The commands described in this section can be used to change the presentation in a presentation record. Note that, in general, they will change the isomorphism type of the group defined by the presentation. Hence, though they sometimes are called as subroutines by Tiet-ze Tietze Transformations), they do not perform Tietze transformations themselves.
AddGenerator( P )
AddGenerator( P, generator )
AddGenerator
adds a new generator to the list of generators.
If you don't specify a second argument, then AddGenerator
will define
a new abstract generator _xi
and save it in a new component
P.i
of the given presentation record where i is the least
positive integer which has not yet been used as a generator number.
Though this new generator will be printed as _xi
, you will have to
use the external variable P.i
if you want to access it.
If you specify a second argument, then generator must be an abstract
generator which does not yet occur in the presentation. AddGenerator
will add it to the presentation and save it in a new component P.i
in the same way as described for _xi above.
AddRelator( P, word )
AddRelator
adds the word word to the list of relators. word must
be a word in the generators of the given presentation.
RemoveRelator( P, n )
RemoveRelator
removes the nth relator and then resorts the list of
relators in the given presentation record P.
GAP 3.4.4