def test_cyclic_inverses(n):
C = group.cyclic(n)
for i in xrange(n):
assert C[i].inverse() == C[(n - i) % n]
def test_cyclic_generators(n):
C = group.cyclic(n)
gens = C.find_generators()
assert len(gens) == 1
def test_element_order():
C = group.cyclic(6)
expected = [1,6,3,2,3,6]
for i in xrange(6):
assert len(C[i]) == expected[i]
def test_group_order(n):
C = group.cyclic(n)
assert len(C) == n
def test_construct_cyclic(n):
C = group.cyclic(n)
for i in xrange(n):
for j in xrange(n):
(C[i] * C[j]).name == (i+j)%n
