hikari.symmetry.group
=====================

.. py:module:: hikari.symmetry.group

.. autoapi-nested-parse::

   This file contains class definition and necessary tools for constructing
   and evaluating all symmetry groups.



Classes
-------

.. autoapisummary::

   hikari.symmetry.group.Group


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

.. py:class:: Group(*generators)

   Base immutable class containing information about symmetry groups.
   It stores information for point and space groups and, among others,
   allows for iteration over its `hikari.symmetry.BoundedOperation` elements.


   .. py:class:: System

      Bases: :py:obj:`enum.Enum`


      Enumerator class with information about associated crystal system


      .. py:attribute:: triclinic
         :value: 0



      .. py:attribute:: monoclinic
         :value: 1



      .. py:attribute:: orthorhombic
         :value: 2



      .. py:attribute:: trigonal
         :value: 3



      .. py:attribute:: tetragonal
         :value: 4



      .. py:attribute:: cubic
         :value: 5



      .. py:attribute:: hexagonal
         :value: 6



      .. py:property:: directions
         :type: list[numpy.ndarray]




   .. py:attribute:: BRAVAIS_PRIORITY_RULES
      :value: 'A+B+C=F>R>I>C>B>A>H>P'



   .. py:attribute:: AXIS_PRIORITY_RULES
      :value: '6>61>62>63>64>65>-6>4>41>42>43>-4>-3>3>31>32>2>21'



   .. py:attribute:: PLANE_PRIORITY_RULES
      :value: 'm>a+b=e>a+c=e>b+c=e>a>b>c>n>d'



   .. py:attribute:: __generators
      :value: []



   .. py:attribute:: __operations


   .. py:attribute:: name


   .. py:attribute:: number
      :value: 0



   .. py:method:: from_generators_operations(generators, operations)
      :classmethod:


      Generate group using already complete list of generators and operators.
      Does not check if `operations` are correct or complete for efficiency!
      :param generators: A complete list of group generators
      :param operations: A complete list of group operations
      :return: Symmetry group with given generators and operators.



   .. py:method:: from_hall_symbol(hall_symbol)
      :classmethod:



   .. py:method:: __eq__(other)


   .. py:method:: __lt__(other)


   .. py:method:: __gt__(other)


   .. py:method:: __le__(other)


   .. py:method:: __ge__(other)


   .. py:method:: __repr__()


   .. py:method:: __str__()


   .. py:method:: __hash__()


   .. py:property:: auto_generated_name
      :type: str


      Name of the group generated automatically. Use only as approx.


   .. py:property:: centering_symbol
      :type: str



   .. py:property:: generators
      :type: list[hikari.symmetry.operations.BoundedOperation]



   .. py:property:: operations
      :type: list[hikari.symmetry.operations.BoundedOperation]



   .. py:property:: order
      :type: int



   .. py:property:: is_centrosymmetric
      :type: bool


      True if group has centre of symmetry; False otherwise.


   .. py:property:: is_enantiogenic
      :type: bool


      True if determinant of any operation in group is negative.


   .. py:property:: is_sohncke
      :type: bool


      True if determinant of all operations in group are positive.


   .. py:property:: is_achiral


   .. py:property:: is_chiral


   .. py:property:: is_symmorphic
      :type: bool



   .. py:property:: is_polar
      :type: bool



   .. py:property:: system
      :type: System


      Predicted crystal system associated with this group


   .. py:method:: lauefy()

      :return: New PointGroup with centre of symmetry added to generators.
      :rtype: Group



   .. py:method:: reciprocate()


   .. py:method:: transform(m)

      Transform the group using 4x4 matrix. For reference, see `bilbao
      resources <https://www.cryst.ehu.es/cryst/trmatrix.html>`_ or `IUCr
      pamphlet no. 22 <https://www.iucr.org/education/pamphlets/22>`_.

      :example:

      >>> import numpy
      >>> from hikari.symmetry import SG
      >>> matrix = numpy.array([(1,0,1,0),(0,1,0,0),(-1,0,0,0),(0,0,0,1)])
      >>> SG['P21/c'].transform(matrix).auto_generated_name
      P 21/n

      :param m: A 4x4 array containing information about new base and origin.
      :type m: np.ndarray
      :return: Group with new, transformed basis and origin.
      :rtype: Group