Dear Robert,
> >>> The very purpose of the category framework it to declare in a
> >>> mathematical
> >>> way, this that have a matematical meaning. In the case of a right
> >>> action of A
> >>> on B, on declare that B is a A-RightModule. It is much more
> >>> informative by all
> >>> respect than testing if a random element of A accept to be
> >>> multiplied by a
> >>> random element of B.
> >>
> >> _rmul_ and _lmul_ are only tried if B is an A-module. (We don't (yet)
> >> have the distinction between right and left modules, this is part of
> >> where the "try it out" comes into play).
> >
> > Thanks for this explanation... Should I understand that once we had
> > the
> > correct framework, these are supposed to disappear ?
>
> They won't disappear--the coercion model will simply assume they're
> implemented and use them without trying them out first.
I'm sorry I wasn't clear... In my mind, "They" was supposed to refer to "try
out" an not _rmul_ and _lmul_.
> >> However, not all actions are module actions, e.g. a permutation
> >> acting on an ordered list, or a matrix acting on a quadratic form (to
> >> take two examples that I've been thinking about lately).
> >
> > Permutations acting on lists is not a module structure but this may
> > fits in a
> > category of sets with a group acting on (G-set) no-linearity here.
> > For acting
> > on plain list, (i.e. data structure I would rather not use "*" do
> > denote the
> > operation).
>
> BTW, We already have
>
> sage: [1,10,100] * 5
> [1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100, 1, 10, 100]
I find this ugly !!! Just a little less uglier than
Maple: [1,10,100] * 5
[5,50,500]
> (which is to be like Python) so there is some precedent. Perhaps a
> better example is an element of a galois group acting on a field.
I'm sorry I don't get your point even with this new example. You have a group
(finite or not) acting on a set (finite, discrete or not). And this is an
actual action
g1 . (g2 . x) = (g1 g2) . x
So the field is a G-Set. And you probably need all the usual notion of orbit,
fixed point, stabilizer, centralizer...
Cheers,
Florent
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