def test_right_coset():
D = group.dihedral(4)
F = D.subgroup([D["f0"]])
expected = set(["1","f1"])
coset = F * D["1"]
names = set(c.name for c in coset)
assert names == expected
def test_order_by_subgroup():
D = group.dihedral(6)
R = D.subgroup([D["2"]])
F = D.subgroup([D["f0"]])
ordered = D.order_by_subgroups([R,F])
expected = ['0', '2', '4', '1', '3', '5', 'f0', 'f4', 'f2', 'f5', 'f3', 'f1']
assert ordered == expected
def test_left_coset():
D = group.dihedral(4)
F = D.subgroup([D["f0"]])
expected = set(["1","f3"])
coset = D["1"] * F
names = set(c.name for c in coset)
assert names == expected
def test_dihedral_generators(n):
C = group.dihedral(n)
gens = C.find_generators()
assert len(gens) == 2
assert any([e.name[0] == 'f' for e in gens])
assert any([e.name == '1' for e in gens])
