.. module:: permutation

=============================================================
permutation — Permutations of finitely many positive integers
=============================================================

`GitHub <https://github.com/jwodder/permutation>`_
| `PyPI <https://pypi.org/project/permutation>`_
| `Documentation <https://permutation.readthedocs.io>`_
| `Issues <https://github.com/jwodder/permutation/issues>`_
| `Changelog <https://github.com/jwodder/permutation/blob/master/CHANGELOG.md>`_

``permutation`` provides a `Permutation` class for representing `permutations
<https://en.wikipedia.org/wiki/Permutation>`_ of finitely many positive
integers in Python.  Supported operations & properties include inverses, (group
theoretic) order, parity, composition/multiplication, cycle decomposition,
cycle notation, word representation, Lehmer codes, and, of course, use as a
callable on integers.


Installation
============
``permutation`` requires Python 3.10 or higher.  Just use `pip
<https://pip.pypa.io>`_ for Python 3 (You have pip, right?) to install::

    python3 -m pip install permutation


Examples
========

>>> from permutation import Permutation
>>> p = Permutation(2, 1, 4, 5, 3)
>>> p(1)
2
>>> p(3)
4
>>> p(42)
42
>>> p.to_cycles()
[(1, 2), (3, 4, 5)]
>>> print(p)
(1 2)(3 4 5)
>>> print(p.inverse())
(1 2)(3 5 4)
>>> p.degree
5
>>> p.order
6
>>> p.is_even
False
>>> p.lehmer(5)
27
>>> q = Permutation.cycle(1,2,3)
>>> print(p * q)
(2 4 5 3)
>>> print(q * p)
(1 3 4 5)
>>> for p in Permutation.group(3):
...     print(p)
...
1
(1 2)
(2 3)
(1 3 2)
(1 2 3)
(1 3)

API
===

.. autoclass:: Permutation
    :special-members:
    :no-undoc-members:
    :exclude-members: __eq__, __hash__, __repr__, __weakref__

    .. autoclasstoc::

Indices and tables
==================
* :ref:`genindex`
* :ref:`search`