def test_generators():
assert list(cyclic(6)) == [Permutation([0, 1, 2, 3, 4, 5]), Permutation([1, 2, 3, 4, 5, 0]), \
Permutation([2, 3, 4, 5, 0, 1]), Permutation([3, 4, 5, 0, 1, 2]), \
Permutation([4, 5, 0, 1, 2, 3]), Permutation([5, 0, 1, 2, 3, 4])]
assert list(cyclic(10)) == [Permutation([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), \
Permutation([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]), \
Permutation([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]), \
Permutation([3, 4, 5, 6, 7, 8, 9, 0, 1, 2]), \
Permutation([4, 5, 6, 7, 8, 9, 0, 1, 2, 3]), \
Permutation([5, 6, 7, 8, 9, 0, 1, 2, 3, 4]), \
Permutation([6, 7, 8, 9, 0, 1, 2, 3, 4, 5]), \
Permutation([7, 8, 9, 0, 1, 2, 3, 4, 5, 6]), \
Permutation([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]), \
Permutation([9, 0, 1, 2, 3, 4, 5, 6, 7, 8])]
assert list(alternating(4)) == [Permutation([0, 1, 2, 3]), Permutation([0, 2, 3, 1]), \
Permutation([0, 3, 1, 2]), Permutation([1, 0, 3, 2]), \
Permutation([1, 2, 0, 3]), Permutation([1, 3, 2, 0]), \
Permutation([2, 0, 1, 3]), Permutation([2, 1, 3, 0]), \
Permutation([2, 3, 0, 1]), Permutation([3, 0, 2, 1]), \
Permutation([3, 1, 0, 2]), Permutation([3, 2, 1, 0])]
assert list(symmetric(3)) == [Permutation([0, 1, 2]), Permutation([0, 2, 1]), Permutation([1, 0, 2]), \
Permutation([1, 2, 0]), Permutation([2, 0, 1]), Permutation([2, 1, 0])]
assert list(symmetric(4)) == [Permutation([0, 1, 2, 3]), Permutation([0, 1, 3, 2]), Permutation([0, 2, 1, 3]), \
Permutation([0, 2, 3, 1]), Permutation([0, 3, 1, 2]), Permutation([0, 3, 2, 1]), \
Permutation([1, 0, 2, 3]), Permutation([1, 0, 3, 2]), Permutation([1, 2, 0, 3]), \
Permutation([1, 2, 3, 0]), Permutation([1, 3, 0, 2]), Permutation([1, 3, 2, 0]), \
Permutation([2, 0, 1, 3]), Permutation([2, 0, 3, 1]), Permutation([2, 1, 0, 3]), \
Permutation([2, 1, 3, 0]), Permutation([2, 3, 0, 1]), Permutation([2, 3, 1, 0]), \
Permutation([3, 0, 1, 2]), Permutation([3, 0, 2, 1]), Permutation([3, 1, 0, 2]), \
Permutation([3, 1, 2, 0]), Permutation([3, 2, 0, 1]), Permutation([3, 2, 1, 0])]
assert list(dihedral(2)) == [Permutation([0, 1, 2, 3]), Permutation([1, 0, 3, 2]), \
Permutation([2, 3, 0, 1]), Permutation([3, 2, 1, 0])]
assert list(dihedral(3)) == [Permutation([0, 1, 2]), Permutation([2, 1, 0]), Permutation([1, 2, 0]), \
Permutation([0, 2, 1]), Permutation([2, 0, 1]), Permutation([1, 0, 2])]
assert list(dihedral(5)) == [Permutation([0, 1, 2, 3, 4]), Permutation([4, 3, 2, 1, 0]), \
Permutation([1, 2, 3, 4, 0]), Permutation([0, 4, 3, 2, 1]), \
Permutation([2, 3, 4, 0, 1]), Permutation([1, 0, 4, 3, 2]), \
Permutation([3, 4, 0, 1, 2]), Permutation([2, 1, 0, 4, 3]), \
Permutation([4, 0, 1, 2, 3]), Permutation([3, 2, 1, 0, 4])]
def generate_groups():
alternating_6 = list(gens.alternating(6))
odd_6 = [x for x in list(gens.symmetric(6)) if x not in alternating_6]
return alternating_6, odd_6