def test_cosine_transform():
f = Function("f")
# Test unevaluated form
assert cosine_transform(f(t), t, w) == CosineTransform(f(t), t, w)
assert inverse_cosine_transform(
f(w), w, t) == InverseCosineTransform(f(w), w, t)
assert cosine_transform(1/sqrt(t), t, w) == 1/sqrt(w)
assert inverse_cosine_transform(1/sqrt(w), w, t) == 1/sqrt(t)
assert cosine_transform(1/(
a**2 + t**2), t, w) == sqrt(2)*sqrt(pi)*exp(-a*w)/(2*a)
assert cosine_transform(t**(
-a), t, w) == 2**(-a + Rational(1, 2))*w**(a - 1)*gamma((-a + 1)/2)/gamma(a/2)
assert inverse_cosine_transform(2**(-a +
Rational(1, 2))*w**(a - 1)*gamma(-a/2 + Rational(1, 2))/gamma(a/2), w, t) == t**(-a)
assert cosine_transform(
exp(-a*t), t, w) == sqrt(2)*a/(sqrt(pi)*(a**2 + w**2))
assert inverse_cosine_transform(
sqrt(2)*a/(sqrt(pi)*(a**2 + w**2)), w, t) == exp(-a*t)
assert cosine_transform(exp(-a*sqrt(t))*cos(a*sqrt(
t)), t, w) == a*exp(-a**2/(2*w))/(2*w**Rational(3, 2))
assert cosine_transform(1/(a + t), t, w) == sqrt(2)*(
(-2*Si(a*w) + pi)*sin(a*w)/2 - cos(a*w)*Ci(a*w))/sqrt(pi)
assert inverse_cosine_transform(sqrt(2)*meijerg(((Rational(1, 2), 0), ()), (
(Rational(1, 2), 0, 0), (Rational(1, 2),)), a**2*w**2/4)/(2*pi), w, t) == 1/(a + t)
assert cosine_transform(1/sqrt(a**2 + t**2), t, w) == sqrt(2)*meijerg(
((Rational(1, 2),), ()), ((0, 0), (Rational(1, 2),)), a**2*w**2/4)/(2*sqrt(pi))
assert inverse_cosine_transform(sqrt(2)*meijerg(((Rational(1, 2),), ()), ((0, 0), (Rational(1, 2),)), a**2*w**2/4)/(2*sqrt(pi)), w, t) == 1/(a*sqrt(1 + t**2/a**2))
def test_cosine_transform():
from diofant import Si, Ci
t = symbols("t")
w = symbols("w")
a = symbols("a")
f = Function("f")
# Test unevaluated form
assert cosine_transform(f(t), t, w) == CosineTransform(f(t), t, w)
assert inverse_cosine_transform(f(w), w,
t) == InverseCosineTransform(f(w), w, t)
assert cosine_transform(1 / sqrt(t), t, w) == 1 / sqrt(w)
assert inverse_cosine_transform(1 / sqrt(w), w, t) == 1 / sqrt(t)
assert cosine_transform(1 / (a**2 + t**2), t,
w) == sqrt(2) * sqrt(pi) * exp(-a * w) / (2 * a)
assert cosine_transform(
t**(-a), t, w) == 2**(-a + Rational(1, 2)) * w**(a - 1) * gamma(
(-a + 1) / 2) / gamma(a / 2)
assert inverse_cosine_transform(
2**(-a + Rational(1, 2)) * w**(a - 1) *
gamma(-a / 2 + Rational(1, 2)) / gamma(a / 2), w, t) == t**(-a)
assert cosine_transform(exp(-a * t), t,
w) == sqrt(2) * a / (sqrt(pi) * (a**2 + w**2))
assert inverse_cosine_transform(
sqrt(2) * a / (sqrt(pi) * (a**2 + w**2)), w, t) == exp(-a * t)
assert cosine_transform(exp(-a * sqrt(t)) * cos(a * sqrt(t)), t,
w) == a * exp(-a**2 /
(2 * w)) / (2 * w**Rational(3, 2))
assert cosine_transform(
1 / (a + t), t,
w) == sqrt(2) * ((-2 * Si(a * w) + pi) * sin(a * w) / 2 -
cos(a * w) * Ci(a * w)) / sqrt(pi)
assert inverse_cosine_transform(
sqrt(2) * meijerg(((Rational(1, 2), 0), ()),
((Rational(1, 2), 0, 0),
(Rational(1, 2), )), a**2 * w**2 / 4) / (2 * pi), w,
t) == 1 / (a + t)
assert cosine_transform(1 / sqrt(a**2 + t**2), t, w) == sqrt(2) * meijerg(
((Rational(1, 2), ), ()),
((0, 0), (Rational(1, 2), )), a**2 * w**2 / 4) / (2 * sqrt(pi))
assert inverse_cosine_transform(
sqrt(2) * meijerg(
((Rational(1, 2), ), ()),
((0, 0), (Rational(1, 2), )), a**2 * w**2 / 4) / (2 * sqrt(pi)), w,
t) == 1 / (a * sqrt(1 + t**2 / a**2))