code: def test_diophantine_solution_set():
      s1 = DiophantineSolutionSet([], [])
      assert set(s1) == set()
      assert s1.symbols == ()
      assert s1.parameters == ()
      raises(ValueError, lambda: s1.add((x,)))
      assert list(s1.dict_iterator()) == []
  
      s2 = DiophantineSolutionSet([x, y], [t, u])
      assert s2.symbols == (x, y)
      assert s2.parameters == (t, u)
      raises(ValueError, lambda: s2.add((1,)))
      s2.add((3, 4))
      assert set(s2) == {(3, 4)}
      s2.update((3, 4), (-1, u))
      assert set(s2) == {(3, 4), (-1, u)}
      raises(ValueError, lambda: s1.update(s2))
      assert list(s2.dict_iterator()) == [{x: -1, y: u}, {x: 3, y: 4}]
  
      s3 = DiophantineSolutionSet([x, y, z], [t, u])
      assert len(s3.parameters) == 2
      s3.add((t**2 + u, t - u, 1))
      assert set(s3) == {(t**2 + u, t - u, 1)}
      assert s3.subs(t, 2) == {(u + 4, 2 - u, 1)}
      assert s3(2) == {(u + 4, 2 - u, 1)}
      assert s3.subs({t: 7, u: 8}) == {(57, -1, 1)}
      assert s3(7, 8) == {(57, -1, 1)}
      assert s3.subs({t: 5}) == {(u + 25, 5 - u, 1)}
      assert s3(5) == {(u + 25, 5 - u, 1)}
      assert s3.subs(u, -3) == {(t**2 - 3, t + 3, 1)}
      assert s3(None, -3) == {(t**2 - 3, t + 3, 1)}
      assert s3.subs({t: 2, u: 8}) == {(12, -6, 1)}
      assert s3(2, 8) == {(12, -6, 1)}
      assert s3.subs({t: 5, u: -3}) == {(22, 8, 1)}
      assert s3(5, -3) == {(22, 8, 1)}
      raises(ValueError, lambda: s3.subs(x=1))
      raises(ValueError, lambda: s3.subs(1, 2, 3))
      raises(ValueError, lambda: s3.add(()))
      raises(ValueError, lambda: s3.add((1, 2, 3, 4)))
      raises(ValueError, lambda: s3.add((1, 2)))
      raises(ValueError, lambda: s3(1, 2, 3))
      raises(TypeError, lambda: s3(t=1))
  
      s4 = DiophantineSolutionSet([x, y], [t, u])
      s4.add((t, 11 * t))
      s4.add((-t, 22 * t))
      assert s4(0, 0) == {(0, 0)}
  
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 53 for calling a global function with example usage: test_diophantine_solution_set() without return types