Sample flipper scripts
======================

Here are several small sample scripts that demonstrate some of the features of flipper.

.. contents:: :local:

Mapping classes
---------------

We can compute some basic properties of a mapping class:

.. literalinclude:: samples/encoding.py

All words
---------

Flipper can systematically generate all words in a given generating set.
This is useful for exhaustively searching for mapping classes with rare properties:

.. literalinclude:: samples/all_words.py

Invariant laminations
---------------------

We can see just how good flipper is at finding invariant laminations:

.. literalinclude:: samples/invariant_lamination.py

Pseudo-Anosov distributions
---------------------------

Since flipper can determine the Nielsen--Thupyon type of a mapping class we can use it to explore how the percentage of pseudo-Anosovs grows with respect to word length:

.. literalinclude:: samples/distribution.py

Conjugacy classes
-----------------

Flipper can partition pseudo-Anosov mapping classes into conjugacy classes:

.. literalinclude:: samples/conjugacy.py

Bundles
-------

Flipper can interface with SnapPy to build the mapping tori associated to a mapping class.
When the mapping class is pseudo-Anosov, flipper builds Agol's veering triangulation of the fulling punctured mapping torus and installs the correct Dehn fillings:

.. literalinclude:: samples/bundle.py

Twister
-------

We can check that the mapping tori built by Twister and flipper agree:

.. literalinclude:: samples/twister.py

Censuses
--------

Flipper includes large censuses of monodromies for fibred knots and manifolds:

.. literalinclude:: samples/censuses.py

Knot cusp orders
----------------

Flipper can find fibred knots where the stable lamination has two (6_2) or even one (8_20) prong coming out of the knot:

.. literalinclude:: samples/knot_cusp_orders.py

Hard invariant laminations
--------------------------

There is also a database of mapping classes that flipper has previously had a hard time finding invariant laminations for.
These may be useful test cases for other pieces of software or be worth exploring for interesting mathematical properties:

.. literalinclude:: samples/hard_invariant_lamination.py