Use math.comb() for binomial.eval()

A partial fix for #839

diofant/functions/combinatorial/factorials.py

@@ -528,45 +528,6 @@ def fdiff(self, argindex=1):
         else:
             raise ArgumentIndexError(self, argindex)
 
-    @classmethod
-    def _eval(cls, n, k):
-        assert n.is_Number and k.is_Integer and k != 1 and n != k
-        if n.is_Integer and n >= 0:
-            n, k = int(n), int(k)
-
-            if k > n // 2:
-                k = n - k
-
-            M, result = int(math.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 Integer(result)
-        else:
-            d = result = n - k + 1
-            for i in range(2, k + 1):
-                d += 1
-                result *= d
-                result /= i
-            return result
-
     @classmethod
     def eval(cls, n, k):
         n, k = map(sympify, (n, k))
@@ -580,8 +541,11 @@ def eval(cls, n, k):
                 return Integer(0)
             elif n.is_integer and n.is_nonnegative and d.is_negative:
                 return Integer(0)
-        if k.is_Integer and k > 0 and n.is_Number:
-            return cls._eval(n, k)
+        if n.is_Integer and k.is_Integer and k > 0:
+            if n >= 0:
+                return Integer(math.comb(n, k))
+            else:
+                return Integer((-1)**k*math.comb(abs(n) + k - 1, k))
 
     def _eval_expand_func(self, **hints):
         """Function to expand binomial(n,k) when n is positive integer."""