RE: [Axiom-developer] RE: Aldor and Axiom

[Page, Bill]

On Wednesday, February 15, 2006 12:12 AM Jay Belanger wrote:
> 
> Bill Page writes:
> ...
> >> Hmm.  But aren't there some cases where you want this, like
> >> (say) knowing that 4 is a real integer without having to
> >> explicitly say that? (Sorry that's probably a dumb question).
> >
> > The phrase "real integer" is kind of dumb ... :) What other kinds
> > of integers are there?
> 
> Complex (Gaussian) integers?

Isn't that sort of like saying "complex reals" (sic) are a
kind of real number. ;)

And you forgot "Omnific Integers" ... :)

http://mathworld.wolfram.com/OmnificInteger.html

But I am inclined to agree with Leopold Kronecker:

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kronecker.htm
l

"... he believed in the reduction of all mathematics to
arguments involving only the integers and a finite number
of steps. Kronecker is well known for his remark:-

    God created the integers, all else is the work of man. 

Kronecker believed that mathematics should deal only with finite
numbers and with a finite number of operations. He was the first
to doubt the significance of non-constructive existence proofs."

(With that attitude, surely Kronecker should be counted among
the fathers of modern computer algebra. ;)

So therefore I prefer to think that there is really only one
kind of Integer.

> 
> > I still firmly believe that Aldor is the best way forward.
> > Given that everyone who has posted to the:
> >
> >   http://wiki.axiom-developer.org/FreeAldor
> >
> > petition (including Steven Watt!) has been positive about the
> > idea of making Aldor open source, I think we should just
> > proceed based on that idea.
> 
> Is it that clear that it will become open source?

I am willing to bet on it. In fact I am seriously considering
how we could make the source immediately available under a
provisional license. See the thread on the axiom-legal list.

> It may be that it just takes a while, but is it possible that
> it's taking a while because there are roadblocks that we aren't
> aware of? 
> 

Really, Aldor is "nearly" open source already. All you have to
do to get access to the source code is to ask at aldor.org.
Practically speaking, this means obtaining the approval of
Steven Watt. So far as I know, no one who has asked has ever
been denied access.

Regards,
Bill Page.