#9138: Categories for all rings
--------------------------+-------------------------------------------------
Reporter: jbandlow | Owner: nthiery
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: categories | Keywords: introspection, categories for rings
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies:
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Comment(by nthiery):
Replying to [comment:52 SimonKing]:
> The first patch did not cover all rings - it turned out that many
classes derived from sage.rings.ring.Ring do in fact ''not'' call the
`__init__` method of rings. Hence, in these cases, the category stuff was
not present.
>
> The second patch takes care of some of these cases - I think I shouldn't
vouch for completeness, though. Moreover, I implemented the new coercion
model for some more classes of rings, such as free algebras, quotient
rings, and boolean polynomial rings.
Cool!
> Concerning quotient rings: I hope that the category of this quotient
ring is correctly chosen:
> {{{
> sage: P.<x,y> = QQ[]
> sage: Q = P.quo(P*[x^2+y^2])
> sage: Q.category()
> Join of Category of commutative rings and Category of subquotients of
monoids and Category of quotients of semigroups
> }}}
>
> What do you think: Should it perhaps better be "join of Category of
commutative algebras over Rational Field and Category of subquotients
..."?
> After all, P belongs to the category of commutative algebras over the
rational field.
If multiplication by elements of QQ are implemented (and I assume they
are), then yes I definitely would go for commutative algebras.
> But apart from that, it seems ready for review now.
Nice! I'll work on that in the coming weeks, but can't promise when
with the upcoming Sage days. Please anyone beat me to it!
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:53>
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