def test_factorial_simplify():
# There are more tests in test_factorials.py. These are just to
# ensure that simplify() calls factorial_simplify correctly
from sympy.specfun.factorials import factorial
x = Symbol('x')
assert simplify(factorial(x)/x) == factorial(x-1)
assert simplify(factorial(factorial(x))) == factorial(factorial(x))
def test_hypersimp():
n, k = symbols('nk', integer=True)
assert hypersimp(factorial(k), k) == k + 1
assert hypersimp(factorial(k**2), k) is None
assert hypersimp(2**k/factorial(k)**2, k) == 2/(k+1)**2
assert hypersimp(binomial(n, k), k) == (n-k)/(k+1)
assert hypersimp(binomial(n+1, k), k) == (n-k+1)/(k+1)
term = (4*k+1)*factorial(k)/factorial(2*k+1)
assert hypersimp(term, k) == (4*k + 5)/(6 + 16*k**2 + 28*k)
term = 1/((2*k-1)*factorial(2*k+1))
assert hypersimp(term, k) == (2*k-1)/(2*k+1)/(2*k+2)/(2*k+3)
term = binomial(n, k)*(-1)**k/factorial(k)
assert hypersimp(term, k) == (k - n)/(k+1)**2
