#15229: Improved use of category framework for IntegerModRing
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Reporter: SimonKing | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: categories | Resolution:
Keywords: sd53 category | Merged in:
integermodring | Reviewers:
Authors: Simon King | Work issues:
Report Upstream: N/A | Commit:
Branch: | 2a08a447be22e4307372524c4b94ca0577d927c9
u/SimonKing/ticket/15229 | Stopgaps:
Dependencies: |
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Comment (by SimonKing):
Replying to [comment:52 nthiery]:
> I for myself would tend to just support the {{{category=Fields()}}}
syntax.
>
> Imagine a case where the parent could have five different axioms
depening on the input; then you'd have to support five arguments when only
one does the trick uniformly. That's not a completely insane thought: e.g.
for non-commutative groebner basis your could have as axioms: finite
dimensional, finite, commutative, nozerodivisors, ... ).
I think the above discussion gives good arguments why the ''factory'' for
integer mod rings should not allow general freedom in the choice of a
category: The factory needs to ensure uniqueness of instances. Some
choices of a category play well with uniqueness: You want full sub-
categories, and you want that containment in the sub-category does not
rely on additional data (a ring intrinsically either is or is not a
field). But other categories ''should'' result in a non-equal copy of the
ring; for example, a Hopf algebra structure is not an intrinsic property
and should thus not use a globally unique copy of a ring.
Hence, the constructor of `IntegerModRing_generic` (or what's the name of
the class?) should (and already does) of course accept a `category`
argument. But here, we talk about the factory that manages quotients of
the integer ring.
I say: The factory should make it possible that the user asserts that the
resulting ring is in fact a field, to avoid expensive primality tests.
However, if you want to prescribe any fancy category for the resulting
ring, you should either refine the category after the ring has been
returned by the factory, or you should create a new factory (for quotient
rings providing a fancy Hopf algebra structure) that is orthogonal to the
`IntegerModRing` factory.
In any case: Are there open questions from the discussion? AFAIK, the
current branch addresses all questions. What is missing for a review?
--
Ticket URL: <http://trac.sagemath.org/ticket/15229#comment:55>
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