test_simplify.py 文件源码

def test_besselsimp():
    from sympy import besselj, besseli, besselk, bessely, jn, yn, exp_polar, cosh, cosine_transform
    assert besselsimp(exp(-I*pi*y/2)*besseli(y, z*exp_polar(I*pi/2))) == \
        besselj(y, z)
    assert besselsimp(exp(-I*pi*a/2)*besseli(a, 2*sqrt(x)*exp_polar(I*pi/2))) == \
        besselj(a, 2*sqrt(x))
    assert besselsimp(sqrt(2)*sqrt(pi)*x**(S(1)/4)*exp(I*pi/4)*exp(-I*pi*a/2) *
                      besseli(-S(1)/2, sqrt(x)*exp_polar(I*pi/2)) *
                      besseli(a, sqrt(x)*exp_polar(I*pi/2))/2) == \
        besselj(a, sqrt(x)) * cos(sqrt(x))
    assert besselsimp(besseli(S(-1)/2, z)) == \
        sqrt(2)*cosh(z)/(sqrt(pi)*sqrt(z))
    assert besselsimp(besseli(a, z*exp_polar(-I*pi/2))) == \
        exp(-I*pi*a/2)*besselj(a, z)
    assert cosine_transform(1/t*sin(a/t), t, y) == \
        sqrt(2)*sqrt(pi)*besselj(0, 2*sqrt(a)*sqrt(y))/2