Transition of combinatorial computations of Polyhedron to Combinatorial Type

[gh-kliem]

In #26887 we created a new class, that handles the calculations depending only on the combinatorial type more quickly.

The goal of this ticket is to make use of this class through Polyhedron_base.

Add methods:

• #28621: Add method combinatorial_polyhedron
• #28646: face_generator
• facet graph

Replace the existing computation:

• #28625: f_vector,
• #28646 faces,
• #28626: graph/vertex_graph,
• vertex_adjacency_matrix
• vertex_digraph
• facet_adjacency_matrix,
• face_lattice.

Migrate code to CombinatorialPolyhedron?:

• is_prism

[embray]

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

[gh-kliem]

Last 10 new commits:

​9b69f50	added documentation and examples to each module
​4e8fd8c	correct hyperlinks
​72ac3b0	documentation fix
​611099f	Do not iterate twice for CombinatorialPolyhedron.facets()
​d38e130	added combinatorial face
​ca60665	improved docstring in list_of_all_faces
​abe00b6	fixed small issues
​8765313	A number of small edits.
​d419d72	Merge branch 'public/26887' of git://trac.sagemath.org/sage into public/27063
​25407f8	faces, f_vector, vertex_graph, vertex_digraph, neighborliness now use CombinatorialPolyhedron

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​c4ccf86

face lattice by CombinatorialPolyhedron

[embray]

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[jipilab]

Concerning the .faces() method. Currently, .iter_face only deals with proper faces. ... is that the intended behavior?

From an old list (so maybe some of them are renamed), I also saw the following methods make use of .face_lattice, and probably would benefit from the combinatorial polyhedra:

• adjacency_matrix
• facet_adjacency_matrix
• facial_adjacencies
• is_simple
• vertex_adjacency_matrix

It would be nice to make a thorough checking of which methods make use of "old style face lattice" things. It would be bad to not make the whole Polyhedron objects not benefit from this new class...

[gh-kliem]

Replying to jipilab:

Concerning the .faces() method. Currently, .iter_face only deals with proper faces. ... is that the intended behavior?

This is simply, because my method of intersecting faces and avoiding double counting has no guarantee to hit the empty face in the unbounded case. So one has to manually add it anyway. I would prefer leaving it like this in FaceIterator. But I can see that one wants to add those two extra faces (or only one for the empty polyhedron) when wrapping the class.

From an old list (so maybe some of them are renamed), I also saw the following methods make use of .face_lattice, and probably would benefit from the combinatorial polyhedra:

• adjacency_matrix
• facet_adjacency_matrix
• facial_adjacencies

what does it do, I can't find it

• is_simple

not anymore

• vertex_adjacency_matrix

It would be nice to make a thorough checking of which methods make use of "old style face lattice" things. It would be bad to not make the whole Polyhedron objects not benefit from this new class...

Yes, that's my plan. If I actually go through with it and make CombinatorialPolyhedron a parent of Polyhedron_base, as was proposed in #10777, then CombinatorialPolyhedron should do all calculations that depend only on the incidence matrix.

[jipilab]

Replying to gh-kliem:

Replying to jipilab:

Concerning the .faces() method. Currently, .iter_face only deals with proper faces. ... is that the intended behavior?

This is simply, because my method of intersecting faces and avoiding double counting has no guarantee to hit the empty face in the unbounded case. So one has to manually add it anyway. I would prefer leaving it like this in FaceIterator. But I can see that one wants to add those two extra faces (or only one for the empty polyhedron) when wrapping the class.

Sounds good.

From an old list (so maybe some of them are renamed), I also saw the following methods make use of .face_lattice, and probably would benefit from the combinatorial polyhedra:

• adjacency_matrix
• facet_adjacency_matrix
• facial_adjacencies

what does it do, I can't find it

Then, fine.

