def test_mathieus():
assert isinstance(mathieus(a, q, z), mathieus)
assert mathieus(a, 0, z) == sin(sqrt(a) * z)
assert conjugate(mathieus(a, q, z)) == mathieus(conjugate(a), conjugate(q), conjugate(z))
assert diff(mathieus(a, q, z), z) == mathieusprime(a, q, z)
def test_mathieusprime():
assert isinstance(mathieusprime(a, q, z), mathieusprime)
assert mathieusprime(a, 0, z) == sqrt(a) * cos(sqrt(a) * z)
assert diff(mathieusprime(a, q, z),
z) == (-a + 2 * q * cos(2 * z)) * mathieus(a, q, z)
def test_mathieusprime():
assert isinstance(mathieusprime(a, q, z), mathieusprime)
assert mathieusprime(a, 0, z) == sqrt(a) * cos(sqrt(a) * z)
assert diff(mathieusprime(a, q, z), z) == (-a + 2 * q * cos(2 * z)) * mathieus(a, q, z)
def test_mathieus():
assert isinstance(mathieus(a, q, z), mathieus)
assert mathieus(a, 0, z) == sin(sqrt(a) * z)
assert conjugate(mathieus(a, q, z)) == mathieus(conjugate(a), conjugate(q),
conjugate(z))
assert diff(mathieus(a, q, z), z) == mathieusprime(a, q, z)
