code: def test_diophantine_permute_sign():
      from sympy.abc import a, b, c, d, e
  
      eq = a**4 + b**4 - (2**4 + 3**4)
      base_sol = {(2, 3)}
      assert diophantine(eq) == base_sol
      complete_soln = set(signed_permutations(base_sol.pop()))
      assert diophantine(eq, permute=True) == complete_soln
  
      eq = a**2 + b**2 + c**2 + d**2 + e**2 - 234
      assert len(diophantine(eq)) == 35
      assert len(diophantine(eq, permute=True)) == 62000
      soln = {(-1, -1), (-1, 2), (1, -2), (1, 1)}
      assert (
          diophantine(
              10 * x**2 + 12 * x * y + 12 * y**2 - 34, permute=True
          )
          == soln
      )
  
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 49 for calling a global function with example usage: test_diophantine_permute_sign() without return types