Opened 9 months ago
Last modified 6 weeks ago
#31800 new enhancement
CombinatorialPolyhedron indexed by nonminimal Hrepresentations
Reported by:  mkoeppe  Owned by:  

Priority:  major  Milestone:  sage9.6 
Component:  geometry  Keywords:  
Cc:  ghkliem, yzh  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 (8)
comment:1 Changed 8 months ago by
comment:2 Changed 8 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:3 Changed 8 months ago by
Yes, this sounds about right
comment:4 Changed 8 months ago by
 Branch set to u/mkoeppe/combinatorialpolyhedron_indexed_by_non_minimal_h_representations
comment:5 Changed 8 months ago by
 Commit set to 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 8 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 6 months ago by
 Milestone changed from sage9.4 to sage9.5
comment:8 Changed 6 weeks ago by
 Milestone changed from sage9.5 to sage9.6
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.