def test_freely_reduced():
generators = frozenset(Word(c) for c in 'abcde')
e = identity = Word('e')
F = FreeGroup(generators, identity)
a = Word('a')
b = Word('b')
a_inv = F.inverse(a)
b_inv = F.inverse(b)
assert freely_reduced(F, a + a_inv) == identity
assert freely_reduced(F, a + b + b_inv + a_inv) == identity
assert freely_reduced(F, a + a + b + b_inv + a_inv) == a
assert freely_reduced(F, a + e + b) == a + b
def test_power():
a, b, c, e = (Word(c) for c in 'abce')
F = FreeGroup({a, b, c, e}, e)
for x in (a, b, c, e):
assert F.power(x, 0) == e
assert F.power(x, 1) == x
assert freely_reduced(F, x + F.power(x, -1)) == e
assert F.power(x, 2) == x + x
assert F.power(x, 3) == x + x + x
def test_inverse():
a, b, c, e = (Word(c) for c in 'abce')
F = FreeGroup({a, b, c, e}, e)
abc = a + b + c
abc_inv = F.inverse(abc)
assert freely_reduced(F, abc + abc_inv) == e