code: def test_binomial_rewrite():
      n = Symbol("n", integer=True)
      k = Symbol("k", integer=True)
      x = Symbol("x")
  
      assert binomial(n, k).rewrite(factorial) == factorial(n) / (
          factorial(k) * factorial(n - k)
      )
      assert binomial(n, k).rewrite(gamma) == gamma(n + 1) / (
          gamma(k + 1) * gamma(n - k + 1)
      )
      assert binomial(n, k).rewrite(ff) == ff(n, k) / factorial(k)
      assert binomial(n, x).rewrite(ff) == binomial(n, x)
  
imports: from sympy.concrete.products import Product
  from sympy.core.function import expand_func
  from sympy.core.mod import Mod
  from sympy.core.mul import Mul
  from sympy.core import EulerGamma
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol, symbols
  from sympy.functions.combinatorial.factorials import ff, rf, binomial, factorial, factorial2
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.functions.special.gamma_functions import gamma, polygamma
  from sympy.polys.polytools import Poly
  from sympy.series.order import O
  from sympy.simplify.simplify import simplify
  from sympy.core.expr import unchanged
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.factorials import subfactorial
  from sympy.functions.special.gamma_functions import uppergamma
  from sympy.testing.pytest import XFAIL, raises, slow
label_desc: Use image node_id 16 for calling a global function with example usage: test_binomial_rewrite() without return types