Opened 19 months ago
Last modified 3 months ago
#31800 new enhancement
CombinatorialPolyhedron indexed by nonminimal Hrepresentations
Reported by:  Matthias Köppe  Owned by:  

Priority:  major  Milestone:  sage9.8 
Component:  geometry  Keywords:  
Cc:  ghkliem, Yuan Zhou  Merged in:  
Authors:  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/mkoeppe/combinatorialpolyhedron_indexed_by_non_minimal_h_representations (Commits, GitHub, GitLab)  Commit:  2105731534f0b4de12410d0d8b6a009feb449ff9 
Dependencies:  Stopgaps: 
Description
Given a (not necessarily minimal) Hrepresentation, for example as a list, and a polyhedron, construct a CombinatorialPolyhedron
that uses the given Hrepresentation objects (or indices of the list) instead of the polyhedron's minimal Hrepresentation objects.
Change History (10)
comment:1 Changed 19 months ago by
comment:2 Changed 19 months ago by
Basically, you want almost something as face_as_combinatorial_polyhedron
from #30469.
(Slack matrix is basically the same as incidence matrix and should use the code from Polyhedron_base.incidence_matrix
to do the conversion.
Given an incidence matrix, you want to delete all rows and columns of allones (maybe, that is a problem with lines though and with cones). Then you want to remove all nonmaximal "facets" and all nonminimal "vertices". Finally we need to know how the new labels correspond to the old labels.
Did I get that right?
comment:4 Changed 19 months ago by
Branch:  → u/mkoeppe/combinatorialpolyhedron_indexed_by_non_minimal_h_representations 

comment:5 Changed 19 months ago by
Commit:  → 2105731534f0b4de12410d0d8b6a009feb449ff9 

Here's a draft of the interface that I would find useful
New commits:
2105731  Polyhedron_base.{incidence_matrix,slack_matrix,combinatorial_polyhedron}: Extend interface

comment:6 Changed 19 months ago by
What I get from this is the following:
Let F
be the meet of the given facets and G
be the join of the given vertices. Obtain the interval [F, G]
as combinatorial polyhedron (with specified order of Vrep and Hrep).
Is this what you had in mind?
comment:7 Changed 17 months ago by
Milestone:  sage9.4 → sage9.5 

comment:8 Changed 12 months ago by
Milestone:  sage9.5 → sage9.6 

comment:9 Changed 8 months ago by
Milestone:  sage9.6 → sage9.7 

comment:10 Changed 3 months ago by
Milestone:  sage9.7 → sage9.8 

I think actually I only need versions of
incidence_matrix
(and maybeslack_matrix
) that allow using some given lists of Vreps and Hreps instead of the minimal representations.