def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1/log(z)
assert Li(z).rewrite(li) == li(z) - li(2)
def test_li():
z = Symbol("z")
zr = Symbol("z", extended_real=True)
zp = Symbol("z", positive=True)
zn = Symbol("z", negative=True)
assert li(0) == 0
assert li(1) == -oo
assert li(oo) == oo
assert isinstance(li(z), li)
assert diff(li(z), z) == 1/log(z)
assert conjugate(li(z)) == li(conjugate(z))
assert conjugate(li(-zr)) == li(-zr)
assert conjugate(li(-zp)) == conjugate(li(-zp))
assert conjugate(li(zn)) == conjugate(li(zn))
assert li(z).rewrite(Li) == Li(z) + li(2)
assert li(z).rewrite(Ei) == Ei(log(z))
assert li(z).rewrite(uppergamma) == (-log(1/log(z))/2 - log(-log(z)) +
log(log(z))/2 - expint(1, -log(z)))
assert li(z).rewrite(Si) == (-log(I*log(z)) - log(1/log(z))/2 +
log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)))
assert li(z).rewrite(Ci) == (-log(I*log(z)) - log(1/log(z))/2 +
log(log(z))/2 + Ci(I*log(z)) + Shi(log(z)))
assert li(z).rewrite(Shi) == (-log(1/log(z))/2 + log(log(z))/2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(Chi) == (-log(1/log(z))/2 + log(log(z))/2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(hyper) == (log(z)*hyper((1, 1), (2, 2), log(z)) -
log(1/log(z))/2 + log(log(z))/2 + EulerGamma)
assert li(z).rewrite(meijerg) == (-log(1/log(z))/2 - log(-log(z)) + log(log(z))/2 -
meijerg(((), (1,)), ((0, 0), ()), -log(z)))
def test_limit():
assert gruntz(x, x) == oo
assert gruntz(-x, x) == -oo
assert gruntz(-x, x) == -oo
assert gruntz((-x)**2, x) == oo
assert gruntz(-x**2, x) == -oo
assert gruntz((1 / x) * log(1 / x), x) == 0 # Gruntz: p15, 2.11
assert gruntz(1 / x, x) == 0
assert gruntz(exp(x), x) == oo
assert gruntz(-exp(x), x) == -oo
assert gruntz(exp(x) / x, x) == oo
assert gruntz(1 / x - exp(-x), x) == 0
assert gruntz(x + 1 / x, x) == oo
assert gruntz((1 / x)**(1 / x), x) == 1 # Gruntz: p15, 2.11
assert gruntz((exp(1 / x) - 1) * x, x) == 1
assert gruntz(1 + 1 / x, x) == 1
assert gruntz(-exp(1 / x), x) == -1
assert gruntz(x + exp(-x), x) == oo
assert gruntz(x + exp(-x**2), x) == oo
assert gruntz(x + exp(-exp(x)), x) == oo
assert gruntz(13 + 1 / x - exp(-x), x) == 13
a = Symbol('a')
assert gruntz(x - log(1 + exp(x)), x) == 0
assert gruntz(x - log(a + exp(x)), x) == 0
assert gruntz(exp(x) / (1 + exp(x)), x) == 1
assert gruntz(exp(x) / (a + exp(x)), x) == 1
assert gruntz((3**x + 5**x)**(1 / x), x) == 5 # issue sympy/sympy#3463
assert gruntz(Ei(x + exp(-x)) * exp(-x) * x, x) == 1
assert gruntz(1 / li(x), x) == 0
assert gruntz(1 / Li(x), x) == 0
# issue diofant/diofant#56
assert gruntz((log(E + 1 / x) - 1)**(1 - sqrt(E + 1 / x)), x) == oo
# issue sympy/sympy#9471
assert gruntz((((27**(log(x, 3)))) / x**3), x) == 1
assert gruntz((((27**(log(x, 3) + 1))) / x**3), x) == 27
# issue sympy/sympy#9449
y = Symbol('y')
assert gruntz(x * (abs(1 / x + y) - abs(y - 1 / x)) / 2, x) == sign(y)
# issue sympy/sympy#8481
assert gruntz(m**x * exp(-m) / factorial(x), x) == 0
# issue sympy/sympy#4187
assert gruntz(exp(1 / x) * log(1 / x) - Ei(1 / x), x) == -EulerGamma
assert gruntz(exp(x) * log(x) - Ei(x), x) == oo
# issue sympy/sympy#10382
assert gruntz(fibonacci(x + 1) / fibonacci(x), x) == GoldenRatio
assert gruntz(zeta(x), x) == 1
assert gruntz(zeta(m) * zeta(x), x) == zeta(m)
def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1 / log(z)
pytest.raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
assert Li(z).rewrite(li) == li(z) - li(2)
assert Li(4).evalf(30) == Float('1.92242131492155809316615998937961',
dps=30)
def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1 / log(z)
pytest.raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
assert Li(z).rewrite(li) == li(z) - li(2)