If a given inequality is a facet of the feasible region can be decided by a linear program. This is dual to deciding whether one point from a set of points is a vertex of the convex hull. That latter problem is equivalent to deciding whether or not there is a hyperplane which separates that one poin...

There is one facet per point plus one extra facet for the FAR_FACE (in this case the FAR_FACE is a facet). But you do not have to worry about lifting. polytope > my $points=new Matrix<Rational>([[1,-1,-1],[1,1,-1],[1,-1,1],[1,1,1],[1,0,0]]); $vd=new VoronoiDiagram(SITES=>$points); prefer_now "b...

Ewgenij's recommendation polytope > $Verbose::rules=3; polytope > my $points=new Matrix<Rational>([[1,-1,-1],[1,1,-1],[1,-1,1],[1,1,1],[1,0,0]]); $p=new Polytope<Rational>(POINTS=>$points); prefer_now "beneath_beyond";$p->DUAL_GRAPH->ADJACENCY; save($p,"OUTPUT.xml"); results in r...

Unfortunately, the current setup does not allow for much logging information for the convex hull computations. I clearly understand that this is desirable though. We started to look into some possibilities. Stay tuned. We do not allow partial output. This has to do with the overall design of polymak...

The data type of the HOMOLOGY property is a bit special; actually it is Array<HomologyGroup<Integer>>. This is how you can address an individual group: topaz > $rp2=projective_plane(); topaz > print $rp2->HOMOLOGY->[1]; {(2 1)} 0 Each homology group more or less works like an array (of a pair and a ...

when I visualise a fan via jreality, the output has way more cones than I expect. It seems that cones with more than three rays are subdivided, so that each cone has only three rays. Is that a feature or a bug? With the jReality window active press "alt-shift-left", which opens an extra p...

It seems you are using a version of lrslib other than the one shipped with polymake. Your patch is not necessary for polymake's lrslib. The polymake version fixes a few glitches of the original.

Please give your complete code example. I suspect that LINEALITY_SPACE is missing in your input. RAYS only do not work.

What about the following? topaz > $sc=new SimplicialComplex(INPUT_FACES=>[[5,6,8],[6,8]]); topaz > print rows_labeled($sc->FACETS,undef,$sc->VERTEX_INDICES); 0:5 6 8 The second parameter "undef" can be replaced by something meaningful if you also want to give names to the facets.

Must I always use Polytope<Rational>? Well, if you want to get exact results: yes. However, I should also point out that there are other exact data types, such as QuadraticExtension<Rational>. The data type Polytope<Float> must be used with care since the combinatorics of such polytopes might not b...