code: def test_diopcoverage():
      eq = (2 * x + y + 1) ** 2
      assert diop_solve(eq) == {(t_0, -2 * t_0 - 1)}
      eq = 2 * x**2 + 6 * x * y + 12 * x + 4 * y**2 + 18 * y + 18
      assert diop_solve(eq) == {(t, -t - 3), (-2 * t - 3, t)}
      assert diop_quadratic(x + y**2 - 3) == {(-(t**2) + 3, t)}
  
      assert diop_linear(x + y - 3) == (t_0, 3 - t_0)
  
      assert base_solution_linear(0, 1, 2, t=None) == (0, 0)
      ans = (3 * t - 1, -2 * t + 1)
      assert base_solution_linear(4, 8, 12, t) == ans
      assert base_solution_linear(4, 8, 12, t=None) == tuple(
          _.subs(t, 0) for _ in ans
      )
  
      assert cornacchia(1, 1, 20) is None
      assert cornacchia(1, 1, 5) == {(2, 1)}
      assert cornacchia(1, 2, 17) == {(3, 2)}
  
      raises(ValueError, lambda: reconstruct(4, 20, 1))
  
      assert gaussian_reduce(4, 1, 3) == (1, 1)
      eq = -(w**2) - x**2 - y**2 + z**2
  
      assert (
          diop_general_pythagorean(eq)
          == diop_general_pythagorean(-eq)
          == (
              m1**2 + m2**2 - m3**2,
              2 * m1 * m3,
              2 * m2 * m3,
              m1**2 + m2**2 + m3**2,
          )
      )
  
      assert (
          len(check_param(S(3) + x / 3, S(4) + x / 2, S(2), [x])) == 0
      )
      assert len(check_param(Rational(3, 2), S(4) + x, S(2), [x])) == 0
      assert len(check_param(S(4) + x, Rational(3, 2), S(2), [x])) == 0
  
      assert _nint_or_floor(16, 10) == 2
      assert _odd(1) == (not _even(1)) == True
      assert _odd(0) == (not _even(0)) == False
      assert _remove_gcd(2, 4, 6) == (1, 2, 3)
      raises(TypeError, lambda: _remove_gcd((2, 4, 6)))
      assert sqf_normal(
          2 * 3**2 * 5, 2 * 5 * 11, 2 * 7**2 * 11
      ) == (11, 1, 5)
  
      # it's ok if these pass some day when the solvers are implemented
      raises(
          NotImplementedError,
          lambda: diophantine(x**2 + y**2 + x * y + 2 * y * z - 12),
      )
      raises(NotImplementedError, lambda: diophantine(x**3 + y**2))
      assert diop_quadratic(x**2 + y**2 - 1**2 - 3**4) == {
          (-9, -1),
          (-9, 1),
          (-1, -9),
          (-1, 9),
          (1, -9),
          (1, 9),
          (9, -1),
          (9, 1),
      }
  
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 41 for calling a global function with example usage: test_diopcoverage() without return types