def test_inversion_conditional_output():
from sympy import Symbol, InverseLaplaceTransform
a = Symbol('a', positive=True)
F = sqrt(pi/a)*exp(-2*sqrt(a)*sqrt(s))
f = meijerint_inversion(F, s, t)
assert not f.is_Piecewise
b = Symbol('b', real=True)
F = F.subs(a, b)
f2 = meijerint_inversion(F, s, t)
assert f2.is_Piecewise
# first piece is same as f
assert f2.args[0][0] == f.subs(a, b)
# last piece is an unevaluated transform
assert f2.args[-1][1]
ILT = InverseLaplaceTransform(F, s, t, None)
assert f2.args[-1][0] == ILT or f2.args[-1][0] == ILT.as_integral
def test_integral_transforms():
x = Symbol("x")
k = Symbol("k")
f = Function("f")
a = Symbol("a")
b = Symbol("b")
assert latex(
MellinTransform(f(x), x, k)
) == r"\mathcal{M}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseMellinTransform(f(k), k, x, a, b)
) == r"\mathcal{M}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
LaplaceTransform(f(x), x, k)
) == r"\mathcal{L}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseLaplaceTransform(f(k), k, x, (a, b))
) == r"\mathcal{L}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
FourierTransform(f(x), x, k)
) == r"\mathcal{F}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseFourierTransform(f(k), k, x)
) == r"\mathcal{F}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
CosineTransform(f(x), x, k)
) == r"\mathcal{COS}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseCosineTransform(f(k), k, x)
) == r"\mathcal{COS}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"
assert latex(
SineTransform(f(x), x, k)
) == r"\mathcal{SIN}_{x}\left[\operatorname{f}{\left (x \right )}\right]\left(k\right)"
assert latex(
InverseSineTransform(f(k), k, x)
) == r"\mathcal{SIN}^{-1}_{k}\left[\operatorname{f}{\left (k \right )}\right]\left(x\right)"