I'm trying to compute the minimal faces of a polyhedron P, given through inequalities. The problem seems to be, that the polyhedron is not necessarily pointed. E.g. I tried computing the minimal faces as the Minkowski-sum of a bounded vertex and the lineality space. While doing so I discovered two problems:
1) Defining a not pointed polyhedron via POINTS leads to a polyhedron, which has no lineality space, i.e. is pointed (in this example the polyhedron is a cone, of which I thought polymake 2.10 can handle now):
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polytope > $P = new Polytope<Rational>(POINTS=>[[1,0,0],[0,1,1],[0,-1,-1]]);
polytope > print $P->LINEALITY_DIM;
0
2) The Minkowski-sum of two polyhedra is not, what I would expect it to be. E.g. for every polyhedron P I would expect: P + {0} = P:
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polytope > $P = new Polytope<Rational>(INEQUALITIES=>[[0,1,0,0]]);
polytope > $Z = new Polytope<Rational>(POINTS=>[[1,0,0,0]]);
polytope > $M = minkowski_sum($P,$Z);
polytope > print $M->DIM;
1
I am mostly interested in getting the minimal faces, so any other way I might have overlooked would be as welcome as help regarding the two problems described.