#14084: Wrong domain of the fraction field construction functor
-----------------------------+----------------------------------------------
Reporter: SimonKing | Owner: roed
Type: defect | Status: new
Priority: major | Milestone: sage-5.7
Component: padics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
-----------------------------+----------------------------------------------
Comment (by nbruin):
Replying to [comment:5 nthiery]:
> 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.
For the most part I probably agree with that. However, how does this
relate to additional concepts such as "finitely generated"?
The following is probably not entirely kosher in terms of mathematical
categories, but it may affect the colloquial use of them in computer
algebra:
The Gaussian field `QQ(i)` would generally be considered a finitely
generated field, but as a ring it would not be finitely generated (no
characteristic 0 field is). Of course one should specify over what object
they are finitely generated, and the discrepancy comes from the different
default choices for fields and rings: The prime fields `QQ` and `GF(p)`
for fields versus `ZZ` for commutative rings.
I would love to see that we can use the "category" field as a dynamic
attribute as suggested, because it does make these `is_field` tests
wonderfully fast without requiring complicated additional caching. But I
am concerned that phenomena (or misconceptions) as above might come back
and bite us if we're coming to depend on such tricks extensively. Can you
ease that concern?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14084#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
