def cosets(self):
"""decomposing group of a bilayer with respect to the pair
stabilizer. Coset representatives generate pairs, symmetry
equivalent to self. Returns list of cosets of the decomposition"""
if self._cosets:
return self._cosets
self._cosets = core.cosets_mod(self.stab, self.bilayer.stab, 1)
return self._cosets
def fragments(self, fragments):
nr_frags = len(fragments)
assert nr_frags >= 0
"The layer contains no fragments!"#fragments is non-empty
if nr_frags == 1:
item_fragments = []
basic_fragment = fragments[0]
order_basic = len(basic_fragment.stab)
order_self = len(self.stab)
#basic checks that can be switched off
#1a in __init__
assert order_self % order_basic == 0,\
"Order of Fragment.stab does not divide that of Layer.stab!"
#1b ...
assert all([item in self.stab for item in basic_fragment.stab]),\
"There are symops in Fragment.stab that are not in Layer.stab!"
lcosets = core.cosets_mod(basic_fragment.stab, self.stab)
for lcoset in lcosets:
item_fragments.append(Fragment.leftmult(basic_fragment,
lcoset[0]))
self._fragments = item_fragments
#basic checks to do after coset decomposition
#1c
assert all([core.coset_in_stab((coset, self.stab)) \
for coset in lcosets]),\
"""Cosets of the consituent fragments
do not belong to the stabilizer of the layer!"""
#1d
assert all([core.divides((coset, self.stab)) for coset in lcosets]),\
"""Order of cosets of consituent fragments does not devides
order of the layers's stabilizer"""
else:
self._fragments = fragments
#basic checks that can be switched off
coset_list = [fragment.coset for fragment in self._fragments]
stab_list = [fragment.stab for fragment in self._fragments]
#1e
assert core.cosets_are_disjoint(coset_list), "Cosets are not disjoint!"
#1f
assert all([core.divides((stab, self.stab)) for stab in stab_list]),\
"""Order of stabilizer of some constituent fragments
does not devide order of the layers's stabilizer"""
#1g
assert all([core.coset_in_stab((stab, self.stab)) \
for stab in stab_list]),\
"""Stabilizers of the consituent fragments