class_docstr: Properties
  ==========
  
  [1] `0 \in \Omega` and `\tau(1) = \epsilon`
  [2] `\alpha^x = \beta \Leftrightarrow \beta^{x^{-1}} = \alpha`
  [3] If `\alpha^x = \beta`, then `H \tau(\alpha)x = H \tau(\beta)`
  [4] `\forall \alpha \in \Omega, 1^{\tau(\alpha)} = \alpha`
  
  References
  ==========
  
  .. [1] Holt, D., Eick, B., O'Brien, E.
         "Handbook of Computational Group Theory"
  
  .. [2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
         Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490.
         "Implementation and Analysis of the Todd-Coxeter Algorithm"
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docstr: A variation of ``coincidence`` routine used in the coset-table based
  method of coset enumeration. The only difference being on addition of
  a new coset in coset table(i.e new coset introduction), then it is
  appended to ``deduction_stack``.
  
  See Also
  ========
  
  coincidence
docstr_tok: ["A","variation","of","``","coincidence","``","routine","used","in","the","coset-table","based","method","of","coset","enumeration",".","The","only","difference","being","on","addition","of","a","new","coset","in","coset","table","(","i.e","new","coset","introduction",")",",","then","it","is","appended","to","``","deduction_stack","``",".","See","Also","========","coincidence"]
code: def coincidence_c(self, alpha, beta):
      """
      A variation of ``coincidence`` routine used in the coset-table based
      method of coset enumeration. The only difference being on addition of
      a new coset in coset table(i.e new coset introduction), then it is
      appended to ``deduction_stack``.
  
      See Also
      ========
  
      coincidence
  
      """
      A_dict = self.A_dict
      A_dict_inv = self.A_dict_inv
      table = self.table
      # behaves as a queue
      q = []
      self.merge(alpha, beta, q)
      while len(q) > 0:
          gamma = q.pop(0)
          for x in A_dict:
              delta = table[gamma][A_dict[x]]
              if delta is not None:
                  table[delta][A_dict_inv[x]] = None
                  # only line of difference from ``coincidence`` routine
                  self.deduction_stack.append((delta, x**-1))
                  mu = self.rep(gamma)
                  nu = self.rep(delta)
                  if table[mu][A_dict[x]] is not None:
                      self.merge(nu, table[mu][A_dict[x]], q)
                  elif table[nu][A_dict_inv[x]] is not None:
                      self.merge(mu, table[nu][A_dict_inv[x]], q)
                  else:
                      table[mu][A_dict[x]] = nu
                      table[nu][A_dict_inv[x]] = mu
  
imports: from sympy.combinatorics.free_groups import free_group
  from sympy.printing.defaults import DefaultPrinting
  from itertools import chain, product
  from bisect import bisect_left
label_desc: Use image node_id 10 for calling the CosetTable obj's underlying member method code with example usage: obj.coincidence_c(alpha, beta) without return types