code: def test_dmp_qq_i_factor():
      R, x, y = ring("x, y", QQ_I)
      i = QQ_I(0, 1)
  
      assert R.dmp_qq_i_factor(x**2 + 2 * y**2) == (
          QQ_I(1, 0),
          [(x**2 + 2 * y**2, 1)],
      )
  
      assert R.dmp_qq_i_factor(x**2 + y**2) == (
          QQ_I(1, 0),
          [(x - i * y, 1), (x + i * y, 1)],
      )
  
      assert R.dmp_qq_i_factor(x**2 + y**2 / 4) == (
          QQ_I(1, 0),
          [(x - i * y / 2, 1), (x + i * y / 2, 1)],
      )
  
      assert R.dmp_qq_i_factor(4 * x**2 + y**2) == (
          QQ_I(4, 0),
          [(x - i * y / 2, 1), (x + i * y / 2, 1)],
      )
  
imports: from sympy.polys.rings import ring, xring
  from sympy.polys.domains import FF, ZZ, QQ, ZZ_I, QQ_I, RR, EX
  from sympy.polys import polyconfig
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.polyclasses import ANP
  from sympy.polys.specialpolys import f_polys, w_polys
  from sympy.core.numbers import I
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import sin
  from sympy.ntheory.generate import nextprime
  from sympy.testing.pytest import raises, XFAIL
label_desc: Use image node_id 17 for calling a global function with example usage: test_dmp_qq_i_factor() without return types