test_rde.py 文件源码

def test_solve_poly_rde_no_cancel():
    # deg(b) large
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1 + t**2, t)]})
    assert solve_poly_rde(Poly(t**2 + 1, t), Poly(t**3 + (x + 1)*t**2 + t + x + 2, t),
    oo, DE) == Poly(t + x, t)
    # deg(b) small
    DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
    assert solve_poly_rde(Poly(0, x), Poly(x/2 - S(1)/4, x), oo, DE) == \
        Poly(x**2/4 - x/4, x)
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
    assert solve_poly_rde(Poly(2, t), Poly(t**2 + 2*t + 3, t), 1, DE) == \
        Poly(t + 1, t, x)
    # deg(b) == deg(D) - 1
    DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t**2 + 1, t)]})
    assert no_cancel_equal(Poly(1 - t, t),
    Poly(t**3 + t**2 - 2*x*t - 2*x, t), oo, DE) == \
        (Poly(t**2, t), 1, Poly((-2 - 2*x)*t - 2*x, t))