23.9 Changing Presentations

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.

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GAP 3.4.4
April 1997