def test_commutators():
a = Permutation([1, 0, 2, 4, 3])
b = Permutation([0, 1, 3, 2, 4])
G = PermutationGroup([a,b])
C = G.commutator()
assert C.order() == 3
assert C.is_normal(G)
assert C.is_subgroup(G)
assert not G.is_subgroup(C)
gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
gens = [Permutation(p) for p in gens_cube]
G = PermutationGroup(gens)
C = G.commutator()
assert C.order() == 12
def test_commutators():
a = Permutation([1, 0, 2, 4, 3])
b = Permutation([0, 1, 3, 2, 4])
G = PermutationGroup([a, b])
C = G.commutator()
assert C.order() == 3
assert C.is_normal(G)
assert C.is_subgroup(G)
assert not G.is_subgroup(C)
gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
gens = [Permutation(p) for p in gens_cube]
G = PermutationGroup(gens)
C = G.commutator()
assert C.order() == 12
def test_rubik1():
gens = rubik_cube_generators()
gens1 = [gens[0]] + [p**2 for p in gens[1:]]
G1 = PermutationGroup(gens1)
assert G1.order() == 19508428800
gens2 = [p**2 for p in gens]
G2 = PermutationGroup(gens2)
assert G2.order() == 663552
assert G2.is_subgroup(G1)
C1 = G1.commutator()
assert C1.order() == 4877107200
assert C1.is_subgroup(G1)
assert not G2.is_subgroup(C1)
def test_rubik1():
gens = rubik_cube_generators()
gens1 = [gens[0]] + [p**2 for p in gens[1:]]
G1 = PermutationGroup(gens1)
assert G1.order() == 19508428800
gens2 = [p**2 for p in gens]
G2 = PermutationGroup(gens2)
assert G2.order() == 663552
assert G2.is_subgroup(G1)
C1 = G1.commutator()
assert C1.order() == 4877107200
assert C1.is_subgroup(G1)
assert not G2.is_subgroup(C1)
