text: from sympy import symbols, Derivative, Integral, exp, cos, oo, Function
  from sympy.functions.special.bessel import besselj
  from sympy.functions.special.polynomials import legendre
  from sympy.functions.combinatorial.numbers import bell
  from sympy.printing.conventions import split_super_sub, requires_partial
  
  
  def test_super_sub():
      assert split_super_sub("beta_13_2") == ("beta", [], ["13", "2"])
      assert split_super_sub("beta_132_20") == ("beta", [], ["132", "20"])
      assert split_super_sub("beta_13") == ("beta", [], ["13"])
      assert split_super_sub("x_a_b") == ("x", [], ["a", "b"])
      assert split_super_sub("x_1_2_3") == ("x", [], ["1", "2", "3"])
      assert split_super_sub("x_a_b1") == ("x", [], ["a", "b1"])
      assert split_super_sub("x_a_1") == ("x", [], ["a", "1"])
      assert split_super_sub("x_1_a") == ("x", [], ["1", "a"])
      assert split_super_sub("x_1^aa") == ("x", ["aa"], ["1"])
      assert split_super_sub("x_1__aa") == ("x", ["aa"], ["1"])
      assert split_super_sub("x_11^a") == ("x", ["a"], ["11"])
      assert split_super_sub("x_11__a") == ("x", ["a"], ["11"])
      assert split_super_sub("x_a_b_c_d") == ("x", [], ["a", "b", "c", "d"])
      assert split_super_sub("x_a_b^c^d") == ("x", ["c", "d"], ["a", "b"])
      assert split_super_sub("x_a_b__c__d") == ("x", ["c", "d"], ["a", "b"])
      assert split_super_sub("x_a^b_c^d") == ("x", ["b", "d"], ["a", "c"])
      assert split_super_sub("x_a__b_c__d") == ("x", ["b", "d"], ["a", "c"])
      assert split_super_sub("x^a^b_c_d") == ("x", ["a", "b"], ["c", "d"])
      assert split_super_sub("x__a__b_c_d") == ("x", ["a", "b"], ["c", "d"])
      assert split_super_sub("x^a^b^c^d") == ("x", ["a", "b", "c", "d"], [])
      assert split_super_sub("x__a__b__c__d") == ("x", ["a", "b", "c", "d"], [])
      assert split_super_sub("alpha_11") == ("alpha", [], ["11"])
      assert split_super_sub("alpha_11_11") == ("alpha", [], ["11", "11"])
      assert split_super_sub("") == ("", [], [])
  
  def test_requires_partial():
      x, y, z, t, nu = symbols('x y z t nu')
      n = symbols('n', integer=True)
  
      f = x * y
      assert requires_partial(Derivative(f, x)) is True
      assert requires_partial(Derivative(f, y)) is True
  
      ## integrating out one of the variables
      assert requires_partial(Derivative(Integral(exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
  
      ## bessel function with smooth parameter
      f = besselj(nu, x)
      assert requires_partial(Derivative(f, x)) is True
      assert requires_partial(Derivative(f, nu)) is True
  
      ## bessel function with integer parameter
      f = besselj(n, x)
      assert requires_partial(Derivative(f, x)) is False
      # this is not really valid (differentiating with respect to an integer)
      # but there's no reason to use the partial derivative symbol there. make
      # sure we don't throw an exception here, though
      assert requires_partial(Derivative(f, n)) is False
  
      ## bell polynomial
      f = bell(n, x)
      assert requires_partial(Derivative(f, x)) is False
      # again, invalid
      assert requires_partial(Derivative(f, n)) is False
  
      ## legendre polynomial
      f = legendre(0, x)
      assert requires_partial(Derivative(f, x)) is False
  
      f = legendre(n, x)
      assert requires_partial(Derivative(f, x)) is False
      # again, invalid
      assert requires_partial(Derivative(f, n)) is False
  
      f = x ** n
      assert requires_partial(Derivative(f, x)) is False
  
      assert requires_partial(Derivative(Integral((x*y) ** n * exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
  
      # parametric equation
      f = (exp(t), cos(t))
      g = sum(f)
      assert requires_partial(Derivative(g, t)) is False
  
      # function of unspecified variables
      f = symbols('f', cls=Function)
      assert requires_partial(Derivative(f, x)) is False
      assert requires_partial(Derivative(f, x, y)) is True
  