Hello,

I seem to have run across a potential bug on Sage:
>
> p = previous_prime(2^64)
>> F.<x> = GF(p^2)
>> x * 2**63
>>
>>
> throws a "overflow in t_INT-->long assignment" exception creating the 
> element x * 2**63.
>

This is indeed a bug.  Sage calls the wrong PARI function for this 
conversion: it should convert to a 64-bit *unsigned* integer, but instead 
asks for a 64-bit *signed* integer, hence the overflow.  I opened a bug 
report at http://trac.sagemath.org/ticket/16807; a fix is coming soon.

Peter

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