#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 SimonKing):
Replying to [comment:20 nbruin]:
> I think we really need another way to cache whether a ring is a field
then.
Another instance of a weak cache perhaps? But if I recall correctly, I
played with weak caches of the "is_Field" function -- and the speed was
not competitive.
Also note that changing the category of the ring has indirect advantages:
There may be more parent and element methods become available when passing
to a sub-category.
I would say the change of category is allowed when one could have chosen
that category during initialisation, and if the only reason for ''not''
doing so during initialisation is efficiency: I have seen applications
involving matrix spaces, for which it really did not matter whether the
matrix space is a vector space or an algebra or just a set -- I just don't
remember the ticket number. Hence, in these applications, one would
''postpone'' the initialisation of the category of a matrix space, and
only do it when necessary.
And in the case of ring versus field, I could imagine that there are
examples in which one just needs to know that a given parent is a ring. In
these applications, it would be a waste of time to determine during
creation of the parent whether it actually is a field or not (which may
involve primality tests). Hence, for efficiency, one should postpone the
test of "being a field" until it is really needed.
> Also, this discussion is not of direct relevance to this ticket, so
perhaps we should take the discussion to sage-devel instead.
+1.
The "change of category" has not been introduced here, and not in #13370
either. In fact, in the good old times, it was possible to have `P in
Fields()` and `P not in IntegralDomains()`. Hence, I think of the
refinement of categories as a progress.
I therefore suggest to use a new ticket, if someone finds a more
satisfying solution of the "speed versus immutability problem".
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14084#comment:21>
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