Simon King a écrit :
> Sage has both left and right actions. I would need to look up the
> details, but it is no problem to implement a right action of S2 on S1
> rather than a left action of S1 on S2. Since the mathematical property
> of "being an action" is not relevant in the implementation, you could
> actually still tell Sage that there is a left action of S1 on S2, even
> though mathematically it is the other way around.
Okay, so you were speaking of actions in the sense of the coercion
model, and I thought you meant actions in the mathematical sense. Sorry
again for the misunderstanding.
>>> No, I'd rather expect to coerce x into a *non-commutative* version
>>> of the polynomial ring K[x][d/dx].
>>
>> Yes, what I denoted K[x][d/dx] was the ring of differential operators
>> with polynomial coefficients. Or do you have something else in mind?
>
> Well, I thought you use the usual notation in Sage. And there, square
> brackets denote (commutative) polynomial rings.
(On a side note, ticket #13215 proposes to change that in some cases.)
> I would do
> sage: F.<X,d> = FreeAlgebra(QQ)
> sage: D.<x,dx> = F.g_algebra({d*X:X*d+1})
> sage: dx*x
> x*dx + 1
>
> to create the ring in question. But this is because I am algebraist,
> and I guess "proper" differential operators are implemented somewhere
> else in Sage (dunno where/how/why), and do *not* live in this ring.
As far as I know, rings of differential operators are not yet
implemented in the Sage library, and currently the best way to define a
differential operator is the one you mention. (I think that's also more
or less what you told me in Orsay a few weeks ago.) The external package
ore_algebra[1] that Fredrik Johansson announced a few weeks ago[2]
provides "proper" differential operators, though.
[1]
http://www.risc.jku.at/research/combinat/software/ore_algebra/
[2]
<CAJdUXTLq78H2Mcz2-WH-LNbJ=ypax9la-omicfmgcjyciwt...@mail.gmail.com>
https://groups.google.com/forum/#!topic/sage-devel/S7Wv67C6DvE
Best wishes,
--
Marc
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/groups/opt_out.
