#16269: Cartesian Products of additive groups
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nathann Cohen, | Reviewers:
Nicolas M. Thiéry | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/16269 | aa07ba19487569ef26772c51092c4d5342faff7c
Dependencies: | Stopgaps:
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Comment (by dimpase):
Replying to [comment:6 ncohen]:
> Yo !
>
> > Hmm, do you mean to construct the Cartesian product of fields? Then it
will be a ring, with two operations, addition and multiplication...
>
> Hmmmm.. Well, I guess it may not be very hard to do.
>
> 1) A ring is a additive group (so the + is already implemented) for the
product of rings
You can make any abelian group into a ring by defining multiplication by a
non-zero element a to be identity operation, i.e. ax=x for all x in the
group, and by 0 to be zero, i.e. 0x=0 for all x in the group.
This should be easy to implement - no real code, just some abstract
nonsense :-)
That is, as soon as you have cartesian product of rings, you have what you
need in general...
>
> 2) It has a multiplicative operation, but perhaps the product of
multiplicative associative magma is not detected as such.
but why?
Is it because #10963 will take forever to merge, as it has apparently hit
some kind of OSS unsolvability barrier? :)
> If you can just give Sage the right inheritances, perhaps you have no
real code to implement.
If I were a category theorist and a (C)Python guru by training, perhaps it
will only take me 5 minutes ;-)
--
Ticket URL: <http://trac.sagemath.org/ticket/16269#comment:13>
Sage <http://www.sagemath.org>
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