code: def test_change_mul():
      assert change_mul(x, x) == (None, None)
      assert change_mul(x * y, x) == (None, None)
      assert change_mul(x * y * DiracDelta(x), x) == (
          DiracDelta(x),
          x * y,
      )
      assert change_mul(x * y * DiracDelta(x) * DiracDelta(y), x) == (
          DiracDelta(x),
          x * y * DiracDelta(y),
      )
      assert change_mul(DiracDelta(x) ** 2, x) == (
          DiracDelta(x),
          DiracDelta(x),
      )
      assert change_mul(y * DiracDelta(x) ** 2, x) == (
          DiracDelta(x),
          y * DiracDelta(x),
      )
  
file_path: sympy/sympy/integrals/tests/test_deltafunctions.py
imports: from sympy.core.function import Function
  from sympy.core.numbers import Rational, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.functions.special.delta_functions import DiracDelta, Heaviside
  from sympy.integrals.deltafunctions import change_mul, deltaintegrate
label_desc: Use image node_id 1 for calling a global function with example usage: test_change_mul() without return types