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Mini Shell
Mini Shell
from sympy import (residue, Symbol, Function, sin, I, exp, log, pi, S,
factorial, sqrt, Rational, tan, cot, tanh)
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():
f = x**2*cot(pi*x)/(x**4 + 1)
assert residue(f, x, -sqrt(2)/2 - sqrt(2)*I/2).cancel().together(deep=True)\
== sqrt(2)*(1 - I)/(8*tan(sqrt(2)*pi*(1 + I)/2))
def test_issue_21177():
r = -sqrt(3)*tanh(sqrt(3)*pi/2)/3
a = residue(cot(pi*x)/((x - 1)*(x - 2) + 1), x, S(3)/2 - sqrt(3)*I/2)
b = residue(cot(pi*x)/(x**2 - 3*x + 3), x, S(3)/2 - sqrt(3)*I/2)
assert a == r
assert (b - a).cancel() == 0
Zerion Mini Shell 1.0