Orbits¶
Orbits is free software licensed under the GNU Public license, version 2 or higher, and it is provided without warranty of any kind.
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 \(J = \{1, ..., N\}\) whichis generated by \(k\) isometric 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¶
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.