joss_paper/paper.md

In ansgarwenzel/quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks

title: 'quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks' authors: - affiliation: 1 name: Roger Fenn - affiliation: 2 name: Ansgar Wenzel orcid: 0000-0001-7154-1590 date: "01 May 2018" output: pdf_document nocite: | @item1, @item2 bibliography: paper.bib tags: - Homology - Quandle - Biquandle - Rack - Birack - R - Knot Theory affiliations: - index: 1 name: University of Sussex - index: 2 name: Qbiz UK

Summary

In knot theory several knot invariants have been found over the last decades, particularly in [@Fenn1992a]. Quhomology calculates the rack, quandle and degenerate homology groups of racks and biracks, based primarily on the theory described in [@rogerhomology]. It works for any rack/quandle with finite elements where there are homology coefficients in Zk. The up and down actions can be given either as a function of the elements of Zk or provided as a matrix. When calculating a rack, the down action should coincide with the identity map. We have provided actions for both the general dihedral quandle and the group quandle over S3. We also provide a second function to test if a set with a given action (or with both actions) gives rise to a quandle or biquandle. The program is provided as an R package and can be found at https://github.com/ansgarwenzel/quhomology or a persistent version at [@ansgarwenzel_2017]. A corresponding paper can be found at [@jors53] and a wider introduction can be found in [@sussex65625].

Reuse Potential

This software can be used to calculate the homology groups of most racks and biracks. It is very easy to adapt for application to other eracks/biracks. Furthermore we believe that it can easily be extended to the calculation of Cohomology groups. Finally, the possibility of quickly identifying if a given action/set of actions gives rise to a rack/birack, is very useful.

Requirements

The program requires the R standard installation [@R, @rmasspackage], together with the packages Matrix [@rmatrixpackage] and numbers [@rnumberspackage].

References

ansgarwenzel/quhomology documentation built on May 22, 2019, 11:51 p.m.