def test_expressions_failing():
    assert residue(1/(x**4 + 1), x, exp(I*pi/4)) == -(S(1)/4 + I/4)/sqrt(2)

    n = Symbol('n', integer=True, positive=True)
    assert residue(exp(z)/(z - pi*I/4*a)**n, z, I*pi*a) == \
        exp(I*pi*a/4)/factorial(n - 1)
    assert residue(1/(x**2 + a**2)**2, x, a*I) == -I/4/a**3

def test_basic1():
    assert residue(1 / x, x, 0) == 1
    assert residue(-2 / x, x, 0) == -2
    assert residue(81 / x, x, 0) == 81
    assert residue(1 / x ** 2, x, 0) == 0
    assert residue(0, x, 0) == 0
    assert residue(5, x, 0) == 0
    assert residue(x, x, 0) == 0
    assert residue(x ** 2, x, 0) == 0

def test_basic2():
    assert residue(1 / x, x, 1) == 0
    assert residue(-2 / x, x, 1) == 0
    assert residue(81 / x, x, -1) == 0
    assert residue(1 / x ** 2, x, 1) == 0
    assert residue(0, x, 1) == 0
    assert residue(5, x, 1) == 0
    assert residue(x, x, 1) == 0
    assert residue(x ** 2, x, 5) == 0

def test_basic2():
    x = Symbol("x")
    assert residue(1/x, x, 1) == 0
    assert residue(-2/x, x, 1) == 0
    assert residue(81/x, x, -1) == 0
    assert residue(1/x**2, x, 1) == 0
    assert residue(0, x, 1) == 0
    assert residue(5, x, 1) == 0
    assert residue(x, x, 1) == 0
    assert residue(x**2, x, 5) == 0

def test_expressions():
    assert residue(1 / (x + 1), x, 0) == 0
    assert residue(1 / (x + 1), x, -1) == 1
    assert residue(1 / (x ** 2 + 1), x, -1) == 0
    assert residue(1 / (x ** 2 + 1), x, I) == -I / 2
    assert residue(1 / (x ** 2 + 1), x, -I) == I / 2
    assert residue(1 / (x ** 4 + 1), x, 0) == 0

def test_bug():
    assert residue(2 ** (z) * (s + z) * (1 - s - z) / z ** 2, z, 0) == 1 + s * log(2) - s ** 2 * log(2) - 2 * s

def test_NotImplemented():
    raises(NotImplementedError, lambda: residue(exp(1 / z), z, 0))

def test_functions():
    assert residue(1 / sin(x), x, 0) == 1
    assert residue(2 / sin(x), x, 0) == 2
    assert residue(1 / sin(x) ** 2, x, 0) == 0
    assert residue(1 / sin(x) ** 5, x, 0) == S(3) / 8

def _test_f():
    f = Function("f")
    assert residue(f(x) / x ** 5, x, 0) == f(x).diff(x, 4).subs(x, 0) / 24

def test_functions():
    x = Symbol("x")
    assert residue(1/sin(x), x, 0) == 1
    assert residue(2/sin(x), x, 0) == 2
    assert residue(1/sin(x)**2, x, 0) == 0

def test_issue_3400():
    assert residue(1/(exp(z) - 1), z, 0) == 1

    # github issue 2519:
    assert residue((z**3 + 5)/((z**4 - 1)*(z + 1)), z, -1) == -S(9)/4

def _test_f():
    # FIXME: we get infinite recursion here:
    f = Function("f")
    assert residue(f(x)/x**5, x, 0) == f.diff(x, 4)/24

def test_bug():
    from sympy.abc import s, z
    assert residue(2**(z)*(s+z)*(1-s-z)/z**2, z, 0) == \
           1 + s*log(2) - s**2*log(2) - 2*s

def test_issue_3400():
    assert residue(1/(exp(z) - 1), z, 0) == 1

def test_NotImplemented():
    z = Symbol('z')
    raises(NotImplementedError, lambda: residue(exp(1/z), z, 0))

def test_issue_5654():
    assert residue(1 / (x ** 2 + a ** 2) ** 2, x, a * I) == -I / (4 * a ** 3)

def test_issue_6499():
    assert residue(1 / (exp(z) - 1), z, 0) == 1

def test_expressions_failing():
    x = Symbol('x')
    assert residue(1/(x**4+1), x, exp(I*pi/4)) == -(S(1)/4+I/4)/sqrt(2)