Make the face lattice of a polyhedron a lattice

[jplab]

Currently, the output object of the method face_lattice is not a lattice but a finite poset. This is also a good opportunity to revamp the method Hasse_diagram_from_incidences which is ill-named.

CC: @videlec @mo271 @mkoeppe @fchapoton @jm58660

Component: geometry

Keywords: days93, poset, polytope

Author: Frédéric Chapoton

Branch/Commit: 3ff3b60

Reviewer: Jori Mäntysalo

Issue created by migration from https://trac.sagemath.org/ticket/24846

[novoselt]

comment:1

Is it ill-named or ill-implemented, if it is in need of a revamp?-)

[jplab]

comment:2

I'd say it is not an exclusive "or" in this case...!

The Hasse diagram is an oriented acyclic graph, whereas what is returned is a poset, not the Hasse diagram of that poset... So this is misleading. And I do not see why we could not readily return a LatticePoset object if it is already. (Maybe there are some reasons not to do this?)

This function is very handy sometimes and could be used for (abstract) combinatorial polytopes.

[novoselt]

comment:3

I'm not aware of any reasons to avoid LatticePoset. The current output is either inherited from the old implementation or it was the best I found when rewriting it. One thing I do remember however - some tricks were necessary to construct the poset object fast, naive call to the constructor was taking several times more time than computing that acyclic graph itself.

[jplab]

comment:4

Replying to @novoselt:

I'm not aware of any reasons to avoid LatticePoset. The current output is either inherited from the old implementation or it was the best I found when rewriting it. One thing I do remember however - some tricks were necessary to construct the poset object fast, naive call to the constructor was taking several times more time than computing that acyclic graph itself.

Ah! Ok, good to know! It will be worth benchmarking the difference.

[fchapoton]

Branch: u/chapoton/24846

[fchapoton]

Commit: 4face89

[fchapoton]

New commits:

4face89

make so that face lattice is a lattice

[novoselt]

comment:7

So since I mentioned it before - was there any benchmarking/profiling looking into the speed of creating this lattice? It used to matter a lot to me when I was working with thousands of (quite small) polytopes.