def test_quaternion_generation():
q = Quaternion()
identity = (1, 0, 0, 0)
assert all(i == j for i, j in zip(q, identity))
q_id = Quaternion.identity()
assert all(i == j for i, j in zip(q_id, identity))
def test_quaternion_inverse():
q1 = Quaternion(1, 2, 3, 4)
inv = q1.inverse()
assert q1 * inv == Quaternion.identity()
with pytest.raises(ValueError):
zero_q = Quaternion(0, 0, 0, 0)
zero_q.inverse()
def test_quaternion_pow():
_ = Quaternion.identity()
i = Quaternion(0, 1, 0, 0)
j = Quaternion(0, 0, 1, 0)
k = Quaternion(0, 0, 0, 1)
i2 = i**2
j2 = j**2
k2 = k**2
assert i2 == j2 == k2
def test_quaternion_mul_basis():
_ = Quaternion.identity()
i = Quaternion(0, 1, 0, 0)
j = Quaternion(0, 0, 1, 0)
k = Quaternion(0, 0, 0, 1)
# test identity multiplication
assert _ * i == i
assert i * _ == i
assert j * _ == j
assert _ * j == j
assert _ * k == k
assert k * _ == k
i2 = i * i
j2 = j * j
k2 = k * k
ijk = i * j * k
assert i2 == j2 == k2 == ijk == -_
def test_quaternion_div():
q1 = Quaternion(1, 2, 3, 4)
assert q1 / q1 == Quaternion.identity()
