Braidlab: A Software Package for Braids and Loops

Abstract

Braidlab is a Matlab package for analyzing data using braids. It was designed to be fast, so it can be used on relatively large problems. It uses the object-oriented features of Matlab to provide a class for braids on punctured disks and a class for equivalence classes of simple closed loops. The growth of loops under iterated action by braids is used to compute the topological entropy of braids, as well as for determining the equality of braids. This guide is a survey of the main capabilities of braidlab, with many examples; the help messages of the various commands provide more details. Some of the examples contain novel observations, such as the existence of cycles of the linear effective action for arbitrary braids.