RE: [Axiom-developer] Graphics and Axiom (was Re: touchgraph, hyp ertex, hypergraph)

[Page, Bill]

Martin,

On Friday, January 21, 2005 6:16 AM you wrote:

> ... so if anybody is going to write a domain "graphs"
> (belonging to the category "matroids"...) he should look at
> [pigale and/or tulip].
> ...

I am very much in favor of establishing a project to extend
Axiom's algebraic capabilities in this area. So far, I think
most computer algebra systems (even commercial systems) have
only a rather primative representation of things like "networks".
But you are right to imply that from a mathematical point of
view graphs are a very fundamental structure. For example I
am inclined to think of abstract directed graphs as one of the
fundations for category theory.

Could you elaborate a little on how you see "graphs" as a
domain of the category "matroids"? How do you see the concept
of matroid as fitting into the current structure of Axiom
categories? For example, shall we attempt to relate linear
algebra also to matroids? What about directed graphs and
"oriented matroids" etc.?

Regards,
Bill Page.