Your question mixes two things, existence of a nontrivial LINEALITY_SPACE implies that the polyhedron is not pointed, while existence of a nontrivial LINEAR_SPAN (or AFFINE_HULL for polytopes) implies that the polyhedron is not full-dimensional in its ambient space. Probably you think of the latter. Anyway, here are methods for both:
- to project onto a full dimensional polyhedron there is a user function in polymake that does this for you, see
for the correct call of this function and some explanations about what it does.
This function finds a coordinate projection onto a full dimensional polytope. If there are FACETS or INEQUALITIES given in the polytope, then it does Fourier-Motzkin elimination, unless you specify the "nofm" option. This is usually a good idea if you also know the vertices of your polytope, as Fourier-Motzkin elimination can be expensive (I think that is what you mean with "Gaussian elimination").
- For the other problem you could just define a new polytope with the VERTICES of the first, i.e.
Code: Select all
$q=new Polytope<Rational>(VERTICES=>$p->VERTICES);
I hope this answers your question.