code: def test_solenoidal():
      assert is_solenoidal(Vector.zero) is True
      assert is_solenoidal(i) is True
      assert is_solenoidal(2 * i + 3 * j + 4 * k) is True
      assert is_solenoidal(y * z * i + x * z * j + x * y * k) is True
      assert is_solenoidal(y * j) is False
      assert is_solenoidal(grad_field) is False
      assert is_solenoidal(curl_field) is True
      assert is_solenoidal((-2 * y + 3) * k) is True
      assert (
          is_solenoidal(cos(q) * i + sin(q) * j + cos(q) * P.k) is True
      )
      assert is_solenoidal(z * P.i + P.x * k) is True
  
imports: from sympy.core.function import Derivative
  from sympy.vector.vector import Vector
  from sympy.vector.coordsysrect import CoordSys3D
  from sympy.simplify import simplify
  from sympy.core.symbol import symbols
  from sympy.core import S
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.vector.vector import Dot
  from sympy.vector.operators import curl, divergence, gradient, Gradient, Divergence, Cross
  from sympy.vector.deloperator import Del
  from sympy.vector.functions import is_conservative, is_solenoidal, scalar_potential, directional_derivative, laplacian, scalar_potential_difference
  from sympy.testing.pytest import raises
label_desc: Use image node_id 4 for calling a global function with example usage: test_solenoidal() without return types