On Fri, Mar 07, 2014 at 09:48:11AM -0800, Nils Bruin wrote:
> Shouldn't that be "Does Sage know that R is a finite set *by
> construction*?" If the "is_finite" result gets cached in the categories
> we'd violate immutability of parents, i.e.,
>
> sage: R in FiniteSets()
> False
> sage: R.is_finite()
> True
> sage: R in FiniteSets()
> True
>
> would be bad. I know there are some cases where we've swallowed this
> badness in favour of some gains in efficiency elsewhere. I guess one could
> argue it's the category that gets mutated, not R, but I'm not sure that's
> entirely fair.
Changing on the fly the category of a parent to a subcategory with
more structure (e.g. more operations) would certainly be bad
w.r.t. immutability; it's really creating a different parent.
In the above case however, it's about changing the category to a full
subcategory, which means that no structure is added: you just have
learned more information. In principle, I believe this would be a
feature. GAP does it a lot for example. There are some technicalities
though (upgrading the class of the parent *and* of all its elements)
which means that I am not sure how to do this robustly yet. So yes,
for now, I would be fine with your formulation.
Cheers,
Nicolas
PS: I changed the subject of this e-mail, since we are deviating topic
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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