Hi Robert,
>> I wonder if the category infrastructure would support a pervasive
>> command like
>>
>> R=IntegerModRing(7)
>> R.promote(Fields(), with_check=True)
>> R.category()
>> Category of fields
>>
>> with the construction doing no extra work, and the promote method
>> having defaults and exceptions consistent with John and Nick's
>> "explicit is better" philosophy?
>>
>> I had though about is_field doing the upgrade, but I think these sort
>> of side-effects are confusing.
>
> Side effects are confusing in general, especially with cached parents. I
> would rather have a change_category method that returns a new object with
> the updated category, like
>
> sage: R=IntegerModRing(7)
> sage: R.change_category(Fields()).is_field()
> True
This is perfectly doable, except that, all the element created before will
still be ring element. More precisely if you write:
> sage: R = IntegerModRing(7)
> sage: R1 = change_category(Fields())
then you have a brand new parent with no connection to the former one. You can
set up a coercion R -> R1 but this is very likely to leads to very unexpected
behavior.
Cheers,
Florent
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