test_transforms.py 文件源码

def test_sine_transform():
    from sympy import sinh, cosh, 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)