> < ^ Date: Thu, 21 Apr 1994 11:05:00 +0200
> < ^ From: Volkmar Felsch <Volkmar.Felsch@Math.RWTH-Aachen.DE >
> < ^ Subject: Re: keeping track of the transformations

Chris Wensley writes:

Martin Sch"onert, in his reply to Tim Hsu, writes:

" ..use Tietze transformations.. If one keeps track of the transformations.."

Since this is precisely what I want to do, I am asking how!
Specifically, if a messy presentation with generators _x1 .. _x20 (say)
is reduced, using TzGo , to a presentation with generating set
[ _x3, _x12, _x24 ] ,I want to remember expressions for the
21 eliminated generators as words in the three remaining ones.

I have not been able to discover a solution in the manual but 3 possible
methods suggest themselves. Guidance as to which way to go would be much

1. Avoid using the high-level TzGo and use the low-level commands
so that at each elimination the required formula can be saved. Surely
this would amount to rewriting TzGo ?

2. Edit appropriate parts of the file "fptietze.g" .
This file is 40 pages long, with many interdependant functions,
so I should probably create a host of bugs?
In any case, the functions use the <Tietze record> type, which
appears to be defined elsewhere, possibly in the kernel?

3. Start a LOG file before using TzGo and so produce a file
containing messages of the form:
#I eliminating _x7 = _x18^5*_x5*_x4
As far as I can tell, GAP cannot Read this LOG file, but perhaps it
would be possible to write some utility to convert the LOG file into
a GAP file, Exec this utility, and Read the resulting GAP file?

As the discussion on keeping track of Tietze transformations is too
technical to be continued in the GAP forum, I have sent my answer to
the above letter directly to Chris Wensley. However, I would like to
encourage all those forum members who are interested in that question
to ask me for a copy of that correspondence.

Volkmar Felsch, Aachen

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