Let me try again. This is the current behaviour: sage: P = Polyhedron(vertices=[[-1,0],[1,0]],lines=[[0,1]]); P A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 2 vertices and 1 line sage: P.vertex_graph() Graph on 2 vertices sage: P.faces(0) ()
Let P be a polyhedron defined by vertices/rays/lines. The vertex graph of P returns basically the vertex graph for Q, where Q is defined by the same vertices and rays, but not lines. So sage: P = Polyhedron(vertices=my_vertices, rays=my_rays, lines=my_lines) sage: Q = Polyhedron(vertices=my_vertices, rays=my_rays) have vertex graphs that are canonically isomorphic. I don't think this is the way it should be and the vertex graph in the first case should be empty. If no one disagrees I will apply this change in #28626. <https://trac.sagemath.org/ticket/28626> However, the current behaviour is somewhat fixed by a doctest. As I understand it, the mentioned doctest tries to make a point about sage: P.combinatorial_automorphism_group(vertex_graph_only=True) <https://trac.sagemath.org/ticket/28626> In this case it is stated that the automorphism group can only interchange vertices with vertices, rays with rays and lines with lines. Strictly speaking, this is correct. But an automorphism group obtained from this will never interchange rays with rays or lines with lines. Even worse, it will completely ignore the rays and lines, so that sage: P = Polyhedron(vertices=[[0,0,0],[0,1,1],[1,0,1],[-1,-1,1]],rays=[[0,0 ,1]]); P A 3-dimensional polyhedron in QQ^3 defined as the convex hull of 4 vertices and 1 ray sage: len(P.combinatorial_automorphism_group(vertex_graph_only=True)) 24 This is why I consider the doctest strange. To me it does not make sense to use the vertex graph to obtain the automorphism group. Btw (and really not the point of this post), I'm not sure that the automorphism group of the vertex-facet graph is what one should consider for the automorphism group of an unbounded polyhedron. At least in dimension higher than 4 this might behave differently than at least I would define it. I would instead consider the vertex-facet-graph with an extra marked vertex at infinity. Am Samstag, 19. Oktober 2019 11:52:24 UTC+2 schrieb jplab: > > Hi Jonathan, > > Could you be more precise with what you mean with "projection"? > > What is the status quo? (Please provide a minimal reproducible working > example that shows the contrast along with the proposed wished change that > you have in mind, otherwise we are left to guess what you mean and that is > leaving the door open to a lot of misunderstanding) > > What is the proposed changed? > > What is the assumption in the mentioned doctest? > > For computational aid, when no vertices exists (i.e. there is a lineality > space) the current implementation creates an appropriate vertex. I guess we > have to deal with this eventhough the object does not have a 0-dimensional > face in reality. This is to have consistency between H- and > V-representations. In order to have a consistent V-representation, you need > an anchor point, otherwise just having rays and lines does not determine > uniquely the object. > > That said, if you are interested in making a vertex-graph for unbounded > polyhedra, then, edges should have two vertices. > > One way is to ask to keep only bounded edges in the definition, and the > default behavior gives the vertex graph on bounded edges. If one wants the > full graph with a point at infinity that compactifies the full vertex > graph, then one could do so by adding an optional parameter > "unbounded=False/True". Where the default would be False and return only > compact edges and True would return one more vertex "the vertex at > infinity". > > To me this seems to be the most reasonable behavior. I don't know if this > answer your question. > > Le vendredi 18 octobre 2019 12:09:53 UTC+2, Jonathan Kliem a écrit : >> >> In #28626 <https://trac.sagemath.org/ticket/28626> I want to use >> `CombinatorialPolyhedron` to obtain the vertex graph of polyhedra. >> >> However, I seem to have a different opinion of a vertex graph than is >> currently implemented in sage. >> >> Should the vertex graph of an unpointed polyhedron return the vertex >> graph of the projection or should it be empty? >> >> As of now the method `vertices` returns the defining vertices, which are >> the proper vertices except for unpointed polyhedra. >> >> I don't think this ambiguous meaning of vertex should continue for the >> vertex graph. >> >> However the current behavior is at the moment assumed in a strange >> doctest of `combinatorial_automorphism_group`. >> (E.g. the order of the combinatorial automorphism group does not change >> when you add lines.) >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/91149799-da9b-49a4-b9c0-bd9629a386e3%40googlegroups.com.
