> < ^ Date: Tue, 07 Mar 1995 17:19:00 +0100
> < ^ From: Joachim Neubueser <joachim.neubueser@math.rwth-aachen.de >
< ^ Subject: Re: left actions

Dear Sarah,

While, as always, we do not want to stop anybody from trying out in
GAP whatever (s)he likes, after a little discussion here in Aachen we
feel that we should not encourage writing a 'left action permutation
package', certainly however we do not intend to do that here.

We do not foresee which places would have to be modified in order to
replace one permutation multiplication by the other, i.e. it seems to
be necessary to look carefully at all the stuff involving actions and
this would mean not only present work but also a continuous task,
whenever new routines for permutation groups are added. Moreover it is
of course an excellent source for bugs (I remember a published paper
by a renowned colleague not so long ago where a wrong theorem was just
due to mixing up the two multiplications). Finally, we have all that
nice notation in GAP like i^p for the image of a point i under a
permutation p, which does not match with left action at all.

I understand the reason for using left action in particular with
beginners, they are used to write the square root sign or other
elementary functions in front of the argument. In my teaching of
linear algebra I therefore start with column vectors, multiplied from
the left with matrices, but I use this soon to explain that one might
do it the other way round as well and by the end of the first term the
students have learned that there are two ways of doing this, and that
operation from the right has the advantage that mappings are applied
in that sequence in which we read them in English or German (if we
were e.g. Arabs, we would miss out on that nice argument).

What about changing Newcasle habits rather than GAP, e.g. by
disallusioning first year students to the sad fact that mathematicians
are lousy individualists who have not managed in a couple of thousand
years to get accepted agreement where to write the mapping, right or
left ?

Kind regards Joachim Neubueser

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