Opened 20 months ago

Closed 17 months 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 20 months 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 19 months 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 19 months 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 17 months 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 17 months 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.

Version 0, edited 17 months ago by jipilab (next)

### comment:6 Changed 17 months 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 17 months ago by gh-kliem

• Status changed from needs_work to positive_review

### comment:8 Changed 17 months 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 17 months ago by mkoeppe

• Milestone changed from sage-9.2 to sage-9.1
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