45.6 Changing Presentations

extends the presentation P by a new generator.

Let i be the smallest positive integer which has not yet been used as a generator number in the given presentation. AddGenerator defines a new abstract generator x_i with the name "_xi" and adds it to the list of generators of P.

You may access the generator x_i by typing P!.i. However, this is only practicable if you are running an interactive job because you have to know the value of i. Hence the proper way to access the new generator is to write GeneratorsOfPresentation(P)[Length(GeneratorsOfPresentation(P))].

gap> G := PerfectGroup( 120 );;
gap> H := Subgroup( G, [ G.1^G.2, G.3 ] );;
gap> P := PresentationSubgroup( G, H );
<presentation with 4 gens and 7 rels of total length 21>
gap> AddGenerator( P );
#I  now the presentation has 5 generators, the new generator is _x7
gap> gens := GeneratorsOfPresentation( P );
[ _x1, _x2, _x4, _x5, _x7 ]
gap> gen := gens[Length( gens )];
_x7
gap> gen = P!.7;
true

is an internal function which defines a new abstract generator and adds it to the presentation P. It is called by AddGenerator and by several Tietze transformation commands. As it does not know which global lists have to be kept consistent, you should not call it. Instead, you should call the function AddGenerator, if needed.

adds the relator word to the presentation P, probably changing the group defined by P. word must be an abstract word in the generators of P.

removes the n-th relator from the presentation P, probably changing the group defined by P.

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