code: def _verify_bsgs(group, base, gens):
      """
      Verify the correctness of a base and strong generating set.
  
      Explanation
      ===========
  
      This is a naive implementation using the definition of a base and a strong
      generating set relative to it. There are other procedures for
      verifying a base and strong generating set, but this one will
      serve for more robust testing.
  
      Examples
      ========
  
      >>> from sympy.combinatorics.named_groups import AlternatingGroup
      >>> from sympy.combinatorics.testutil import _verify_bsgs
      >>> A = AlternatingGroup(4)
      >>> A.schreier_sims()
      >>> _verify_bsgs(A, A.base, A.strong_gens)
      True
  
      See Also
      ========
  
      sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims
  
      """
      from sympy.combinatorics.perm_groups import PermutationGroup
  
      strong_gens_distr = _distribute_gens_by_base(base, gens)
      current_stabilizer = group
      for i in range(len(base)):
          candidate = PermutationGroup(strong_gens_distr[i])
          if current_stabilizer.order() != candidate.order():
              return False
          current_stabilizer = current_stabilizer.stabilizer(base[i])
      if current_stabilizer.order() != 1:
          return False
      return True
  
file_path: sympy/sympy/combinatorics/testutil.py
imports: from sympy.combinatorics import Permutation
  from sympy.combinatorics.util import _distribute_gens_by_base
label_desc: Use image node_id 3 for calling a global function with example usage: _verify_bsgs(group, base, gens) and returns: True, False, False