Expose PPL's Not-Necessarily-Closed Polyhedra and Normaliz' Polyhedra with Open Facets using Sage Polyhedra

[mkoeppe]

PPL has NNC_Polyhedron.
Should expose using Sage's Polyhedra classes.

In the context of #20877, NNC polyhedra could play the same role as half-open intervals do in the context of the new piecewise functions.

Normaliz also has the feature of "open facets".

Depends on #32089
Depends on #32159

CC: @kcrisman @kliem @jplab @yuan-zhou

Component: geometry

Issue created by migration from https://trac.sagemath.org/ticket/20879

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,2 +1,4 @@
 PPL has NNC_Polyhedron.
 Should expose using Sage's Polyhedra classes.
+
+In the context of #20877, NNC polyhedra could play the same role as half-open intervals do in the context of the new piecewise functions.

[mkoeppe]

comment:3

An alternative is #31743

[mkoeppe]

Description changed:

--- 
+++ 
@@ -2,3 +2,5 @@
 Should expose using Sage's Polyhedra classes.
 
 In the context of #20877, NNC polyhedra could play the same role as half-open intervals do in the context of the new piecewise functions.
+
+Normaliz also has the feature of "open facets". 

[mkoeppe]

Dependencies: #32089

[mkoeppe]

comment:6

A new Sage class somewhere between ConvexSet_base + ConditionSet and Polyhedron that is able to store convex sets given by finitely many, strict or non-strict linear constraints (not necessarily minimal) would be valuable. In contrast to Polyhedron, it would not insist on eagerly computing a minimal description by facet defining inequalities.

[mkoeppe]

Changed dependencies from #32089 to #32089, #32159