William Stein <[email protected]> writes:

> 2010/1/27 Jaakko Seppälä <[email protected]>:
>> True. I was just thinking that why Sage won't use the law of
>> congruences to evaluate the expression. 84977118993*2^520+1 is not too
>> large number to fit into the memory. Therefore one can use laws of
>> congruences to evaluate mod(2^(2^517)+1,84977118993*2^520+1).
>
> No.  This is would directly violate one of the most basic rules of how
> the Python programming language works (that expressions are
> evaluated), and make the whole language much, much harder to reason
> and work with.
> I'm very glad that Python doesn't do that.

I'm not sure whether you saw my answer yet... It shows that you can have
full evaluation (as in Python), and still work modulo n.  It is only
necessary to have overloading of operations supported.  (and it helps if
you can demand a certain return type)

(I'd be surprised and disappointed if sage cannot do this.)

Martin

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