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Parent (set) of polyhedra with prescribed vertices or facets #31804

Open mkoeppe opened 3 years ago

mkoeppe commented 3 years ago

The parent Polyhedra(QQ, 3) is the set of polyhedra whose vertices/rays/lines are in QQ^3 and whose facets/equalities are in QQ^{3+1}.

We define parents corresponding to more general, finite or infinite, allowed sets of vertices/rays/lines, facets/equalities.

The category PolyhedralSets currently makes every parent an additive monoid (Minkowski sums). This will need to be changed -- the parent will be an additive monoid only if the sets of vertices/rays/lines, facets/equalities are.

Related: #29819, #30198

CC: @jplab @kliem

Component: geometry

Issue created by migration from https://trac.sagemath.org/ticket/31804

mkoeppe commented 3 years ago

Description changed:

--- 
+++ 
@@ -4,5 +4,6 @@

 The category `PolyhedralSets` currently makes every parent an additive monoid (Minkowski sums). This will need to be changed -- the parent will be an additive monoid only if the sets of vertices/rays/lines, facets/equalities are.

+Related: #29819, #30198
mkoeppe commented 3 years ago

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-The parent `Polyhedra(QQ, 3)` is the set of polyhedra whose vertices/rays/lines are in QQ^3 and whose facets/equalities are in `QQ^{3+1}`.
+The parent `Polyhedra(QQ, 3)` is the set of polyhedra whose vertices/rays/lines are in `QQ^3` and whose facets/equalities are in `QQ^{3+1}`.

 We define parents corresponding to more general, finite or infinite, allowed sets of vertices/rays/lines, facets/equalities.