Symbolic computation with finite biquandles

TL;DR

This paper introduces algorithms for computing the second Yang-Baxter cohomology and cocycle invariants of finite biquandles, facilitating knot and link analysis through algebraic invariants.

Contribution

It presents new computational methods for Yang-Baxter cohomology and cocycle invariants of finite biquandles, with implementations in Maple.

Findings

Efficient algorithms for second Yang-Baxter cohomology basis computation.

Method for computing Yang-Baxter cocycle invariants from Gauss codes.

Available Maple implementations for practical use.

Abstract

A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Z_p from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.