def test_symmgroup():
def assert_eq_hash(a, b):
assert hash(a) == hash(b)
assert a == b
assert_eq_hash(group.Identity(), group.Identity())
tr = Grid([8, 4, 3]).translation_group
assert_eq_hash(tr(), tr(0) @ tr(1) @ tr(2))
assert_eq_hash(tr().remove_duplicates(), tr())
assert tr() @ tr() != tr()
assert_eq_hash((tr() @ tr()).remove_duplicates(), tr())
def test_grid_space_group():
g = nk.graph.Chain(8)
_check_symmgroups(g)
assert g.rotation_group().elems == [group.Identity()]
assert len(g.point_group()) == 2 # one reflection
assert len(g.space_group()) == 8 * 2 # translations * reflection
g = nk.graph.Grid([8, 2], pbc=False)
_check_symmgroups(g)
assert len(g.rotation_group()) == 2
assert len(g.point_group()) == 4
assert g.point_group() == g.space_group() # no PBC, no translations
g = nk.graph.Grid([3, 3, 3], pbc=[True, True, False])
_check_symmgroups(g)
assert len(g.rotation_group()) == 8
assert len(g.point_group()) == 16 # D_4 × Z_2
assert len(g.space_group()) == 3 * 3 * 16
g = nk.graph.Grid([3, 3, 3, 3], pbc=[True, True, False, False])
_check_symmgroups(g)
assert len(g.rotation_group()) == 32
assert len(g.point_group()) == 64 # D_4 × D_4
assert len(g.space_group()) == 3 * 3 * 64
g = nk.graph.Hypercube(3, 2)
_check_symmgroups(g)
assert len(g.space_group()) == len(g.automorphisms())
g = nk.graph.Hypercube(4, 2)
_check_symmgroups(g)
# 4x4 square has even higher symmetry
assert len(g.space_group()) < len(g.automorphisms())
def test_grid_translations():
for ndim in 1, 2:
g = Grid([4] * ndim, pbc=True)
translations = g.translation_group()
assert len(translations) == g.n_nodes
_check_symmgroup(g.automorphisms(), translations)
g = Grid([4] * ndim, pbc=False)
translations = g.translation_group()
assert translations.elems == [group.Identity()] # only identity
g = Grid([8, 4, 3], pbc=[True, False, False])
assert len(g.translation_group()) == 8
g = Grid([8, 4, 3], pbc=[True, True, False])
assert len(g.translation_group()) == 8 * 4
assert g.translation_group(2).elems == [group.Identity()] # only identity
g = Grid([8, 4, 3], pbc=[True, True, True])
assert len(g.translation_group()) == 8 * 4 * 3
assert len(g.translation_group(dim=0)) == 8
assert len(g.translation_group(dim=1)) == 4
assert len(g.translation_group(dim=2)) == 3
t1 = g.translation_group()
t2 = (
g.translation_group(dim=0)
@ g.translation_group(dim=1)
@ g.translation_group(dim=2)
)
assert t1 == t2
t2 = (
g.translation_group(dim=2)
@ g.translation_group(dim=1)
@ g.translation_group(dim=0)
)
assert t1 != t2
assert g.translation_group(dim=(0, 1)) == g.translation_group(
0
) @ g.translation_group(1)
def test_inverse(grp):
inv = grp.inverse
for i, j in enumerate(inv):
assert_equal(grp._canonical(grp[i] @ grp[j]),
grp._canonical(group.Identity()))