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Re: [Axiom-developer] Complex exponentiation and 0
From: |
Martin Rubey |
Subject: |
Re: [Axiom-developer] Complex exponentiation and 0 |
Date: |
Tue, 22 Jun 2004 10:11:08 +0000 |
I think Bertfried convinced me. Somehow I did not realize that axiom has
different domains :-) However, I do not yet quite understand how to apply this
insight.
Bertfried Fauser writes:
> From an algebraic point of view, I think its save to assume 0^0=1 in any
> category which has _no_ (non-discrete) topological semantics. As eg. real
> numbers come with a standard topology, 0^0 is not a uniquely definalble
> object.
Shouldn't this mean that 0^0 is undefined in EXPR INT, for example: x^y ? Hmm,
I see: in x^y we do not have a problem since there is no zero...
> Hence as a guidline, every object with allows a "limit" (ie some norm
> established) should _not_ assume that 0^0=1. I don't see problems for say
> natural numbers.
So, in other words, there is no bug, except that in
Vanuxem Grégory writes:
> In complex(Float) and Complex(SingleFloat), we have to change the
> exponentiation so that
> complex(0,0)^complex(0,0.0)
> or
> complex(0,0)^complex(2,2.0)
> doesn't use log.
the *latter* really should give 0?
--------------------------------------------------------------------
Page, Bill writes:
> > 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.
You are right. However, I still think that we can learn things from M^*. So,
what I should have written is: look, M^* does this and that. Are there things
that are mathematically just and we should incorporate?
Still, I strongly agree with you that we should never be tempted to say: "well,
Mx does it this way, therefore we should do so too."
Martin
RE: [Axiom-developer] Complex exponentiation and 0, Page, Bill, 2004/06/21