Implementation: The conjugacy problem in right-angled Artin groups

Abstract

In 2009, Crisp, Godelle and Wiest constructed a linear-time algorithm to solve the conjugacy problem in right-angled Artin groups. This algorithm has now been implemented in Python, and the code is freely available on GitHub. This document provides a summary of how the code works. As well as determining whether two elements $w_1,w_2$ are conjugate in a RAAG $A_{\Gamma }$, our code also returns a conjugating element $x\in A_{\Gamma }$ such that $w_1=x^{-1}{w}_{2}x$, if $w_1$ and $w_2$ are conjugate.

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