Fix Polyhedron.base_extend so it does not ignore the backend parameter

[mforets]

Polyhedra can be instantiated with different backends (CDD, PPL, normaliz, ...), and the base_extend method is supposed to allow to transform between backends, but the parameter is simply ignored (in (Polyhedra_base.base_extend).

Possible follow-up: Also a new method change_backend could be implemented as an alias. (Once done, add it to tutorial, too.)

[jipilab]

base_extend should do the job. But actually... the optional parameter to change the backend is simply not used at all!?!?!?!

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_cdd = P.base_extend(base_ring=ZZ,backend='cdd')
sage: type(P_cdd)
<class 'sage.geometry.polyhedron.backend_ppl.Polyhedra_ZZ_ppl_with_category.element_class'>

This is because in the parent class, the method .base_extend() of parent does not even use the optional parameter backend...

sage: par = P.parent()
sage: par.base_extend??     # this is worth looking at...

I guess one could simply correct that...

Now the question is whether there is a smart way to go from one to another?

[mkoeppe]

See also #22701.

[mforets]

Replying to jipilab:

... This is because in the parent class, the method .base_extend() of parent does not even use the optional parameter backend...

sage: par = P.parent()
sage: par.base_extend??     # this is worth looking at...

good finding, maybe this was a feature that didn't get in at the time.

also, i didn't find a command to get the backend as a string, like P.backend(), or P.get_backend(). it seems that there is no object (list) of available_backends either.

I guess one could simply correct that...

Now the question is whether there is a smart way to go from one to another?

i suggest to just start with the naive way and see how it behaves.

[mkoeppe]

New commits:

​260739d

{Polyhedron_base, Polyhedron_base}.base_extend: Handle backend.

[tscrim]

So my only quip is that this defaults to the automatic backend choice when the backend is not specified. I would expect that the backend be the same backend as what I am currently working with:

sage: P = Polyhedron(vertices=[(1,0), (0,1)], rays=[(1,1)], base_ring=QQ)
sage: P.backend()
'ppl'
sage: P = Polyhedron(vertices=[(1,0), (0,1)], rays=[(1,1)], base_ring=ZZ, backend='normaliz')
sage: P.backend()
'normaliz'
sage: P.base_extend(QQ).backend()
'ppl'

So if you think this is the behavior that it should have, then you should put a .. WARNING:: explaining that the backend is given by the default if not specified.

[mkoeppe]

Replying to tscrim:

So my only quip is that this defaults to the automatic backend choice when the backend is not specified. I would expect that the backend be the same backend as what I am currently working with:

One might expect that, but the backend may simply not be suitable. Consider base_extend of a PPL polytope to AA - only the 'field' backend is suitable.

I'll add some documentation.

[git]

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

​9f61dac

Polyhedron.base_extend docstring: Explain default value of backend

[tscrim]

Thanks. LGTM.