code: def test_AlgebraicField_galois_group():
      k = QQ.alg_field_from_poly(Poly(x**4 + 1))
      G, _ = k.galois_group(by_name=True)
      assert G == S4TransitiveSubgroups.V
  
      k = QQ.alg_field_from_poly(Poly(x**4 - 2))
      G, _ = k.galois_group(by_name=True)
      assert G == S4TransitiveSubgroups.D4
  
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 8 for calling a global function with example usage: test_AlgebraicField_galois_group() without return types