code: def test_dup_cauchy_upper_bound():
      raises(PolynomialError, lambda: dup_cauchy_upper_bound([], QQ))
      raises(
          PolynomialError, lambda: dup_cauchy_upper_bound([QQ(1)], QQ)
      )
      raises(
          DomainError,
          lambda: dup_cauchy_upper_bound([ZZ_I(1), ZZ_I(1)], ZZ_I),
      )
  
      assert (
          dup_cauchy_upper_bound([QQ(1), QQ(0), QQ(0)], QQ) == QQ.zero
      )
      assert dup_cauchy_upper_bound([QQ(1), QQ(0), QQ(-2)], QQ) == QQ(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 2 for calling a global function with example usage: test_dup_cauchy_upper_bound() without return types