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

Download

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

News

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

Features

• 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

• derivations
• dimensions and relations for gbnp package

• 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)

Authors

• L. Vendramin
• M. Graña (retired)

Cite as

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 http://code.google.com/p/rig/

Contributions

You are welcome to contribute with code, patches, ideas, testing, wiki, comments, documentation. Click here to see the list of contributors.

Special thanks go to: W. E. Clark, D. Holt, A. Hulpke, A. Lochmann, G. Royle, M. Saito, D. Stanovsky.

Usage

Follow this link if you don't know how to install the package.

To load the package:

gap> LoadPackage("rig");

If you want to see some examples follow this link.

Examples

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...

References

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

Links

• GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra
• GBNP, GAP Package for Gröbner Bases for Non-commutative Polynomials
• Sage: Open Source Mathematics Software
• Small Connected Quandles and Their Knot Colorings
• KnotInfo: Table of knot invariants, by Chuck Livingston with the assistance of Jae Choon Cha
• A table of virtual knots, by Jeremy Green