:py:mod:`perms.perm_sign`
=========================

.. py:module:: perms.perm_sign

.. autoapi-nested-parse::

   Calculate permutation sign.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   perms.perm_sign.perm_sign



.. py:function:: perm_sign(perm)

   Compute the "sign" of a permutation :cite:`WikiParPerm`.

   The sign (either -1 or 1) of the permutation :code:`perm` is :code:`-1**`inv`, where :code:`inv` is the number of
   inversions contained in :code:`perm`.

   .. rubric:: Examples

   For the following vector

   .. math::
       [1, 2, 3, 4]

   the permutation sign is positive as the number of elements in the vector are even. This can be performed in
   :code:`toqito` as follows.

   >>> from toqito.perms import perm_sign
   >>> perm_sign([1, 2, 3, 4])
   1.0

   For the following vector

   .. math::
       [1, 2, 3, 4, 5]

   the permutation sign is negative as the number of elements in the vector are odd. This can be performed in
   :code:`toqito` as follows.

   >>> from toqito.perms import perm_sign
   >>> perm_sign([1, 2, 4, 3, 5])
   -1.0

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param perm: The permutation vector to be checked.
   :return: The value 1 if the permutation is of even length and the value of
            -1 if the permutation is of odd length.