Dear Javier,
On Thu, Oct 01, 2009 at 10:32:30AM -0700, javier wrote:
>
> Somebody could explain why these are different files?
>
> Assuming that by "all ideals of a ring R" we mean two-sided ideals
> (that should go inside the description!) I don't see what is the
> difference, for a commutative ring R, between ring_ideals(R) and
> commutative_ring_ideals(R). Or am I missing something here?
>
> IMO, there is no need for "commutative_ring_ideals", and the only
> distinction on whether R is commutative or not should be made for
> super_categories. If R is commutative it should return Modules(R) and
> if R is not commutative it should return
> [LeftRingIdeals(R), RightRingIdeals(R), Bimodules(R,R)]
>
> This also brings to attention that there aren't any "LeftRingIdeals"
> or "RightRingIdeals" methods, I think these should also be included in
> the ring_ideals.py file, defined in a similar way as RingIdeals with
> the additional check of commuativity of R, in which case
> LeftRingIdeals, RightRingIdeals and RingIdeals should be identified as
> equal.
Thanks for bringing this up. My point of view, backed up with David is
as follow:
- RingIdeals is indeed about two sided ideals
- The CommutativeRingIdeal category will potentially contain a lot of
code that will be specific to the commutative case (either new
methods or more efficient implementations of other
methods). Merging the two categories would mean not only making a
test in the super_categories method (as you mention above), but
also in all the other methods specific to the commutative case.
Hence the following hierarchy of categories:
LeftModule RightModule
| \ / |
RingLeftIdeals BiModule RingRightIdeals
\ | /
RingIdeals
|
CommutativeRingIdeals
- As you mention, from the user perspective it's redundant to ask for
CommutativeRingIdeals(QQ). So, when RingIdeals(QQ) is called, Sage
could detect that QQ is commutative, and automatically return the
former (+ play a trick so that CommutativeRingIdeals.super_categories
could still actually create RingIdeals(QQ)).
- Same thing for AlgebraIdeals.
I added those bits to the documentation, leaving the current code
unchanged. I vote for delaying the actual implementation of
Ring[Left/Right]Ideals until actually needing them. I am also lazy
implementing the trick above now, unless there is a vast agreement on
it.
Does this sound ok?
Cheers,
Nicolas
PS: in the same vein: should Modules(R) automatically return
VectorSpaces(R) when R is a field?
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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