In order to speed up the Tietze transformation routines, each relator in a presentation P is internally represented by a list of positive or negative generator numbers, i.e., each factor of the proper GAP word is represented by the position number of the corresponding generator with respect to the current list of generators, or by the respective negative number, if the factor is the inverse of a generator. Note that the numbering of the generators in Tietze words is always relative to a generator list and bears no relation to the internal numbering of generators in a family of associative words.
TietzeWordAbstractWord( word, fgens ) F
assumes fgens to be a list of free group generators and word to be an abstract word in these generators. It converts word into a Tietze word, i. e., a list of positive or negative generator numbers.
AbstractWordTietzeWord( word, fgens ) F
assumes fgens to be a list of free group generators and word to be a Tietze word in these generators, i. e., a list of positive or negative generator numbers. It converts word to an abstract word,
gap> F := FreeGroup( "a", "b", "c" ,"d");
<free group on the generators [ a, b, c, d ]>
gap> tzword := TietzeWordAbstractWord(
> Comm(F.4,F.2) * (F.3^2 * F.2)^-1, GeneratorsOfGroup( F ){[2,3,4]} );
[ -3, -1, 3, -2, -2 ]
gap> AbstractWordTietzeWord( tzword, GeneratorsOfGroup( F ){[2,3,4]} );
d^-1*b^-1*d*c^-2
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GAP 4 manual