Symbolic computation with finite quandles

Abstract

Algorithms are described and Maple implementations are provided for finding all quandles of order $n$, as well as computing all homomorphisms between two finite quandles or from a finitely presented quandle (e.g., a knot quandle) to a finite quandle, computing the automorphism group of a finite quandle, etc. Several of these programs work for arbitrary binary operation tables and hence algebraic structures other than quandles. We also include a stand-alone C program which finds quandles of order $n$ and provide URLs for files containing the results for $n=6,$ 7 and 8.