def test_sine_transform():
from sympy import EulerGamma
t = symbols("t")
w = symbols("w")
a = symbols("a")
f = Function("f")
# Test unevaluated form
assert sine_transform(f(t), t, w) == SineTransform(f(t), t, w)
assert inverse_sine_transform(f(w), w, t) == InverseSineTransform(f(w), w, t)
assert sine_transform(1 / sqrt(t), t, w) == 1 / sqrt(w)
assert inverse_sine_transform(1 / sqrt(w), w, t) == 1 / sqrt(t)
assert sine_transform((1 / sqrt(t)) ** 3, t, w) == sqrt(w) * gamma(S(1) / 4) / (2 * gamma(S(5) / 4))
assert sine_transform(t ** (-a), t, w) == 2 ** (-a + S(1) / 2) * w ** (a - 1) * gamma(-a / 2 + 1) / gamma(
(a + 1) / 2
)
assert inverse_sine_transform(
2 ** (-a + S(1) / 2) * w ** (a - 1) * gamma(-a / 2 + 1) / gamma(a / 2 + S(1) / 2), w, t
) == t ** (-a)
assert sine_transform(exp(-a * t), t, w) == sqrt(2) * w / (sqrt(pi) * (a ** 2 + w ** 2))
assert inverse_sine_transform(sqrt(2) * w / (sqrt(pi) * (a ** 2 + w ** 2)), w, t) == exp(-a * t)
assert sine_transform(log(t) / t, t, w) == -sqrt(2) * sqrt(pi) * (log(w ** 2) + 2 * EulerGamma) / 4
assert sine_transform(t * exp(-a * t ** 2), t, w) == sqrt(2) * w * exp(-w ** 2 / (4 * a)) / (4 * a ** (S(3) / 2))
assert inverse_sine_transform(sqrt(2) * w * exp(-w ** 2 / (4 * a)) / (4 * a ** (S(3) / 2)), w, t) == t * exp(
-a * t ** 2
)
def test_sine_transform():
from sympy import EulerGamma
t = symbols("t")
w = symbols("w")
a = symbols("a")
f = Function("f")
# Test unevaluated form
assert sine_transform(f(t), t, w) == SineTransform(f(t), t, w)
assert inverse_sine_transform(f(w), w,
t) == InverseSineTransform(f(w), w, t)
assert sine_transform(1 / sqrt(t), t, w) == 1 / sqrt(w)
assert inverse_sine_transform(1 / sqrt(w), w, t) == 1 / sqrt(t)
assert sine_transform((1 / sqrt(t))**3, t, w) == 2 * sqrt(w)
assert sine_transform(
t**(-a), t,
w) == 2**(-a + S(1) / 2) * w**(a - 1) * gamma(-a / 2 + 1) / gamma(
(a + 1) / 2)
assert inverse_sine_transform(
2**(-a + S(1) / 2) * w**(a - 1) * gamma(-a / 2 + 1) /
gamma(a / 2 + S(1) / 2), w, t) == t**(-a)
assert sine_transform(exp(-a * t), t,
w) == sqrt(2) * w / (sqrt(pi) * (a**2 + w**2))
assert inverse_sine_transform(
sqrt(2) * w / (sqrt(pi) * (a**2 + w**2)), w, t) == exp(-a * t)
assert sine_transform(
log(t) / t, t,
w) == -sqrt(2) * sqrt(pi) * (log(w**2) + 2 * EulerGamma) / 4
assert sine_transform(
t * exp(-a * t**2), t,
w) == sqrt(2) * w * exp(-w**2 / (4 * a)) / (4 * a**(S(3) / 2))
assert inverse_sine_transform(
sqrt(2) * w * exp(-w**2 / (4 * a)) / (4 * a**(S(3) / 2)), w,
t) == t * exp(-a * t**2)