> < ^ From:

< ^ Subject:

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

> < [top]