On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri <jhpalmier...@gmail.com> wrote:
>
>
>
> On Oct 22, 1:25 am, Kwankyu Lee <ekwan...@gmail.com> wrote:
>> Hi,
>>
>> The following scares me.
>>
>> sage: 0^0
>> 1
>> sage: F.<a>=GF(5)
>> sage: F(0)^0
>> Traceback (most recent call last):
>> ...
>> ArithmeticError: 0^0 is undefined.
>>
>> For any x, x^0 is 1 by definition.
>
> I always thought that for any y, 0^y = 0. :)
>
> Anyway, 0^0 is undefined in mathematics, so it's good that it's
> undefined in Sage.
It's defined for Sage *integers*:
sage: 0^0
1
Among other reasons, this is for compatibility with Python and many,
many other programs:
sage: int(0)^int(0)
1
sage: maple('0^0')
1
sage: gap('0^0')
1
sage: gp('0^0')
1
William
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