Racks in GAP

Version 1

Released 2014-05-24

This project is maintained by Leandro Vendramin

A GAP package for racks, quandles, Nichols algebras

Rig is a GAP package for computations related to racks, quandles, knots, virtual knots, Nichols algebras.

Latest stable version here (tar.gz), or here (zip), version 1.

Now Rig contains all indecomposable quandles of size <48! Check out the sequence A181771.

Racks and quandles

- groups associated to finite racks and quandles
- complete list of non-isomorphic indecomposable quandles of order < 48
- rack and quandle homology
- quandle colorings of knots
- quandle 2-cocycle invariants of knots
- Nelson’s polynomials invariants

Nichols algebras

- derivations
- dimensions and relations for gbnp package

Databases

- indecomposable quandles of size <48
- planar diagrams for knots of <13 crossings (from Livingstone’s website)
- planar diagrams for virtual knots up to <6 crossings (from Green’s website)

- L. Vendramin
- M. Graña (retired)

If you have used Rig in the preparation of a paper please cite it as:

L. Vendramin. Rig, a GAP package for racks, quandles and Nichols algebras. Available at https://github.com/gap-packages/rig/

You are welcome to contribute with code, patches, ideas, testing, wiki, comments, documentation. See the wiki for the list of contributors. Special thanks go to: W. E. Clark, D. Holt, A. Hulpke, A. Lochmann, G. Royle, M. Saito, D. Stanovsky.

See the wiki to learn how to install the package.

To load the package:

gap> LoadPackage(“rig”); If you want to see some examples follow this link.

Here you will find many examples (constructions of racks and quandles, quandle 2-cocycles abelian extensions, quandle colorings and 2-cocyle invariants of knots, calculations related to Nichols algebras…

Here you can find a comprehensive list of references relevant to quandles and related topics (work in progress). Help me to improve this list!

- GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra [http://www.gap-system.org/]
- GBNP, GAP Package for Gröbner Bases for Non-commutative Polynomials [http://mathdox.org/products/gbnp/]
- Sage: Open Source Mathematics Software [http://www.sagemath.org/]
- Small Connected Quandles and Their Knot Colorings [http://shell.cas.usf.edu/~saito/QuandleColor/]
- KnotInfo: Table of knot invariants, by C. Livingston and J. Cha [http://www.indiana.edu/~knotinfo/]
- A table of virtual knots, by Jeremy Green [http://www.math.toronto.edu/drorbn/Students/GreenJ/index.html]