next_relation

virtual void libsemigroups::FroidurePinBase::next_relation(word_type &relation) = 0

This member function changes relation in-place to contain the next relation of the presentation defining this.

This member function changes relation in-place so that one of the following holds:

• relation is a vector consisting of a libsemigroups::letter_type and a libsemigroups::letter_type such that FroidurePin::generator(relation[0]) == FroidurePin::generator(relation[1]), i.e. if the semigroup was defined with duplicate generators;

• relation is a vector consisting of a libsemigroups::element_index_type, libsemigroups::letter_type, and libsemigroups::element_index_type such that

  this[relation[0]] * FroidurePin::generator(relation[1]) ==
  this[relation[2]]
  

• relation is empty if there are no more relations.

FroidurePin::next_relation is guaranteed to output all relations of length 2 before any relations of length 3. If called repeatedly after FroidurePin::reset_next_relation, and until relation is empty, the values placed in relation correspond to a length-reducing confluent rewriting system that defines the semigroup.

This member function can be used in conjunction with FroidurePin::factorisation to obtain a presentation defining the semigroup.

See

FroidurePin::reset_next_relation.