test_gosper.py 文件源码

def test_gosper_sum():
    assert gosper_sum(1, (k, 0, n)) == 1 + n
    assert gosper_sum(k, (k, 0, n)) == n*(1 + n)/2
    assert gosper_sum(k**2, (k, 0, n)) == n*(1 + n)*(1 + 2*n)/6
    assert gosper_sum(k**3, (k, 0, n)) == n**2*(1 + n)**2/4

    assert gosper_sum(2**k, (k, 0, n)) == 2*2**n - 1

    assert gosper_sum(factorial(k), (k, 0, n)) is None
    assert gosper_sum(binomial(n, k), (k, 0, n)) is None

    assert gosper_sum(factorial(k)/k**2, (k, 0, n)) is None
    assert gosper_sum((k - 3)*factorial(k), (k, 0, n)) is None

    assert gosper_sum(k*factorial(k), k) == factorial(k)
    assert gosper_sum(
        k*factorial(k), (k, 0, n)) == n*factorial(n) + factorial(n) - 1

    assert gosper_sum((-1)**k*binomial(n, k), (k, 0, n)) == 0
    assert gosper_sum((
        -1)**k*binomial(n, k), (k, 0, m)) == -(-1)**m*(m - n)*binomial(n, m)/n

    assert gosper_sum((4*k + 1)*factorial(k)/factorial(2*k + 1), (k, 0, n)) == \
        (2*factorial(2*n + 1) - factorial(n))/factorial(2*n + 1)

    # issue 6033:
    assert gosper_sum(
        n*(n + a + b)*a**n*b**n/(factorial(n + a)*factorial(n + b)), \
        (n, 0, m)) == -a*b*(exp(m*log(a))*exp(m*log(b))*factorial(a)* \
        factorial(b) - factorial(a + m)*factorial(b + m))/(factorial(a)* \
        factorial(b)*factorial(a + m)*factorial(b + m))