from sympy import sin, cos, exp, cot, I, symbols

x, y, z, n = symbols("x,y,z,n")


def test_has():
    assert cot(x).has(x)
    assert cot(x).has(cot)
    assert not cot(x).has(sin)
    assert sin(x).has(x)
    assert sin(x).has(sin)
    assert not sin(x).has(cot)


def test_sin_exp_rewrite():
    assert sin(x).rewrite(sin, exp) == -I / 2 * (exp(I * x) - exp(-I * x))
    assert sin(x).rewrite(sin, exp).rewrite(exp, sin) == sin(x)
    assert cos(x).rewrite(cos, exp).rewrite(exp, cos) == cos(x)
    assert (sin(5 * y) - sin(2 * x)).rewrite(sin, exp).rewrite(exp, sin) == sin(
        5 * y
    ) - sin(2 * x)
    assert sin(x + y).rewrite(sin, exp).rewrite(exp, sin) == sin(x + y)
    assert cos(x + y).rewrite(cos, exp).rewrite(exp, cos) == cos(x + y)
    # This next test currently passes... not clear whether it should or not?
    assert cos(x).rewrite(cos, exp).rewrite(exp, sin) == cos(x)
