symmray.symmetries
==================

.. py:module:: symmray.symmetries

.. autoapi-nested-parse::

   Definitions of various symmetries.



Classes
-------

.. autoapisummary::

   symmray.symmetries.Symmetry
   symmray.symmetries.ZN
   symmray.symmetries.Z2
   symmray.symmetries.U1
   symmray.symmetries.Z2Z2
   symmray.symmetries.U1U1


Functions
---------

.. autoapisummary::

   symmray.symmetries.sign_scalar
   symmray.symmetries.sign_tuple
   symmray.symmetries.get_zn_symmetry_cls
   symmray.symmetries.get_symmetry
   symmray.symmetries.calc_phase_permutation


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

.. py:class:: Symmetry

   Bases: :py:obj:`abc.ABC`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: __slots__
      :value: ()



   .. py:method:: valid(*charges)
      :abstractmethod:


      Check if all charges are valid for the symmetry.



   .. py:method:: combine(*charges)
      :abstractmethod:


      Combine / add charges according to the symmetry.



   .. py:method:: sign(charge, dual=True)
      :abstractmethod:


      Negate a charge according to the symmetry and flag ``dual``.



   .. py:method:: parity(charge)
      :abstractmethod:


      Return the parity, 0 or 1, of a charge according to the symmetry.



   .. py:method:: random_charge(seed=None)
      :abstractmethod:


      Return a random valid charge, for testing purposes.



   .. py:method:: __str__()


   .. py:method:: __eq__(other)


   .. py:method:: __hash__()


   .. py:method:: __repr__()


.. py:function:: sign_scalar(charge, dual=True)

.. py:function:: sign_tuple(charge, dual=True)

.. py:class:: ZN

   Bases: :py:obj:`Symmetry`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: __slots__
      :value: ('N',)



   .. py:method:: valid(*charges: int) -> bool

      Check if all charges are valid for the symmetry.



   .. py:method:: combine(*charges: int) -> int

      Combine / add charges according to the symmetry.



   .. py:method:: sign(charge: int, dual=True) -> int

      Negate a charge according to the symmetry and flag ``dual``.



   .. py:method:: parity(charge: int) -> int

      Return the parity, 0 or 1, of a charge according to the symmetry.



   .. py:method:: random_charge(seed=None) -> int

      Return a random valid charge, for testing purposes.



   .. py:method:: __reduce__()


.. py:class:: Z2

   Bases: :py:obj:`ZN`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: N
      :value: 2



   .. py:method:: sign(charge: int, dual=True) -> int

      Negate a charge according to the symmetry and flag ``dual``.



.. py:function:: get_zn_symmetry_cls(N: int) -> type

   Get a ZN symmetry class.


.. py:class:: U1

   Bases: :py:obj:`Symmetry`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: __slots__
      :value: ()



   .. py:method:: valid(*charges: int) -> bool

      Check if all charges are valid for the symmetry.



   .. py:method:: combine(*charges: int) -> int

      Combine / add charges according to the symmetry.



   .. py:method:: sign(charge: int, dual=True) -> int

      Negate a charge according to the symmetry and flag ``dual``.



   .. py:method:: parity(charge: int) -> int

      Return the parity, 0 or 1, of a charge according to the symmetry.



   .. py:method:: random_charge(seed=None) -> int

      Return a random valid charge, for testing purposes.



.. py:class:: Z2Z2

   Bases: :py:obj:`Symmetry`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: __slots__
      :value: ()



   .. py:method:: valid(*charges: tuple[int, int]) -> bool

      Check if all charges are valid for the symmetry.



   .. py:method:: combine(*charges: tuple[int, int]) -> tuple[int, int]

      Combine / add charges according to the symmetry.



   .. py:method:: sign(charge: tuple[int, int], dual=True) -> tuple[int, int]

      Negate a charge according to the symmetry and flag ``dual``.



   .. py:method:: parity(charge: tuple[int, int]) -> int

      Return the parity, 0 or 1, of a charge according to the symmetry.



   .. py:method:: random_charge(seed=None) -> tuple[int, int]

      Return a random valid charge, for testing purposes.



.. py:class:: U1U1

   Bases: :py:obj:`Symmetry`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: __slots__
      :value: ()



   .. py:method:: valid(*charges: tuple[int, int]) -> bool

      Check if all charges are valid for the symmetry.



   .. py:method:: combine(*charges: tuple[int, int]) -> tuple[int, int]

      Combine / add charges according to the symmetry.



   .. py:method:: sign(charge: tuple[int, int], dual=True) -> tuple[int, int]

      Negate a charge according to the symmetry and flag ``dual``.



   .. py:method:: parity(charge: tuple[int, int]) -> int

      Return the parity, 0 or 1, of a charge according to the symmetry.



   .. py:method:: random_charge(seed=None) -> tuple[int, int]

      Return a random valid charge, for testing purposes.



.. py:function:: get_symmetry(symmetry: str | Symmetry) -> Symmetry

   Get a symmetry instance by name.

   :param symmetry: The symmetry to get.
   :type symmetry: str or Symmetry

   :returns: The symmetry instance.
   :rtype: Symmetry


.. py:function:: calc_phase_permutation(parities: tuple[int, Ellipsis], perm: tuple[int, Ellipsis] = None) -> int

   Given sequence of parities and a permutation, compute the phase of the
   permutation acting on the odd charges. I.e. whether the number of swaps
   of odd sectors is even or odd.

   :param parities: The parities of the sectors.
   :type parities: tuple of int
   :param perm: The permutation of axes, by default None, which flips all axes.
   :type perm: tuple of int, optional

   :returns: The phase of the permutation, either 1 or -1.
   :rtype: int