Orbits
======

*Orbits* is free software licensed under the GNU Public license, version 2 or higher,
and it is provided `without warranty of any kind`__.

__ http://www.gnu.org/licenses/gpl-2.0-standalone.html#section11

In a remarkable `paper
<http://www.ams.org/journals/tran/2006-358-09/S0002-9947-05-03919-X/S0002-9947-05-03919-X.pdf>`_
by Ian Agol, Joel Hass and Bill Thurston it was shown that the problem of
deciding whether a knot has a genus :math:`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 :math:`J = \{1, ..., N\}` which
   |   is generated by :math:`k` isometric pairings between subintervals of :math:`J`,
   |   compute the number of equivalence classes.

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

*Orbits* is a python module which implements their algorithm.

.. toctree::
   :maxdepth: 2
   :caption: Contents:

   module

Installation
------------

*Orbits* 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.

Indices and tables
------------------

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`