test_rde.py 文件源码

def test_weak_normalizer():
    a = Poly((1 + x)*t**5 + 4*t**4 + (-1 - 3*x)*t**3 - 4*t**2 + (-2 + 2*x)*t, t)
    d = Poly(t**4 - 3*t**2 + 2, t)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
    r = weak_normalizer(a, d, DE, z)
    assert r == (Poly(t**5 - t**4 - 4*t**3 + 4*t**2 + 4*t - 4, t),
        (Poly((1 + x)*t**2 + x*t, t), Poly(t + 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE) == (Poly(1, t), r[1])
    r = weak_normalizer(Poly(1 + t**2), Poly(t**2 - 1, t), DE, z)
    assert r == (Poly(t**4 - 2*t**2 + 1, t), (Poly(-3*t**2 + 1, t), Poly(t**2 - 1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2)]})
    r = weak_normalizer(Poly(1 + t**2), Poly(t, t), DE, z)
    assert r == (Poly(t, t), (Poly(0, t), Poly(1, t)))
    assert weak_normalizer(r[1][0], r[1][1], DE, z) == (Poly(1, t), r[1])