Trac #20110: Speed up Polyhedron_base.graph()

Currently, `Polyhedron_base.graph()` intersects with the base set of all
vertices in every of the ''n'' over 2 loop iterations in line 3321,
where ''n'' is the number of vertices. This is useless as far as I can
see, because the sets that are being intersected cannot possibly ever
contain something that is not a vertex.

Leaving out this additional intersection speeds up the process of
constructing the graph significantly. I tested it on a 4 GHz machine for
the polyhedron `polytopes.associahedron(['E', 7])`, and with my patch it
only took close to two minutes instead of 5:15. Other examples like
`polytopes.associahedron(['E', 8])` also suggest a ''significant''
speedup, although I don't have precise measurements from the same
machine.

I also tested that the resulting graph is actually the same for some
polyhedra.

URL: http://trac.sagemath.org/20110
Reported by: jplitza
Ticket author(s): Jan-Philipp Litza
Reviewer(s): Volker Braun

src/sage/geometry/polyhedron/base.py

@@ -3310,15 +3310,14 @@ def vertex_graph(self):
 
         d = self.dim()
         n = len(vertices)
-        X = set(range(n))
 
         pairs = []
         for i,j in combinations(range(n),2):
             common_ineq = vertex_ineq_incidence[i]&vertex_ineq_incidence[j]
             if not common_ineq: # or len(common_ineq) < d-2:
                 continue
 
-            if len(X.intersection(*[ineq_vertex_incidence[k] for k in common_ineq])) == 2:
+            if len(set.intersection(*[ineq_vertex_incidence[k] for k in common_ineq])) == 2:
                 pairs.append((i,j))
 
         from sage.graphs.graph import Graph