#14084: Wrong domain of the fraction field construction functor
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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 nbruin):
I think we really need another way to cache whether a ring is a field
then. What you describe is indeed the case:
{{{
sage: R=ZZ.quo(7)
sage: R in IntegralDomains() ##1
False
sage: R in Fields()
True
sage: R in IntegralDomains() ##2
True
}}}
you can see that the call `R in Fields()` has mutated the parent in an
essential way. The kind of call that people HAVE to use to look at the
category field because it is not trustworthy by itself even can change
depending on what happens with the parent elsewhere!
Whether `##1` is a bug or not depends on how you interpret the question:
Are we asking the mathematical truth (which in general might be
undecidable) or are we asking what sage knows about the object by
construction? The first would of course be nicer, but computer algebra
systems often settle for the second.
The important thing here is to illustrate how easy it is to mutate parents
in a significant way if you start mucking with their category.
Personally I think it's fine if `ZZ.quo(7)` doesn't advertise itself as a
`field by construction`. People can ask for `GF(7)` instead, which luckily
does give back a non-identical parent:
{{{
sage: R=ZZ.quo(7)
sage: R2=GF(7)
sage: id(R)
85206256
sage: id(R2)
17095856
}}}
By the way:
{{{
sage: R.category()
Join of Category of commutative rings and Category of subquotients of
monoids and Category of quotients of semigroups and Category of finite
enumerated sets
sage: R2.category()
Join of Category of subquotients of monoids and Category of quotients of
semigroups and Category of finite fields
}}}
I have to say those values do a good job of dissuading people from ever
looking at them!
Also, this discussion is not of direct relevance to this ticket, so
perhaps we should take the discussion to sage-devel instead.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14084#comment:20>
Sage <http://www.sagemath.org>
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