On Tuesday, October 7, 2014 7:14:57 PM UTC+1, Nils Bruin wrote:
>
> I'd say in p-adics elements simply carry around their own precision. The 
> different parents simply supply a cap on how big that precision can be.
>

Thats just another way of saying that they implement precision both in the 
parent and the element. Maybe it sounds better, fine. Still means that you 
have to manually implement the coercion to the right precision instead of 
using the coercion framework.
 

> I think this is all driven by Sage's use of ==, which means: after 
>> coercion. Which is surely what you expect in interactive use, but 
>> devastating once you use it for caching decisions:
>>
> Indeed, and calling "==" on floats or power series is almost surely the 
> wrong thing to do.
>

Comparison for power series makes perfect sense to me, coerce to the lowest 
common precision and then compare coefficients. Its just that the 
mathematical expectation is at odds with the Python implementation of 
associative containers.

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