test_cg.py 文件源码

def test_cg_simp_sum():
    x, a, b, c, cp, alpha, beta, gamma, gammap = symbols(
        'x a b c cp alpha beta gamma gammap')
    # Varshalovich 8.7.1 Eq 1
    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)
                   )) == x*(2*a + 1)*KroneckerDelta(b, 0)
    assert cg_simp(x * Sum(CG(a, alpha, b, 0, a, alpha), (alpha, -a, a)) + CG(1, 0, 1, 0, 1, 0)) == x*(2*a + 1)*KroneckerDelta(b, 0) + CG(1, 0, 1, 0, 1, 0)
    assert cg_simp(2 * Sum(CG(1, alpha, 0, 0, 1, alpha), (alpha, -1, 1))) == 6
    # Varshalovich 8.7.1 Eq 2
    assert cg_simp(x*Sum((-1)**(a - alpha) * CG(a, alpha, a, -alpha, c,
                   0), (alpha, -a, a))) == x*sqrt(2*a + 1)*KroneckerDelta(c, 0)
    assert cg_simp(3*Sum((-1)**(2 - alpha) * CG(
        2, alpha, 2, -alpha, 0, 0), (alpha, -2, 2))) == 3*sqrt(5)
    # Varshalovich 8.7.2 Eq 4
    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)*KroneckerDelta(gamma, gammap)
    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, c, gammap), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(gamma, gammap)
    assert cg_simp(Sum(CG(a, alpha, b, beta, c, gamma)*CG(a, alpha, b, beta, cp, gamma), (alpha, -a, a), (beta, -b, b))) == KroneckerDelta(c, cp)
    assert cg_simp(Sum(CG(
        a, alpha, b, beta, c, gamma)**2, (alpha, -a, a), (beta, -b, b))) == 1
    assert cg_simp(Sum(CG(2, alpha, 1, beta, 2, gamma)*CG(2, alpha, 1, beta, 2, gammap), (alpha, -2, 2), (beta, -1, 1))) == KroneckerDelta(gamma, gammap)