#14084: Wrong domain of the fraction field construction functor
------------------------------+---------------------------------------------
Reporter: SimonKing | Owner: roed
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.7
Component: padics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:18 nbruin]:
> Replying to [comment:17 nthiery]:
> > For robust results, one should always specify the category.
> But that's the issue: The category ''is'' specified:
>
> Hypothetical dialogue (I'm sorry it has to be this academic--I don't
presently have an actual example).
> {{{
> sage: QQ.category()
> Category of Commutative Rings
> sage: QQ.is_finitely_generated()
> False
> }}}
> Sage confirms that at this point, it's considering `QQ` as a commutative
ring and as such is not finitely generated.
> {{{
> sage: QQ in Fields()
> True
> sage: QQ.category()
> Category of Fields
> sage: QQ.is_finitely_generated()
> True
> }}}
> Since the category here is `Fields` the question about finite generation
should be considered there. Since it's a prime field I don't see how any
other answer than `True` could be considered there.
Sorry, I have been ambiguous. What I mean is that, for the answer to
be well defined, one should specify the category at the time one asks
whether the object is finitely generated. Something like:
{{{
sage: Q.is_finitely_generated(Fields())
}}}
or
{{{
sage: Q.is_finitely_generated_field()
}}}
Then,
{{{
sage: Q.is_finitely_generated()
}}}
would return the answer for the current category of Q; but that's just
a lousy syntactic sugar, for the user convenience, when there is no
ambiguity.
> This suggests to me that the concept of finite generation is not
> well-behaved w.r.t. restricting to ''full subcategories''.
It's just not well defined if you don't specify explicitly for which
category you are asking the question.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14084#comment:22>
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