We give examples of performance for large sets. An important way for describing groups is by finite presentations. Large presentations arise in practice which are poorly suited for either human or computer use. Presentation simplification processes which take bad presentations and produce good presentations have been developed. Substantial use is made of substring searching and appropriate techniques for this context are described.
Effective use is made of signatures and change flags.
Change flags are shown to be the most beneficial of the methods tested here, with very significant performance improvement. Experimental performance figures are given. Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith normal form of an integer matrix.