Here's the problem. I have a finite set of vectors $F \subset \mathbb{Z}_{\geq 0}^d$.
I define $P$ to be the convex polytope $conv(F)$ i.e. the convex hull of $F$.
Given $u_1, u_2 \in F$, is the line segment $[u_1,u_2]$ an edge of $P$?
I'm looking for a program that will answer this efficiently i.e I want to be able to simply feed it with $(a)$ a file containing the vectors of $F$ e.g
0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0
0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0
0 0 0 0 0 0 1 1 0 2 0 0 0 0 0 0
0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0
and $(b)$ two special vectors in $F$ e.g.
$u_1 =$ 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0
$u_2 =$ 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0
and I want it to return $YES$ if $[u_1,u_2]$ is an edge of $P$ and $NO$ otherwise. The file that I feed the program may or may not contain interior points (all points in $F$ may not be vertices of $P$).