Polyhedron.to_linear_program should select solver by base_ring

[mkoeppe]

This is a follow-up on #20301.
#20296 provides a way to select a suitable solver by its base_ring.

Polyhedron.to_linear_program should do that.

Note, for exact polyhedra, this will change the behavior of to_linear_program from inexact computation to exact computation, which will be much slower (but note, speed is irrelevant for this method, because when the Polyhedron was set up, already the double description has been computed eagerly.)

To restore the old behavior, the user would need to pass an explicit base_ring=RDF or solver=... argument to to_linear_program.
(The patch adds many examples that illustrate this.)

CC: @dimpase @videlec @novoselt

Component: geometry

Author: Matthias Koeppe

Branch/Commit: 7b7aa5e

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20415

[mkoeppe]

Branch: u/mkoeppe/polyhedron_to_linear_program_should_select_solver_by_base_ring

[mkoeppe]

New commits:

20d6c5a	get_backend: Pass base_ring to PPLBackend, raise an error if not QQ
4b42d4a	get_solver: Take base_ring's fraction field
7b7aa5e	to_linear_program: Select solver according to base_ring, which can be overriden by keyword argument

[mkoeppe]

Commit: 7b7aa5e

[mkoeppe]

Description changed:

--- 
+++ 
@@ -3,5 +3,6 @@
 
 `Polyhedron.to_linear_program` should do that. 
 
-Note, for exact polyhedra, this will change the behavior of `to_linear_program` from inexact computation to exact computation, which will be much slower. To restore the old behavior, the user would need to pass an explicit `base_ring=RDF` argument to `to_linear_program`.
+Note, for exact polyhedra, this will change the behavior of `to_linear_program` from inexact computation to exact computation, which will be much slower. To restore the old behavior, the user would need to pass an explicit `base_ring=RDF` or `solver=...` argument to `to_linear_program`.
+(The patch adds many examples that illustrate this.)
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -3,6 +3,8 @@
 
 `Polyhedron.to_linear_program` should do that. 
 
-Note, for exact polyhedra, this will change the behavior of `to_linear_program` from inexact computation to exact computation, which will be much slower. To restore the old behavior, the user would need to pass an explicit `base_ring=RDF` or `solver=...` argument to `to_linear_program`.
+Note, for exact polyhedra, this will change the behavior of `to_linear_program` from inexact computation to exact computation, which will be much slower (but note, speed is irrelevant for this method, because when the `Polyhedron` was set up, already the double description has been computed eagerly.)
+
+To restore the old behavior, the user would need to pass an explicit `base_ring=RDF` or `solver=...` argument to `to_linear_program`.
 (The patch adds many examples that illustrate this.)
 

[dimpase]

Reviewer: Dima Pasechnik

[dimpase]

comment:4

looks good to me.

[vbraun]

Changed branch from u/mkoeppe/polyhedron_to_linear_program_should_select_solver_by_base_ring to 7b7aa5e