• is_simple

not anymore

Good

• vertex_adjacency_matrix

It would be nice to make a thorough checking of which methods make use of "old style face lattice" things. It would be bad to not make the whole Polyhedron objects not benefit from this new class...

Yes, that's my plan. If I actually go through with it and make CombinatorialPolyhedron a parent of Polyhedron_base, as was proposed in #10777, then CombinatorialPolyhedron should do all calculations that depend only on the incidence matrix.

Great! Then, one should also take care to not let the Polyhedron_base overwrite them, but duh... I'm sure you know what your doing... :)

[gh-kliem]

Replying to jipilab:

Great! Then, one should also take care to not let the Polyhedron_base overwrite them, but duh... I'm sure you know what your doing... :)

Well, you can always access overwritten methods using super.

Does it make sense to leave a method as e.g. simple in Polyhedron_base just to have a more specific docstring? Otherwise we would eventually end up with docstrings gathering all examples from Polyhedron, LatticePolytope and Cone.

[jipilab]

Replying to gh-kliem:

Replying to jipilab:

Great! Then, one should also take care to not let the Polyhedron_base overwrite them, but duh... I'm sure you know what your doing... :)

Well, you can always access overwritten methods using super.

Does it make sense to leave a method as e.g. simple in Polyhedron_base just to have a more specific docstring? Otherwise we would eventually end up with docstrings gathering all examples from Polyhedron, LatticePolytope and Cone.

I am not 100% sure about this. I believe that the method would stay in Polyhedron_base (think about the documentation online too) because one expects to see it there (and one does not directly think about the CombinatorialPolyhedron class directly, maybe) and the method would be only a couple of lines long and calling the combinatorial algorithm using super with the appropriate parameters.

On the long run, CombinatorialPolyhedron will contain the bulk of codes that strictly makes use of combinatorial data and Polyhedron_base things that use the geometry.

Further, concerning the present ticket, I believe it would make sense to make it a preparation ticket. Then each method would have 1 ticket. This way the changes will be more manageable.

Another open question: currently how is the relation between a Polyhedron object and a CombinatorialPolyhedron object? I guess that as of now, since the double description is computed by default, it is worth maybe creating the combinatorial counter part as an attribute and make it accessible via a method say named .combinatorial_polyhedron. This might make it easier to then transfer the computations to the combinatorial type.

When I create a combinatorial polyhedron from a polyhedron, it seems to keep the polyhedron object. Ideally, it would be nice to be able to go back and forth between them like it is for LP and Polyhedron (okay, it is not fully bakc and forth but still).

... and it would be nice if the methods of CombinatorialPolyhedron have exactly the same names for the same things H_representation vs Hrepr.

[gh-kliem]

Ok, this is a bunch of things. I realized that at some point it makes sense to create some sort of meta ticket for CombinatorialPolyhedron, also I realize that this ticket is more an agenda than anything else.

First of all, we should figure out, whether Polyhedron shall inherit from CombinatorialPolyhedron as a base class or whether its better to have it as a (lazy) method available.

Having it as a base class was proposed in #10777.

Maybe I should start a discussion on sage-devel to see what (interested) people think.

[gh-kliem]

I'm going to put this on needs review, so that people looking at #22420 will notice.

This way I can avoid adding each of the tickets to #22420.

If there is a better way of doing it, please tell me.

[jipilab]

Replying to gh-kliem:

I'm going to put this on needs review, so that people looking at #22420 will notice.

This way I can avoid adding each of the tickets to #22420.

If there is a better way of doing it, please tell me.

Putting it at needs review is not the appropriate status. In #22420, change the title of the #27063 ticket to "TASK: XXX", where XXX is the current title. Then, what is written will be sufficient to understand what is going on in this ticket. No need to add every single ticket from here, to #22420.

[jipilab]

Finally, it might make sense to move code to CombinatorialPolyhedron. E.g. is_prism can be checked there and should only be checked there to avoid code duplication.

Yes, I agree, I adapted the description of the ticket.