66.7 Word reduction

IsReducedWordRWS(rws,w)

Test whether the word w in the generators of the rewriting system rws (or, equivalently, in the generators of the underlying group of rws) is reduced or not, and return true or false.

IsReducedWordRWS can only be used after KB or Automata has been run successfully on rws. In the former case, if KB halted without a confluent set of rules, then irreducible words are not necessarily in normal form (but reducible words are definitely not in normal form). If KB completes with a confluent rewriting system or Automata completes successfully, then it is guaranteed that all irreducible words are in normal form.

ReduceWordRWS(rws,w)

Reduce the word w in the generators of the rewriting system rws (or, equivalently, in the generators of the underlying group of rws), and return the result.

ReduceWordRWS can only be used after KB or Automata has been run successfully on rws. In the former case, if KB halted without a confluent set of rules, then the irreducible word returned is not necessarily in normal form. If KB completes with a confluent rewriting system or Automata completes successfully, then it is guaranteed that all irreducible words are in normal form.

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GAP 3.4.4
April 1997