code: def test_dup_count_complex_roots_implicit():
      R, x = ring("x", ZZ)
  
      # z*(z-1)*(z+1)*(z-I)*(z+I)
      f = x**5 - x
  
      assert R.dup_count_complex_roots(f) == 5
  
      assert R.dup_count_complex_roots(f, sup=(0, 0)) == 3
      assert R.dup_count_complex_roots(f, inf=(0, 0)) == 3
  
imports: from sympy.polys.rings import ring
  from sympy.polys.domains import ZZ, QQ, ZZ_I, EX
  from sympy.polys.polyerrors import DomainError, RefinementFailed, PolynomialError
  from sympy.polys.rootisolation import dup_cauchy_upper_bound, dup_cauchy_lower_bound, dup_mignotte_sep_bound_squared
  from sympy.testing.pytest import raises
label_desc: Use image node_id 19 for calling a global function with example usage: test_dup_count_complex_roots_implicit() without return types