> I thought the union command made sense, but I think I understand why
> you don't like it.

as I understood it, p1.union(p2) currently returns the convex hull of the
vertices of p1 and p2. and _not_ the set union of p1 and p2. So I wonder
1) is this method really worth existing ? (it is 1 line length)
2) if it is, we should rename it to something less misleading

> I have been thinking about what the right sort of
> classes need to be created to handle more general polytopes - i.e. non-
> convex polytopes like some stellated ones, which can be thought of as
> the union of convex polytopes in the sense you are thinking of (I
> hope).  It seems to me that it would be good to have more structure
> than simply a list of polytopes, but I am not sure what that should
> be.

I have no idea on the proper way to this either. Maybe sage as a meta
class like "set" or something like that ?

> A polyhedron with just rays should be valid.

do you agree that p = Polyhedron(rays=[[0,1],[1,0]]) is invalid ?

> I know my code is quite
> buggy for unbounded polyhedra - all of my use cases are for Newton
> polytopes, so I have mostly tested things on bounded polytopes with
> exact coordinates.  I am more than happy to referee patches on that.

I need polyhedral convex cones to work, so I will test them.

> There is one patch I have that hasn't been merged -
> http://trac.sagemath.org/sage_trac/ticket/4676.  It adds some new
> methods (Gale transform, edge truncation, perspective projection) -
> but doesn't address what you are talking about so its pretty
> orthogonal to what you talking about.

ok

> Where is your patch?  Is it on trac somewhere?  - if so I can't find
> it.

I forgot to attach it to my email, sorry. I just requested a trac account,
I'll put it there for easier review, and assign to you ;).
Should I use mercurial for producing the patch ?

--
Regards
Sébastien

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