#14084: Wrong domain of the fraction field construction functor
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Reporter: SimonKing | Owner: nthiery
Type: defect | Status: new
Priority: major | Milestone: sage-5.7
Component: categories | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:3 nbruin]:
> ... but
> {{{
> sage: k=Qp(7)
> sage: k.category()
> Category of commutative rings
> sage: k in Fields()
> True
> sage: k.category()
> Category of fields
> }}}
> which is a little uncomfortable in its own right. You'd think that a
category is part of the defining properties of the parent, so changing it
seems to fly into the face of immutability of parents.
>
> If we have to keep it like this, we'd have to be very clear that one
should only test if a parent is IN a given category; never rely on the
category reported by "<parent>.category()". It certainly flies in the face
of what I thought sage did: I thought specifying a parent implied
specifying the category in which you want to consider it, and that if you
want to consider a number field as a `QQ`-vector space instead, one should
explicitly apply a functor and use a map (or perhaps conversion if you
want to be implicit about it) to go between the two.
The above is in fact alright because Fields is a full subcategory of
Rings. So by going from one to the other, one don't change the
structure under consideration. One is just learning more properties of
this structure.
I certainly agree that I would not want the category of my parent to
change from Vector Space to Ring, because then I am adding a new
structure (the multiplication).
Full subcategories are not yet modeled in Sage, but this is in the
plans, because that's what we want to go further with homsets.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14084#comment:5>
Sage <http://www.sagemath.org>
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