QuandleRUN: algorithms for Quandle Theory

Computer algebra involves developing algorithms to carry out exact computations involving algebraic structures. Quandles are algebraic structures that can benefit from the help of computational tools and attention from the community, much like groups. This project introduces a modern tool able to work with quandles: congruences, subuniverses, isomorphisms, and monomorphisms, among others; built on the solid mathematical foundations of the most recent developments in Quandle Theory, and Universal Algebra as well as computational tools that withstood the test of time such as Magma and Rig and modern ones such as CREAM, it is able to obtain useful results at a competitive speed. As an example, it will be shown how to compute and visualise connections among connected quandles.

A new algorithm for computing the congruences of connected quandles, based on the work of dr. Marco Bonatto, will be introduced.