code: def test_canonicalize_no_dummies():
      base1, gens1 = get_symmetric_group_sgs(1)
      base2, gens2 = get_symmetric_group_sgs(2)
      base2a, gens2a = get_symmetric_group_sgs(2, 1)
  
      # A commuting
      # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4]
      # T_c = A^a A^b A^c; can = list(range(5))
      g = Permutation([2, 1, 0, 3, 4])
      can = canonicalize(g, [], 0, (base1, gens1, 3, 0))
      assert can == list(range(5))
  
      # A anticommuting
      # A^c A^b A^a; ord = [a,b,c]; g = [2,1,0,3,4]
      # T_c = -A^a A^b A^c; can = [0,1,2,4,3]
      g = Permutation([2, 1, 0, 3, 4])
      can = canonicalize(g, [], 0, (base1, gens1, 3, 1))
      assert can == [0, 1, 2, 4, 3]
  
      # A commuting and symmetric
      # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5]
      # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5]
      g = Permutation([1, 3, 2, 0, 4, 5])
      can = canonicalize(g, [], 0, (base2, gens2, 2, 0))
      assert can == [0, 2, 1, 3, 4, 5]
  
      # A anticommuting and symmetric
      # A^{b,d}*A^{c,a}; ord = [a,b,c,d]; g = [1,3,2,0,4,5]
      # T_c = -A^{a c}*A^{b d}; can = [0,2,1,3,5,4]
      g = Permutation([1, 3, 2, 0, 4, 5])
      can = canonicalize(g, [], 0, (base2, gens2, 2, 1))
      assert can == [0, 2, 1, 3, 5, 4]
      # A^{c,a}*A^{b,d} ; g = [2,0,1,3,4,5]
      # T_c = A^{a c}*A^{b d}; can = [0,2,1,3,4,5]
      g = Permutation([2, 0, 1, 3, 4, 5])
      can = canonicalize(g, [], 0, (base2, gens2, 2, 1))
      assert can == [0, 2, 1, 3, 4, 5]
  
file_path: sympy/sympy/combinatorics/tests/test_tensor_can.py
imports: from sympy.combinatorics.permutations import Permutation, Perm
  from sympy.combinatorics.tensor_can import perm_af_direct_product, dummy_sgs, riemann_bsgs, get_symmetric_group_sgs, canonicalize, bsgs_direct_product
  from sympy.combinatorics.testutil import canonicalize_naive, graph_certificate
  from sympy.testing.pytest import skip, XFAIL
label_desc: Use image node_id 5 for calling a global function with example usage: test_canonicalize_no_dummies() without return types