[PPL-devel] Proof

[P M Hill]

Hi Angela,

-- 

On Thu, 7 Jun 2001, Angela Stazzone wrote:

> Hi Pat,
> can you help me to find a formal proof (or an example it is not true) to
> the following assertion?
> 
> EXTREMAL RAYS ARE STABLE WHEN COMBINED
>  WITH ANY VECTOR OF THE LINEALITY SPACE.
> 
> I found it in H. Leverge - A note on Chernikova's Algorithm -
> Publication Interne 635 - February 1992 - page 9.
> 
> I guess "stable" means that the combination between an extremal ray with
> an element of the lin. space is an extremal ray.
> 
> I think it is intuitive that it's true, but I can't find a formal proof!

It can't be true. Have a look at the definition of extreme ray.
It is extreme if it is NOT the positive combination of two other rays.
Note that a line is just two rays in opposite directions.
I would be interested to know what Leverge means by "stable".
I've been trying to guess, but without any success.

ciao,
  Pat