, Rack and Degenerate Homology groups of Racks and Biracks (as well as Quandles and Biquandles). In addition, a test is provided to ascertain if a given set with one or two given functions is indeed a biquandle or not.

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