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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
objects!
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.
Martin
- [Axiom-developer] sbcl and Axiom, C Y, 2006/07/25
- RE: [Axiom-developer] sbcl and Axiom, Page, Bill, 2006/07/25
- RE: [Axiom-developer] sbcl and Axiom, C Y, 2006/07/25
- Re: [Axiom-developer] sbcl and Axiom, root, 2006/07/26
- Re: [Axiom-developer] sbcl and Axiom, C Y, 2006/07/26
- Re: [Axiom-developer] sbcl and Axiom, root, 2006/07/26
- [Axiom-developer] Poster at Mathinfo 06, Martin Rubey, 2006/07/26
- Re: [Axiom-developer] Poster at Mathinfo 06, Ralf Hemmecke, 2006/07/27
- Re: [Axiom-developer] Polynomials, abstract objects, provisos,
Martin Rubey <=
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, Ralf Hemmecke, 2006/07/28
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, Martin Rubey, 2006/07/29
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, Ralf Hemmecke, 2006/07/29
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, Martin Rubey, 2006/07/29
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, root, 2006/07/29
- Re: [Axiom-developer] Polynomials, abstract objects, provisos, Ralf Hemmecke, 2006/07/29
- Re: [Axiom-developer] sbcl and Axiom, Antoine Hersen, 2006/07/26
- Re: [Axiom-developer] sbcl and Axiom, root, 2006/07/26
- Re: [Axiom-developer] sbcl and Axiom, root, 2006/07/26
- RE: [Axiom-developer] sbcl and Axiom, Page, Bill, 2006/07/26