# Orbits

## Description

In a remarkable paper by Ian Agol, Joel Hass and Bill Thurston it was shown that the problem of deciding whether a knot has a genus g spanning surface is NP complete. Along the way, the authors described an algorithm for solving the following problem:

• Given an equivalence relation on the set J = {1, ..., N} which
is generated by k order preserving or order reversing pairings
between subintervals of J, compute the number of equivalence
classes.

They showed that the running time of the algorithm is amazingly fast -- bounded by a polynomial in k log N.

Orbits is a python module which implements their algorithm.

## Installation

This is a simple python module consisting of a single file. To install it run

python setup.py install


or, on linux,

sudo python setup.py install


A simple example computation is provided in the file example.py.