On Fri, 19 Jun 2020, 09:05 John Cremona, <john.crem...@gmail.com> wrote:

> I would like to vote for exponentiation for a right group action.  This is
> standard mathematical notation (as has already been said), at least in
> several fields that I know of.  Using the shift operators looks too much
> like a computer-sciency solution to me.  Sage has always tried to keep its
> notation close to what a mathematician (including students) would expect --
> for example (almost the only one), re-purposing ^ to mean exponentiation
> rather than the python default.
>

I don't know how to reconcile this with group theory use of exponentiation
for the conjugation action(s).


> All students learning permutations get confused about the order of
> multiplcation and just need to learn that there are two conventions and you
> *have to* know which is being used when you read something since otherwise
> half of what you read will not make sense.
>
> When I was a student I had two tutors who I handed work in to each week.
> One was (is) a group theorist (
> https://en.wikipedia.org/wiki/Peter_M._Neumann) for whom we had to write
> xf for the result of applying function f to object x, so fg meant "do f
> then g".  The other was/is an analyst who only allowed f(x) and the other
> convention.  I had to keep both happy (and get the right answers) so I
> leant fast.
>
> John
>
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