#11068: Basic implementation of one- and twosided ideals of non-commutative
rings,
and quotients by twosided ideals
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Reporter: SimonKing | Owner:
AlexGhitza
Type: enhancement | Status:
needs_work
Priority: major | Milestone:
sage-4.7
Component: algebra | Keywords:
onesided twosided ideal noncommutative ring
Author: | Upstream:
N/A
Reviewer: | Merged:
Work_issues: Add examples; move code from ring.py to rings.py |
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Comment(by nthiery):
Replying to [comment:7 SimonKing]:
> I guess, a quotient ring of a ring R should belong to the category
`R.category().Quotients()`.
+1
> Doing, so, there are further problems, since some crucial methods
> such as `lift` have a completely different meaning in
> sage.rings.quotient_rings and sage.categories.quotients.
That's precisely the issue that stopped me starting the refactoring of
quotient, because there was a design discussion to be run first on
sage-devel to see which syntax should be prefered:
- that currently used in the category framework for sub quotients:
P.lift either a plain Python method, or better the lift
function as a morphism
P.lift(x) lifts x to the ambient space of P
- or that used in sage.rings.quotient_rings:
P.lift()(x) lifts x to the ambient space of P
P.lift() the lifting morphism
I personally prefer the former, first from a syntactical point of
view, and because it make it easy in practice to implement lift.
Note: at first sight, it seems easy to make the change in this
direction while retaining backward compatibility by just patching
sage.ring.quotient_rings so that P.lift(x) delegates the work to
P.lift()(x).
Do you mind running this dicussion on sage-devel?
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11068#comment:9>
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