test_rde.py 文件源码

def test_spde():
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
    raises(NonElementaryIntegralException, lambda: spde(Poly(t, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
    assert spde(Poly(t**2 + x*t*2 + x**2, t), Poly(t**2/x**2 + (2/x - 1)*t, t),
    Poly(t**2/x**2 + (2/x - 1)*t, t), 0, DE) == \
        (Poly(0, t), Poly(0, t), 0, Poly(0, t), Poly(1, t))
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t0/x**2, t0), Poly(1/x, t)]})
    assert spde(Poly(t**2, t), Poly(-t**2/x**2 - 1/x, t),
    Poly((2*x - 1)*t**4 + (t0 + x)/x*t**3 - (t0 + 4*x**2)/(2*x)*t**2 + x*t, t), 3, DE) == \
        (Poly(0, t), Poly(0, t), 0, Poly(0, t),
        Poly(t0*t**2/2 + x**2*t**2 - x**2*t, t))
    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
    assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
    3*x**4/4 + x**3 - x**2 + 1, x), 4, DE) == \
        (Poly(0, x), Poly(x/2 - S(1)/4, x), 2, Poly(x**2 + x + 1, x), Poly(5*x/4, x))
    assert spde(Poly(x**2 + x + 1, x), Poly(-2*x - 1, x), Poly(x**5/2 +
    3*x**4/4 + x**3 - x**2 + 1, x), n, DE) == \
        (Poly(0, x), Poly(x/2 - S(1)/4, x), -2 + n, Poly(x**2 + x + 1, x), Poly(5*x/4, x))
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1, t)]})
    raises(NonElementaryIntegralException, lambda: spde(Poly((t - 1)*(t**2 + 1)**2, t), Poly((t - 1)*(t**2 + 1), t), Poly(1, t), 0, DE))