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Re: [Axiom-developer] Graph theory

From: Ralf Hemmecke
Subject: Re: [Axiom-developer] Graph theory
Date: Sun, 12 Nov 2006 15:22:45 +0100
User-agent: Thunderbird (X11/20061025)

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.

Actually, "Set" is a bad choice for the domain of finite sets that all
have the same type of elements. It should at least be called
"FiniteSet". But then, would make "Set" as a _domain_ in the sense of
mathematics be an interesting domain at all?

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

That is OK, I think.

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

As a category, I agree, but there is not *the* graph domain.


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