Affine way of thinking causes confusion with trivial hyperplane

[lkastner]

In polymake everything is homogeneous and polytopes are treated internally as cones most of the time where the actual polytope sits at height one. I.e. we have the coordinates [height, x_1, x_2, ...] in polymake. Every polytope comes with the hyperplane height>=0. For unbounded polyhedra, this hyperplane is also a facet, which we need to compute rays and lineality correctly. Now there are the following tasks:

• When a polyhedron is created from inequalities in Oscar, even if they are non_redundant from the affine point of view, it can be necessary to add this hyperplane for the polymake computation. This depends on whether the result would be bounded. However, we might not want to check boundedness upon creation, but still if the user gives us a non_redundant presentation this should not just be piped into INEQUALITIES.
• When the user asks for facets, should the trivial facet appear?

[lkastner]

@alexej-jordan Are you aware of this issue? Do you have an idea?

[lkastner]

This issue is not trivial at all and my initial description was wrong. Even unbounded polytopes do not need to have the trivial hyperplane as a facet, namely if the intersection with the trivial hyperplane has a lower dimension than the facet dimension of the polyhedron.

Therefore the consensus is now: Remove the non_redundant option for constructing a Polyhedron. Users that want to give non-redundant data have to do so by going via Polymake.jl, which is acceptable, since the projective viewpoint of polymake was explicitly chosen for resolving this mess (and others).