test_orthopolys.py 文件源码

def test_legendre_poly():
    raises(ValueError, lambda: legendre_poly(-1, x))

    assert legendre_poly(1, x, polys=True) == Poly(x)

    assert legendre_poly(0, x) == 1
    assert legendre_poly(1, x) == x
    assert legendre_poly(2, x) == Q(3, 2)*x**2 - Q(1, 2)
    assert legendre_poly(3, x) == Q(5, 2)*x**3 - Q(3, 2)*x
    assert legendre_poly(4, x) == Q(35, 8)*x**4 - Q(30, 8)*x**2 + Q(3, 8)
    assert legendre_poly(5, x) == Q(63, 8)*x**5 - Q(70, 8)*x**3 + Q(15, 8)*x
    assert legendre_poly(6, x) == Q(
        231, 16)*x**6 - Q(315, 16)*x**4 + Q(105, 16)*x**2 - Q(5, 16)

    assert legendre_poly(1).dummy_eq(x)
    assert legendre_poly(1, polys=True) == Poly(x)