def eval(cls, x, k=None):
if k is S.Zero:
return cls(x)
elif k is None:
k = S.Zero
if k is S.Zero:
if x is S.Zero:
return S.Zero
if x is S.Exp1:
return S.One
if x == -1/S.Exp1:
return S.NegativeOne
if x == -log(2)/2:
return -log(2)
if x is S.Infinity:
return S.Infinity
if k.is_nonzero:
if x is S.Zero:
return S.NegativeInfinity
if k is S.NegativeOne:
if x == -S.Pi/2:
return -S.ImaginaryUnit*S.Pi/2
elif x == -1/S.Exp1:
return S.NegativeOne
elif x == -2*exp(-2):
return -C.Integer(2)
def eval(cls, n):
n = sympify(n)
if n.is_Number:
if n is S.Zero:
return S.One
elif n.is_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 C.Integer(result)
if n.is_negative:
return S.Zero
def eval(cls, arg):
try:
arg = as_int(arg)
if arg < 0:
raise ValueError
return C.Integer(cls._eval(arg))
except ValueError:
if sympify(arg).is_Number:
raise ValueError("argument must be a nonnegative integer")
def eval(cls, n, k):
n, k = map(sympify, (n, k))
if k.is_Number:
if k.is_Integer:
if k < 0:
return S.Zero
elif k == 0 or n == k:
return S.One
elif n.is_Integer and n >= 0:
n, k = int(n), int(k)
if k > n:
return S.Zero
elif k > n // 2:
k = n - k
M, result = int(_sqrt(n)), 1
for prime in sieve.primerange(2, n + 1):
if prime > n - k:
result *= prime
elif prime > n // 2:
continue
elif prime > M:
if n % prime < k % prime:
result *= prime
else:
N, K = n, k
exp = a = 0
while N > 0:
a = int((N % prime) < (K % prime + a))
N, K = N // prime, K // prime
exp = a + exp
if exp > 0:
result *= prime**exp
return C.Integer(result)
else:
result = n - k + 1
for i in xrange(2, k + 1):
result *= n - k + i
result /= i
return result
elif k.is_negative:
return S.Zero
elif (n - k).simplify().is_negative:
return S.Zero
else:
d = n - k
if d.is_Integer:
return cls.eval(n, d)
def eval(cls, r, k):
r, k = map(sympify, (r, k))
if k.is_Number:
if k is S.Zero:
return S.One
elif k.is_Integer:
if k.is_negative:
return S.Zero
else:
if r.is_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 C.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 C.gamma(r + 1) / (C.gamma(r - k + 1) * C.gamma(k + 1))
def _eval_expand_func(self, *args):
arg = self.args[0].expand()
if arg.is_Add:
for i, coeff in enumerate(arg.args[:]):
if arg.args[i].is_Number:
terms = C.Add(*(arg.args[:i] + arg.args[i + 1:]))
if coeff.is_Rational:
if coeff.q != 1:
terms += C.Rational(1, coeff.q)
coeff = C.Integer(int(coeff))
else:
continue
return gamma(terms) * C.RisingFactorial(terms, coeff)
return self.func(*self.args)
def _eval(self, n, k):
# n.is_Number and k.is_Integer and k != 1 and n != k
if k.is_Integer:
if n.is_Integer and n >= 0:
n, k = int(n), int(k)
if k > n:
return S.Zero
elif k > n // 2:
k = n - k
M, result = int(_sqrt(n)), 1
for prime in sieve.primerange(2, n + 1):
if prime > n - k:
result *= prime
elif prime > n // 2:
continue
elif prime > M:
if n % prime < k % prime:
result *= prime
else:
N, K = n, k
exp = a = 0
while N > 0:
a = int((N % prime) < (K % prime + a))
N, K = N // prime, K // prime
exp = a + exp
if exp > 0:
result *= prime**exp
return C.Integer(result)
else:
d = result = n - k + 1
for i in range(2, k + 1):
d += 1
result *= d
result /= i
return result
