code: def test_output_type():
      A = ReferenceFrame("A")
      v = A.x + A.y
      d = v | v
      zerov = Vector(0)
      zerod = Dyadic(0)
  
      # dot products
      assert isinstance(d & d, Dyadic)
      assert isinstance(d & zerod, Dyadic)
      assert isinstance(zerod & d, Dyadic)
      assert isinstance(d & v, Vector)
      assert isinstance(v & d, Vector)
      assert isinstance(d & zerov, Vector)
      assert isinstance(zerov & d, Vector)
      raises(TypeError, lambda: d & S.Zero)
      raises(TypeError, lambda: S.Zero & d)
      raises(TypeError, lambda: d & 0)
      raises(TypeError, lambda: 0 & d)
      assert not isinstance(v & v, (Vector, Dyadic))
      assert not isinstance(v & zerov, (Vector, Dyadic))
      assert not isinstance(zerov & v, (Vector, Dyadic))
      raises(TypeError, lambda: v & S.Zero)
      raises(TypeError, lambda: S.Zero & v)
      raises(TypeError, lambda: v & 0)
      raises(TypeError, lambda: 0 & v)
  
      # cross products
      raises(TypeError, lambda: d ^ d)
      raises(TypeError, lambda: d ^ zerod)
      raises(TypeError, lambda: zerod ^ d)
      assert isinstance(d ^ v, Dyadic)
      assert isinstance(v ^ d, Dyadic)
      assert isinstance(d ^ zerov, Dyadic)
      assert isinstance(zerov ^ d, Dyadic)
      assert isinstance(zerov ^ d, Dyadic)
      raises(TypeError, lambda: d ^ S.Zero)
      raises(TypeError, lambda: S.Zero ^ d)
      raises(TypeError, lambda: d ^ 0)
      raises(TypeError, lambda: 0 ^ d)
      assert isinstance(v ^ v, Vector)
      assert isinstance(v ^ zerov, Vector)
      assert isinstance(zerov ^ v, Vector)
      raises(TypeError, lambda: v ^ S.Zero)
      raises(TypeError, lambda: S.Zero ^ v)
      raises(TypeError, lambda: v ^ 0)
      raises(TypeError, lambda: 0 ^ v)
  
      # outer products
      raises(TypeError, lambda: d | d)
      raises(TypeError, lambda: d | zerod)
      raises(TypeError, lambda: zerod | d)
      raises(TypeError, lambda: d | v)
      raises(TypeError, lambda: v | d)
      raises(TypeError, lambda: d | zerov)
      raises(TypeError, lambda: zerov | d)
      raises(TypeError, lambda: zerov | d)
      raises(TypeError, lambda: d | S.Zero)
      raises(TypeError, lambda: S.Zero | d)
      raises(TypeError, lambda: d | 0)
      raises(TypeError, lambda: 0 | d)
      assert isinstance(v | v, Dyadic)
      assert isinstance(v | zerov, Dyadic)
      assert isinstance(zerov | v, Dyadic)
      raises(TypeError, lambda: v | S.Zero)
      raises(TypeError, lambda: S.Zero | v)
      raises(TypeError, lambda: v | 0)
      raises(TypeError, lambda: 0 | v)
  
imports: from sympy.core.singleton import S
  from sympy.physics.vector import Vector, ReferenceFrame, Dyadic
  from sympy.testing.pytest import raises
label_desc: Use image node_id 1 for calling a global function with example usage: test_output_type() without return types