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Re: [Axiom-developer] Polynomials, abstract objects, provisos

From: Martin Rubey
Subject: Re: [Axiom-developer] Polynomials, abstract objects, provisos
Date: 29 Jul 2006 09:19:09 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.3

Ralf Hemmecke <address@hidden> writes:

> [recursive vs. distributed polynomials]

> > I don't know how we should model "abstract polynomials", but I'm not even 
> > sure
> > whether we should have such a thing.
> That would be possible, but suppose you want to do a Gröbner basis
> computation. Who is going to choose the most efficient data representation?


I have no idea what you are talking about, sorry. I was referring to Tim's (?)
idea that we could say something like:

p: Abstract POLY INT

i.e., not assign p a value,

and still do interesting things with it. And I doubt that this is something
within reach, as it is, in my opinion, rather orthogonal to the philosophy of
the current Axiom Algebra.

Something easier to grasp is probably:

z: Abstract Complex INT

and then be able to say 

w := conjugate z.

In other words: there would be no data representation as we are used to

Again, note that although I find this an interesting subject, I believe that it
is currently out of reach.


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