code: def test_power_representation():
      tests = [
          (1729, 3, 2),
          (234, 2, 4),
          (2, 1, 2),
          (3, 1, 3),
          (5, 2, 2),
          (12352, 2, 4),
          (32760, 2, 3),
      ]
  
      for test in tests:
          n, p, k = test
          f = power_representation(n, p, k)
  
          while True:
              try:
                  l = next(f)
                  assert len(l) == k
  
                  chk_sum = 0
                  for l_i in l:
                      chk_sum = chk_sum + l_i**p
                  assert chk_sum == n
  
              except StopIteration:
                  break
  
      assert list(power_representation(20, 2, 4, True)) == [
          (1, 1, 3, 3),
          (0, 0, 2, 4),
      ]
      raises(ValueError, lambda: list(power_representation(1.2, 2, 2)))
      raises(ValueError, lambda: list(power_representation(2, 0, 2)))
      raises(ValueError, lambda: list(power_representation(2, 2, 0)))
      assert list(power_representation(-1, 2, 2)) == []
      assert list(power_representation(1, 1, 1)) == [(1,)]
      assert list(power_representation(3, 2, 1)) == []
      assert list(power_representation(4, 2, 1)) == [(2,)]
      assert list(power_representation(3**4, 4, 6, zeros=True)) == [
          (1, 2, 2, 2, 2, 2),
          (0, 0, 0, 0, 0, 3),
      ]
      assert list(power_representation(3**4, 4, 5, zeros=False)) == []
      assert list(power_representation(-2, 3, 2)) == [(-1, -1)]
      assert list(power_representation(-2, 4, 2)) == []
      assert list(power_representation(0, 3, 2, True)) == [(0, 0)]
      assert list(power_representation(0, 3, 2, False)) == []
      # when we are dealing with squares, do feasibility checks
      assert (
          len(list(power_representation(4**10 * (8 * 10 + 7), 2, 3)))
          == 0
      )
      # there will be a recursion error if these aren't recognized
      big = 2**30
      for i in [13, 10, 7, 5, 4, 2, 1]:
          assert list(sum_of_powers(big, 2, big - i)) == []
  
imports: from sympy.core.add import Add
  from sympy.core.mul import Mul
  from sympy.core.numbers import Rational, oo, pi
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.matrices.dense import Matrix
  from sympy.ntheory.factor_ import factorint
  from sympy.simplify.powsimp import powsimp
  from sympy.core.function import _mexpand
  from sympy.core.sorting import default_sort_key, ordered
  from sympy.functions.elementary.trigonometric import sin
  from sympy.solvers.diophantine import diophantine
  from sympy.solvers.diophantine.diophantine import diop_DN, diop_solve, diop_ternary_quadratic_normal, diop_general_pythagorean, diop_ternary_quadratic, diop_linear, diop_quadratic, diop_general_sum_of_squares, diop_general_sum_of_even_powers, descent, diop_bf_DN, divisible, equivalent, find_DN, ldescent, length, reconstruct, partition, power_representation, prime_as_sum_of_two_squares, square_factor, sum_of_four_squares, sum_of_three_squares, transformation_to_DN, transformation_to_normal, classify_diop, base_solution_linear, cornacchia, sqf_normal, gaussian_reduce, holzer, check_param, parametrize_ternary_quadratic, sum_of_powers, sum_of_squares, _diop_ternary_quadratic_normal, _nint_or_floor, _odd, _even, _remove_gcd, _can_do_sum_of_squares, DiophantineSolutionSet, GeneralPythagorean, BinaryQuadratic
  from sympy.testing.pytest import slow, raises, XFAIL
  from sympy.utilities.iterables import signed_permutations
label_desc: Use image node_id 38 for calling a global function with example usage: test_power_representation() without return types