#20110: Speed up Polyhedron_base.graph()
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   Reporter:  jplitza                |            Owner:
       Type:  enhancement            |           Status:  new
   Priority:  trivial                |        Milestone:  sage-7.1
  Component:  geometry               |         Keywords:
  Merged in:                         |          Authors:
  Reviewers:                         |  Report Upstream:  N/A
Work issues:                         |           Branch:
     Commit:                         |  u/jplitza/polyhedron_graph
  0a2602fcba8d18b204dbcd23f8a106f9bc63d55d|     Dependencies:
   Stopgaps:                         |
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 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.

--
Ticket URL: <http://trac.sagemath.org/ticket/20110>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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