from sympy import (residue, Symbol, Function, sin, I, exp, log, pi,
                   factorial, sqrt, Rational, cot)
from sympy.testing.pytest import XFAIL, raises
from sympy.abc import x, z, a, s


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


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) == Rational(3, 8)


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
    assert residue(1/(x**4 + 1), x, exp(I*pi/4)).equals(-(Rational(1, 4) + I/4)/sqrt(2))
    assert residue(1/(x**2 + a**2)**2, x, a*I) == -I/4/a**3


@XFAIL
def test_expressions_failing():
    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)


def test_NotImplemented():
    raises(NotImplementedError, lambda: residue(exp(1/z), z, 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_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_issue_14037():
    assert residue(sin(x**50)/x**51, x, 0) == 1


def test_issue_21176():
    assert residue(x**2*cot(pi*x)/(x**4 + 1), x, -sqrt(2)/2 - sqrt(2)*I/2) == 0
