code: def test_nontriv_local():
      R = QQ.old_poly_ring(x, y, z, order=ilex)
  
      def contains(I, f):
          return R.ideal(*I).contains(f)
  
      assert contains([x, y], x)
      assert contains([x, y], x + y)
      assert not contains([x, y], 1)
      assert not contains([x, y], z)
      assert contains([x**2 + y, x**2 + x], x - y)
      assert not contains(
          [x + y + z, x * y + x * z + y * z, x * y * z], x**2
      )
      assert contains([x * (1 + x + y), y * (1 + z)], x)
      assert contains([x * (1 + x + y), y * (1 + z)], x + y)
  
file_path: sympy/sympy/polys/agca/tests/test_ideals.py
imports: from sympy.polys import QQ, ilex
  from sympy.abc import x, y, z
  from sympy.testing.pytest import raises
label_desc: Use image node_id 4 for calling a global function with example usage: test_nontriv_local() and returns: R