Add .change_ring() method for polyhedra

[mforets]

Polyhedra can be defined in different rings, and this method allows to transform between rings (compare to the similar feature for matrices).

TODO:

• Once done, add it to tutorial

CC: @mkoeppe @jplab

Component: geometry

Keywords: days84, polytope

Author: Laith Rastanawi

Branch/Commit: c9b92db

Reviewer: Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/22574

[jplab]

comment:1

There is currently:

sage: P = Polyhedron(vertices=[(1,0), (0,1)], rays=[(1,1)], base_ring=ZZ);  P
A 2-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices and 1 ray
sage: P_QQ = P.base_extend(QQ); P_QQ
A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 2 vertices and 1 ray

Could there be a boolean parameter such as inplace (similar as in graphs and simplicial complexes...) to determine if one should create a new object or just change the base ring?

I am wondering how much changing the base ring changes the internals of the polyhedron object. Would many things break? We can try and see...

[mkoeppe]

comment:2

I think there is no value in trying to implement inplace -- the various base rings are handled by different classes after all. Moreover, right now polyhedra are immutable - and it would be strange to be able to mutate the base ring but nothing else.

[jplab]

comment:3

Replying to @mkoeppe:

I think there is no value in trying to implement inplace -- the various base rings are handled by different classes after all. Moreover, right now polyhedra are immutable - and it would be strange to be able to mutate the base ring but nothing else.

Agreed.

Further, I don't really like the fact that hidden in base_extend is the possibility to change the backend, which as a matter of fact doesn't work. This is not user-friendly to say the least. I would therefore also deprecate the keyword completely and point to a .change_backend() method (see #22575). I guess that such a method will take care to handle the modifications of base ring if need be...

[jplab]

Description changed:

--- 
+++ 
@@ -1 +1,4 @@
 Polyhedra can be defined in different rings, and this method allows to transform between rings (compare to the similar feature for matrices).
+
+TODO:
+- Once done, add it to tutorial

[LaisRast]

Branch: u/gh-LaisRast/change_ring

[LaisRast]

New commits:

5f61767

add change_ring to base.py and parent.py

[LaisRast]

Commit: 5f61767

[sagetrac-git]

Changed commit from 5f61767 to 6cdd9d5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6cdd9d5

add documentation

[jplab]

comment:8

Hi,

Here are a couple of things I saw:

• Adapt the convention for the input, see for example vertex_facet_graph:

+        - ``backend`` -- the new backend, see
+            :func:`~sage.geometry.polyhedron.constructor.Polyhedron`.
+            If ``None`` (the default), use the same defaulting behavior
+            as described there; it is not attempted to keep the same
+            backend.

• It would be good to have more examples with all the potential pairings.

• Further, it would be nice to handle the potential error in the function when coercing from QQ to ZZ and return a message like: 'Can not change the ring to ZZ: a coordinate is rational'. And these examples should be added after the examples that do work.