Opened 3 years ago

Closed 2 years ago

# Add simplicity and simpliciality to polyhedra

Reported by: Owned by: gh-kliem major sage-9.1 geometry simplicity, simpliciality, polytopes jipilab, gh-LaisRast Jonathan Kliem Jean-Philippe Labbé N/A 573dbfc 573dbfc89f7b67015c6779e986159dcddf894c87

### Description

In #27086 we have implemented simplicity and simpliciality for combinatorial polyhedra. We expose this methods in Polyhedron_base.

The methods return the largest k such that the polytope is k-simple/simplicial. In case of unbounded polyhedra a NotImplementedError is raised.

A polytope is k-simplicial if every k-face is a simplex. It is k-simple if its dual/polar is k-simplicial.

### comment:1 Changed 3 years ago by gh-kliem

• Branch set to public/29186
• Commit set to 34068512da0d10e02d27c32812d868517aba3a35
• Status changed from new to needs_review

New commits:

 ​3406851 added simplicity and simpliciality to polyhedra

### comment:2 Changed 3 years ago by jipilab

• Reviewers set to Jean-Philippe Labbé
• Status changed from needs_review to needs_work

-        Return the largest k such that the polytope is k-simple.
-
-        Return the dimension in case of a simplex.
-
-        A polytope P is k-simple, if every (d-1-k)-face
-        is contained in exactly k+1 facets of P for 1 <= k <= d-1.
-
-        Equivalently it is k-simple if the polar/dual polytope is k-simplicial.
+        Return the largest integer k such that the polytope is k-simple.
+
+        A polytope P is k-simple, if every (d-1-k)-face
+        is contained in exactly k+1 facets of P for 1 <= k <= d-1.
+        Equivalently it is k-simple if the polar/dual polytope is k-simplicial.
+        If self is a simplex, it returns its dimension.


similarly:

-        Return the largest k such that the polytope is k-simplicial.
-
-        Return the dimension in case of a simplex.
-
-        A polytope is k-simplicial, if every k-face is a simplex.
+        Return the largest interger k such that the polytope is k-simplicial.
+
+        A polytope is k-simplicial, if every k-face is a simplex.
+        If self is a simplex, returns its dimension.


Once this is fixed and the bots gives a green light, you can set this on positive review on my behalf.

### comment:3 Changed 3 years ago by gh-kliem

• Branch changed from public/29186 to public/29186-reb
• Commit changed from 34068512da0d10e02d27c32812d868517aba3a35 to 297c6869b2a25f1508c5923d71ba6a2cbbf608f7
• Status changed from needs_work to needs_review

New commits:

 ​c9ff832 added simplicity and simpliciality to polyhedra ​297c686 improved documentation

### comment:4 Changed 2 years ago by mkoeppe

• Milestone changed from sage-9.1 to sage-9.2

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

### comment:5 Changed 2 years ago by jipilab

• Status changed from needs_review to needs_work

Small things:

+        is contained in exactly k+1 facets of P for 1 <= k <= d-1.


You can use \leq there.

Otherwise, looks good, once this is done you can put this on positive review on my behalf.

Last edited 2 years ago by jipilab (previous) (diff)

### comment:6 Changed 2 years ago by gh-kliem

• Branch changed from public/29186-reb to public/29186-reb2
• Commit changed from 297c6869b2a25f1508c5923d71ba6a2cbbf608f7 to 573dbfc89f7b67015c6779e986159dcddf894c87

New commits:

 ​d6e1bf6 added simplicity and simpliciality to polyhedra ​f4689d3 improved documentation ​573dbfc latex \lex

### comment:7 Changed 2 years ago by gh-kliem

• Status changed from needs_work to positive_review

### comment:8 Changed 2 years ago by vbraun

• Branch changed from public/29186-reb2 to 573dbfc89f7b67015c6779e986159dcddf894c87
• Resolution set to fixed
• Status changed from positive_review to closed

### comment:9 Changed 2 years ago by mkoeppe

• Milestone changed from sage-9.2 to sage-9.1
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