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RE: [Axiom-developer] Graph theory

From: Bill Page
Subject: RE: [Axiom-developer] Graph theory
Date: Fri, 10 Nov 2006 22:00:37 -0500

On November 9, 2006 10:23 AM Martin Rubey wrote:
> I'll write something up as soon as possible. But this won't be
> before November~19, since I'm under pressure until then.


> However, I talked a bit with Ralf about this before the axiom 
> workshop, and then I think he was more interested in graphs as 
> datastructures, which doesn't interest me at all.
> I'm into Matroids, Simplicial Complexes, Graphs, Digraphs, 
> Polytopes etc. I have thought only about Categories, not
> implementations.

I think one of the neat things about Axiom is that it is usually
not necessary or even desirable to make a distinction between
data structures and mathematical structures. Data structures are
just another kind of "mathematical" object.

For example, is an Axiom set, i.e. a member of the domain Set, a
data structure or a mathematical structure? Should we call the
domain Set a mathematical structure or only the category SetCategory
to which it belongs? And of course not everything that we would
like to call a set in Axiom is finite.

Essentially the only requirement of SetCategory is that the domain
has equality and inequality.

I think a Graph in Axiom has to be something nearly as fundamental
as a Set.

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