Fix equation handling of Polyhedron.to_linear_program() and thus integral_points_count(preprocess=True)

[mkoeppe]

As reported in https://groups.google.com/d/msg/sage-devel/TuF0CidR-JI/8-zpcu-MCgAJ, the preprocessing code in integral_points_count sometimes fails. This is ultimately because Polyhedron.to_linear_program does not handle equations correctly.

sage: P = Polyhedron(vertices=[[19]])
sage: P.to_linear_program().show()
Maximization:
  

Constraints:
  constraint_0: -19 <= x_0 <= -19
Variables:
  x_0 is a continuous variable (min=-oo, max=+oo)
sage: P.to_linear_program().polyhedron().vertices_list()
[[-19]]

CC: @simon-king-jena @videlec @jplab

Component: geometry

Author: Matthias Koeppe

Branch/Commit: 6ad4bf7

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/24154

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,4 +1,18 @@
 As reported in https://groups.google.com/d/msg/sage-devel/TuF0CidR-JI/8-zpcu-MCgAJ, the preprocessing code in `integral_points_count` sometimes fails. This is ultimately because `Polyhedron.to_linear_program` does not handle equations correctly.
+
+```
+sage: P = Polyhedron(vertices=[[19]])
+sage: P.to_linear_program().show()
+Maximization:
+  
+
+Constraints:
+  constraint_0: -19 <= x_0 <= -19
+Variables:
+  x_0 is a continuous variable (min=-oo, max=+oo)
+sage: P.to_linear_program().polyhedron().vertices_list()
+[[-19]]
+```
 
 
 

[mkoeppe]

Branch: u/mkoeppe/fix_equation_handling_polyhedron_to_linear_program

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

New commits:

6ad4bf7

24154: Fix equation handling of Polyhedron.to_linear_program()

[mkoeppe]

Commit: 6ad4bf7

[dimpase]

Reviewer: Dima Pasechnik

[dimpase]

comment:5

OK, makes sense.

[vbraun]

Changed branch from u/mkoeppe/fix_equation_handling_polyhedron_to_linear_program to 6ad4bf7