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

[Martin Rubey]

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