Robert,

> Most of the graph theory functions have a bunch of options for the
> format of the output, I'd say this would follow that trend, taking the
> old behavior as default.

Ok. I will try to extract edge based paths from generic graph
functions, depending on a new option.

> > For now only a minor one: is it easy to draw a graph with LaTeX
> > formulas labeling edges?
> I haven't seen anyone do things like this outside of GraphViz, which I
> believe is an optional SPKG, due to licensing issues.

Okay, will dig more.

> > There could appear nested graphs hiding in vertices, how to depict
> > these?..
>
> This would involve making two separate graphics objects and figuring
> out how to add them together to get the right effect. I wouldn't be
> surprised if it involved a fair amount of source code hacking.

I've found graphics arithmetic (plot += element) exciting, for a
glance. If this could be exported to .tex, then text elements typeset
as formulas and then imported back in vector... somewhat like
rendering .tex to HTML with embedded images, why not? I was once
excited opening LaTeX-generated PDF in Scribus and being able to see
and tweak every curve of symbols.

> > A possible direction of our seminar students' work is to
> > investigate drawing/navigation/UI/animation capabilities regarding
> > automata.
>
> Sounds like fun!

It should be! Our early programming courses somewhat lack
__consistent__ modelling instruments (Turing machines, Markov normal
algorithms, grammars, finite automata). If we deploy a local
notebook... I've thought once about Maple-based effort in this
direction (maplet, they call it), it turned out too heavyweight, not
to mention proprietary.

Secondly, Python is known being good for teaching programming (not in
ours, unfortunately, though there is a bright exception), why not
teach mathematical programming as well?.. The gap between chalkboard
constructs and real practice could be narrowed, thanks to interactive
nature of both Python and Sage.

--Pavel.
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