def test_polarify():
z = Symbol('z', polar=True)
f = Function('f')
ES = {}
assert polarify(-1) == (polar_lift(-1), ES)
assert polarify(1 + I) == (polar_lift(1 + I), ES)
assert polarify(exp(x), subs=False) == exp(x)
assert polarify(1 + x, subs=False) == 1 + x
assert polarify(f(I) + x, subs=False) == f(polar_lift(I)) + x
assert polarify(x, lift=True) == polar_lift(x)
assert polarify(z, lift=True) == z
assert polarify(f(x), lift=True) == f(polar_lift(x))
assert polarify(1 + x, lift=True) == polar_lift(1 + x)
assert polarify(1 + f(x), lift=True) == polar_lift(1 + f(polar_lift(x)))
newex, subs = polarify(f(x) + z)
assert newex.subs(subs) == f(x) + z
mu = Symbol("mu")
sigma = Symbol("sigma", positive=True)
# Make sure polarify(lift=True) doesn't try to lift the integration
# variable
assert polarify(
Integral(sqrt(2)*x*exp(-(-mu + x)**2/(2*sigma**2))/(2*sqrt(pi)*sigma),
(x, -oo, oo)), lift=True) == Integral(sqrt(2)*(sigma*exp_polar(0))**exp_polar(I*pi) *
exp((sigma*exp_polar(0))**(2*exp_polar(I*pi))*exp_polar(I*pi)*polar_lift(-mu + x) **
(2*exp_polar(0))/2)*exp_polar(0)*polar_lift(x)/(2*sqrt(pi)), (x, -oo, oo))
def test_polarify():
z = Symbol('z', polar=True)
f = Function('f')
ES = {}
assert polarify(-1) == (polar_lift(-1), ES)
assert polarify(1 + I) == (polar_lift(1 + I), ES)
assert polarify(exp(x), subs=False) == exp(x)
assert polarify(1 + x, subs=False) == 1 + x
assert polarify(f(I) + x, subs=False) == f(polar_lift(I)) + x
assert polarify(x, lift=True) == polar_lift(x)
assert polarify(z, lift=True) == z
assert polarify(f(x), lift=True) == f(polar_lift(x))
assert polarify(1 + x, lift=True) == polar_lift(1 + x)
assert polarify(1 + f(x), lift=True) == polar_lift(1 + f(polar_lift(x)))
newex, subs = polarify(f(x) + z)
assert newex.subs(subs) == f(x) + z
mu = Symbol("mu")
sigma = Symbol("sigma", positive=True)
# Make sure polarify(lift=True) doesn't try to lift the integration
# variable
assert polarify(
Integral(sqrt(2)*x*exp(-(-mu + x)**2/(2*sigma**2))/(2*sqrt(pi)*sigma),
(x, -oo, oo)), lift=True) == Integral(sqrt(2)*(sigma*exp_polar(0))**exp_polar(I*pi) *
exp((sigma*exp_polar(0))**(2*exp_polar(I*pi))*exp_polar(I*pi)*polar_lift(-mu + x) **
(2*exp_polar(0))/2)*exp_polar(0)*polar_lift(x)/(2*sqrt(pi)), (x, -oo, oo))