RE: [Axiom-developer] Complex exponentiation and 0

[Page, Bill]

On Monday, June 21, 2004 6:27 AM Martin Rubey
address@hidden wrote:
> > > 
> > > According to Martin comment, 0^0 is not mathematically defined.
> > > 
> >
> 
> The problem is that the function f(x,y) = x^y is not continuous
> at x=y=0

Yes, of course. But what does that have to do with the case where
y is an integer?

> ... 
> I think it's dangerous to say that 0^0=1, although it's natural
> in many cases:
> 
> http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node14.html
>

It seems to me that Alex López-Ortiz's arguments above are correct.
Therefore I do not understand why you say "it's dangerous".
 
> In fact, I'm not sure what we would gain if axiom assumes 
> 0^0=1 throughout.

I assume you mean when '0' denotes an integer?

> I think, before we decide to adopt this strategy, we should 
> have examples which were otherwise cumbersome to deal with.

See Alex López-Ortiz's article that you reference above.

> 
> Maybe as a guide:
> 
> Mathematica 5.0 for Linux
> ...
>     |\^/|     Maple 8 (IBM INTEL LINUX)
> ...                                       0
> 
> MuPad also says 0^0=1
> ...

I my perhaps less than humble opinion: No!

I think Axiom should *not* use Mathematica, Maple, MuPad or
Maxima as a guide. Axiom should only appeal to the mathematics
involved. In one way or another all of M^4 (and others) make
compromises when it comes to fundamentals. I think Axiom was
built with greater respect for the underlying mathematics and
that is something that we must retain and nurture. It is the
main thing that distinguises Axiom from the others.

Regards,
Bill Page.