On Friday, March 7, 2014 8:33:50 AM UTC-8, Nicolas M. ThiƩry wrote:
>
> - R in FiniteSets(): 
>   Does Sage already know that R is a finite set? 
>
> - R.is_finite(): 
>   Is R finite? Answering may require a lengthy calculation; A 
>   NotImplementedError would be a valid "answer". 
>
 
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.
 

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