def _eval_apply(cls, r, k):
r, k = map(Basic.sympify, (r, k))
if isinstance(k, Basic.Number):
if isinstance(k, Basic.Zero):
return S.One
elif isinstance(k, Basic.Integer):
if k.is_negative:
return S.Zero
else:
if isinstance(r, Basic.Integer) and r.is_nonnegative:
r, k = int(r), int(k)
if k > r:
return S.Zero
elif k > r / 2:
k = r - k
M, result = int(sqrt(r)), 1
for prime in sieve.primerange(2, r+1):
if prime > r - k:
result *= prime
elif prime > r / 2:
continue
elif prime > M:
if r % prime < k % prime:
result *= prime
else:
R, K = r, k
exp = a = 0
while R > 0:
a = int((R % prime) < (K % prime + a))
R, K = R / prime, K / prime
exp = a + exp
if exp > 0:
result *= prime**exp
return Basic.Integer(result)
else:
result = r - k + 1
for i in xrange(2, k+1):
result *= r-k+i
result /= i
return result
if k.is_integer:
if k.is_negative:
return S.Zero
else:
return Basic.gamma(r+1)/(Basic.gamma(r-k+1)*Basic.gamma(k+1))
def _eval_apply(cls, n):
n = Basic.sympify(n)
if isinstance(n, Basic.Number):
if isinstance(n, Basic.Zero):
return S.One
elif isinstance(n, Basic.Integer):
if n.is_negative:
return S.Zero
else:
n, result = n.p, 1
if n < 20:
for i in range(2, n+1):
result *= i
else:
N, bits = n, 0
while N != 0:
if N & 1 == 1:
bits += 1
N = N >> 1
result = cls._recursive(n)*2**(n-bits)
return Basic.Integer(result)
if n.is_integer:
if n.is_negative:
return S.Zero
else:
return Basic.gamma(n+1)
def _eval_rewrite_as_gamma(self, r, k):
return Basic.gamma(r+1) / (Basic.gamma(r-k+1)*Basic.gamma(k+1))
def _eval_rewrite_as_gamma(self, x, k):
return (-1)**k * Basic.gamma(-x + k) / Basic.gamma(-x)
def _eval_rewrite_as_gamma(self, x, k):
return Basic.gamma(x + k) / Basic.gamma(x)
def _eval_rewrite_as_gamma(self, arg):
return Basic.gamma(1 + arg)
