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

From: Martin Rubey
Subject: Re: [Axiom-developer] Polynomials, abstract objects, provisos
Date: 28 Jul 2006 10:00:34 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.3

Hi Ralf,

Ralf Hemmecke <address@hidden> writes:

> > A polynomial really is a polynomial.
> Another difference between mathematics and computational mathematics...  If
> polynomials where just polynomials why then was there some clever guy who
> thought about implementing recursive and distributed multivariate
> polynomials?  When it comes to efficiency, the datastructure matters.

There is a misunderstanding happening here. In fact, one of the strengths of
Axiom is that we have different datastructures for the same mathematical

What I meant is something entirely different: in Axiom, any object is a
"concrete" mathematical object. I think that in some sense, "assumptions" of
other CAS should be modelled in Axiom by different domains.

I think that efficiency in Axiom is to a big part due to the fact that at any
point of a computation, everything of an object is known.

I don't know how we should model "abstract polynomials", but I'm not even sure
whether we should have such a thing.

Concerning provisos, this really affects only the domain EXPR, in my opinion.


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