code: def test_galois_group_not_monic_over_ZZ():
      """
      Check that we can work with polys that are not monic over ZZ.
      """
      for deg in range(1, 7):
          T, G, alt = test_polys_by_deg[deg][0]
          assert galois_group(T / 2, by_name=True) == (G, alt)
  
file_path: sympy/sympy/polys/numberfields/tests/test_galoisgroups.py
imports: from sympy.abc import x
  from sympy.combinatorics.galois import S1TransitiveSubgroups, S2TransitiveSubgroups, S3TransitiveSubgroups, S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups
  from sympy.polys.domains.rationalfield import QQ
  from sympy.polys.numberfields.galoisgroups import tschirnhausen_transformation, galois_group, _galois_group_degree_4_root_approx, _galois_group_degree_5_hybrid
  from sympy.polys.numberfields.subfield import field_isomorphism
  from sympy.polys.polytools import Poly
  from sympy.testing.pytest import raises
label_desc: Use image node_id 5 for calling a global function with example usage: test_galois_group_not_monic_over_ZZ() without return types