[Axiom-developer] Re: [Aldor-l] operations working in general, but not in special cases -- help needed

[Martin Rubey]

"Christian Aistleitner" <address@hidden> writes:
> I am not familiar with matroids, so let me get this straightened out.
> 
> 1. Graphic non-planar matroids do not provide a way to compute a dual
>    element.

Well, no. The dual of a graphic non-planar matroids is not a graphic matroid
again. It is perfectly well defined on the level of matroids. 

Consider the rationals versus the integers. Then only units are invertible in
the integers, but all non-zero elements are invertible in the rationals.

> 2. Graphic planar matroids are able to compute duals for all elements.

yes.

> 3. Graphic non-planar three-connected Matroids do not have duals at all.

no. See 1.

> 4. Graphic three-connected Matroids allow recovering of vertices.

yes.

> 5. Planar graphic matroids are called "matroids".

yes.

I think that William Sit got it right -- and his solution is simple, too -- but
I don't have time right now to check the details. He sent his mail also to
Aldor-l, so you should have gotten it...

Are we going to meet on the workshop?

Martin