def cyclic_form(self):
"""Return the indices of the corners in cyclic notation.
The indices are given relative to the original position of corners.
See Also
========
corners, array_form
"""
return Perm._af_new(self.array_form).cyclic_form
def cyclic_form(self):
"""Return the indices of the corners in cyclic notation.
The indices are given relative to the original position of corners.
See Also
========
corners, array_form
"""
return Perm._af_new(self.array_form).cyclic_form
def _naive_list_centralizer(self, other, af=False):
from sympy.combinatorics.perm_groups import PermutationGroup
"""
Return a list of elements for the centralizer of a subgroup/set/element.
Explanation
===========
This is a brute force implementation that goes over all elements of the
group and checks for membership in the centralizer. It is used to
test ``.centralizer()`` from ``sympy.combinatorics.perm_groups``.
Examples
========
>>> from sympy.combinatorics.testutil import _naive_list_centralizer
>>> from sympy.combinatorics.named_groups import DihedralGroup
>>> D = DihedralGroup(4)
>>> _naive_list_centralizer(D, D)
[Permutation([0, 1, 2, 3]), Permutation([2, 3, 0, 1])]
See Also
========
sympy.combinatorics.perm_groups.centralizer
"""
from sympy.combinatorics.permutations import _af_commutes_with
if hasattr(other, 'generators'):
elements = list(self.generate_dimino(af=True))
gens = [x._array_form for x in other.generators]
commutes_with_gens = lambda x: all(
_af_commutes_with(x, gen) for gen in gens)
centralizer_list = []
if not af:
for element in elements:
if commutes_with_gens(element):
centralizer_list.append(Permutation._af_new(element))
else:
for element in elements:
if commutes_with_gens(element):
centralizer_list.append(element)
return centralizer_list
elif hasattr(other, 'getitem'):
return _naive_list_centralizer(self, PermutationGroup(other), af)
elif hasattr(other, 'array_form'):
return _naive_list_centralizer(self, PermutationGroup([other]), af)
def _naive_list_centralizer(self, other, af=False):
from sympy.combinatorics.perm_groups import PermutationGroup
"""
Return a list of elements for the centralizer of a subgroup/set/element.
This is a brute force implementation that goes over all elements of the
group and checks for membership in the centralizer. It is used to
test ``.centralizer()`` from ``sympy.combinatorics.perm_groups``.
Examples
========
>>> from sympy.combinatorics.testutil import _naive_list_centralizer
>>> from sympy.combinatorics.named_groups import DihedralGroup
>>> D = DihedralGroup(4)
>>> _naive_list_centralizer(D, D)
[Permutation([0, 1, 2, 3]), Permutation([2, 3, 0, 1])]
See Also
========
sympy.combinatorics.perm_groups.centralizer
"""
from sympy.combinatorics.permutations import _af_commutes_with
if hasattr(other, "generators"):
elements = list(self.generate_dimino(af=True))
gens = [x._array_form for x in other.generators]
commutes_with_gens = lambda x: all(_af_commutes_with(x, gen) for gen in gens)
centralizer_list = []
if not af:
for element in elements:
if commutes_with_gens(element):
centralizer_list.append(Permutation._af_new(element))
else:
for element in elements:
if commutes_with_gens(element):
centralizer_list.append(element)
return centralizer_list
elif hasattr(other, "getitem"):
return _naive_list_centralizer(self, PermutationGroup(other), af)
elif hasattr(other, "array_form"):
return _naive_list_centralizer(self, PermutationGroup([other]), af)