code: def test_distribute_gens_by_base():
      base = [0, 1, 2]
      gens = [
          Permutation([0, 1, 2, 3]),
          Permutation([0, 1, 3, 2]),
          Permutation([0, 2, 3, 1]),
          Permutation([3, 2, 1, 0]),
      ]
      assert _distribute_gens_by_base(base, gens) == [
          gens,
          [
              Permutation([0, 1, 2, 3]),
              Permutation([0, 1, 3, 2]),
              Permutation([0, 2, 3, 1]),
          ],
          [Permutation([0, 1, 2, 3]), Permutation([0, 1, 3, 2])],
      ]
  
file_path: sympy/sympy/combinatorics/tests/test_util.py
imports: from sympy.combinatorics.named_groups import SymmetricGroup, DihedralGroup, AlternatingGroup
  from sympy.combinatorics.permutations import Permutation
  from sympy.combinatorics.util import _check_cycles_alt_sym, _strip, _distribute_gens_by_base, _strong_gens_from_distr, _orbits_transversals_from_bsgs, _handle_precomputed_bsgs, _base_ordering, _remove_gens
  from sympy.combinatorics.testutil import _verify_bsgs
label_desc: Use image node_id 3 for calling a global function with example usage: test_distribute_gens_by_base() without return types