On Sun, Oct 18, 2009 at 1:22 AM, Martin Rubey
<martin.ru...@math.uni-hannover.de> wrote:
>
> William Stein <wst...@gmail.com> writes:
>
>> The above definition of binomial is documented if you type "binomial?"
>> in Sage. This is also arguable the standard usage of "binomial",
>> since it is the same in Mathematica, Maple, Maxima, Pari, GAP, and
>> Magma:
>>
>> sage: mathematica('Binomial[-7,1]')
>> -7
>> sage: maple('binomial(-7,1)')
>> -7
>> sage: pari('binomial(-7,1)')
>> -7
>> sage: maxima('binomial(-7,1)')
>> -7
>> sage: gap('Binomial(-7,1)')
>> -7
>> sage: magma('Binomial(-7,1)')
>> -7
>>
>>> Axiom returns 0 in this case.
>>
>> Based on the above, maybe Axiom should be changed?
>
> FriCAS give 0 for the input above, *but* this is only half of the story.
> In FriCAS (and Axiom, and I believe Sage too), the answer of a
> computation depends on the domain of the input. Eg.:
>
> (1) -> 0::INT^0::NNI
>
> (1) 1
> Type: PositiveInteger
> (2) -> 0.0^0.0
>
> >> Error detected within library code:
> 0^0 is undefined
I'm confused. What does "0^0" precisely have to do with Johann's
question? I thought that since "binomial(x,1) = x" it would be
reasonable to defined binomial(-7,1) = -7.
Are you writing at length about 0^0 only by analogy to give an example
of a function F(x) such that the value of F depends on the parent (or
type) of x such that applying F does not commute with some natural
inclusion of sets? Or does 0^0 have something in particular to do
with binomials?
Thanks for any clarification!
William
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