Subgroup method

The subgroup method is an algorithm used in the field of group theory. It is used to find the word (group theory) of an element. It doesn't always return the minimal word, but it can return optimal words based on the series of subgroups that is used.

Input: g Output: solution for g

  function(g)
       sequence := (set of subgroups that will be used, depending on the method.)
       word := []
       for subgroup in sequence
            coset_representatives := []
            <fill coset_representatives>
            for operation in coset_representatives
                 if OPERATE(g, operation) is in the next subgroup then
                      append operation onto word
                      g = OPERATE(g, operation)
                      break