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: Define a function p_p from from [1..n] to A* as
  an additional component of the modified coset table.
  
  Parameters
  ==========
  
  \alpha \in \Omega
  x \in A*
  
  See Also
  ========
  
  define
docstr_tok: ["Define","a","function","p_p","from","from","[","1","..","n","]","to","A","*","as","an","additional","component","of","the","modified","coset","table",".","Parameters","==========","\\alpha","\\in","\\Omega","x","\\in","A","*","See","Also","========","define"]
code: def modified_define(self, alpha, x):
      r"""
      Define a function p_p from from [1..n] to A* as
      an additional component of the modified coset table.
  
      Parameters
      ==========
  
      \alpha \in \Omega
      x \in A*
  
      See Also
      ========
  
      define
  
      """
      self.define(alpha, x, modified=True)
  
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 26 for calling the CosetTable obj's underlying member method code with example usage: obj.modified_define(alpha, x) without return types