A taste of flipper
==================

The flipper GUI can be started by using the command::

    > flipper.app

flipper includes many pre-made examples under the ``File > Open example...`` menu.
For example the twice-punctured torus is show below.
Here we can apply mapping classes directly to curves drawn on the surface.

.. image:: ../images/ex1.png
    :scale: 100 %
    :alt: Long curve on S_{1,2}
    :align: center

flipper can also create new mapping classes by composing together old ones.
Additionally, several of their properties, including their Nielsen--Thurston type and dilatation, can be computed.
 
.. image:: ../images/ex2.png
    :scale: 100 %
    :alt: Invariant lamination of abC on S_{1,2}
    :align: center

However, to access the full power of flipper it should be imported into a Python interpreter::

    >>> import flipper
    >>> S = flipper.load('S_1_2')
    >>> h = S.mapping_class('abC')
    >>> h.nielsen_thurston_type()
    'Pseudo-Anosov'
    >>> d = h.dilatation()
    >>> d
    2.296630?
    >>> d.approximate_string(accuracy=50)
    '2.29663026288653824570494191773617027122260685258284?'
    >>> d.minimal_polynomial()
    1 - 2*x - 2*x^3 + x^4
    >>> h.hitting_matrix()
    [
    [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
    [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0],
    [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
    [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1],
    [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
    [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1],
    [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]
    ]

Here we can also access large censuses of monodromies::

    >>> census = flipper.census('knots')  # Census of fibred knots.
    >>> for s, w, _ in census:
    ...     h = flipper.load(s).mapping_class(w)
    ...     if h.dilatation() < 1.2:
    ...             print(s, w)
    ... 
    ('S_5_1', 'abcdefghil')  # There is only one known example of a fibred knot whose monodromy has dilatation < 1.2.
    

These are great for finding unusual examples and counter-examples to conjectures.
You can build more using::

    census = S.all_mapping_classes(length=5)