toqito.perms.perm_sign
======================

.. py:module:: toqito.perms.perm_sign

.. autoapi-nested-parse::

   Calculates the permutation sign.





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

.. py:function:: perm_sign(perm)

   Compute the "sign" of a permutation [@WikiParPerm].

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

   .. rubric:: Examples

   For the following vector

   \[
       [1, 2, 3, 4]
   \]

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

   ```python exec="1" source="above"
   from toqito.perms import perm_sign

   print(perm_sign([1, 2, 3, 4]))
   ```

   For the following vector

   \[
       [1, 2, 3, 4, 5]
   \]

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

   ```python exec="1" source="above"
   from toqito.perms import perm_sign

   print(perm_sign([1, 2, 4, 3, 5]))
   ```

   :param perm: The permutation vector to be checked.

   :returns: The value 1 if the permutation is of even length and the value of -1 if the permutation is of odd length.