test_orthopolys.py 文件源码

def test_laguerre_poly():
    raises(ValueError, lambda: laguerre_poly(-1, x))

    assert laguerre_poly(1, x, polys=True) == Poly(-x + 1)

    assert laguerre_poly(0, x) == 1
    assert laguerre_poly(1, x) == -x + 1
    assert laguerre_poly(2, x) == Q(1, 2)*x**2 - Q(4, 2)*x + 1
    assert laguerre_poly(3, x) == -Q(1, 6)*x**3 + Q(9, 6)*x**2 - Q(18, 6)*x + 1
    assert laguerre_poly(4, x) == Q(
        1, 24)*x**4 - Q(16, 24)*x**3 + Q(72, 24)*x**2 - Q(96, 24)*x + 1
    assert laguerre_poly(5, x) == -Q(1, 120)*x**5 + Q(25, 120)*x**4 - Q(
        200, 120)*x**3 + Q(600, 120)*x**2 - Q(600, 120)*x + 1
    assert laguerre_poly(6, x) == Q(1, 720)*x**6 - Q(36, 720)*x**5 + Q(450, 720)*x**4 - Q(2400, 720)*x**3 + Q(5400, 720)*x**2 - Q(4320, 720)*x + 1

    assert laguerre_poly(0, x, a) == 1
    assert laguerre_poly(1, x, a) == -x + a + 1
    assert laguerre_poly(2, x, a) == x**2/2 + (-a - 2)*x + a**2/2 + 3*a/2 + 1
    assert laguerre_poly(3, x, a) == -x**3/6 + (a/2 + Q(
        3)/2)*x**2 + (-a**2/2 - 5*a/2 - 3)*x + a**3/6 + a**2 + 11*a/6 + 1

    assert laguerre_poly(1).dummy_eq(-x + 1)
    assert laguerre_poly(1, polys=True) == Poly(-x + 1)