On Tuesday, October 7, 2014 10:03:54 AM UTC-7, Volker Braun wrote:
>
> p-adics are even more weird, they coerce in the wrong direction. And, to 
> patch up that mistake, have a precision in the parent and another precision 
> in the element:
>

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.
 

> 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. For the same reason, one shouldn't put floats as keys 
into dictionaries or cache float-argument functions. 
 

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