Polyhedron._acted_upon_ should handle left multiplication by matrices, linear transformations

[mkoeppe]

sage: b3 = polytopes.Birkhoff_polytope(3)
sage: b3.ambient_dim()
9
sage: proj_mat=matrix([[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0]])
b3_proj = proj_mat * b3
Traceback (most recent call last)
.....
.... sage/geometry/polyhedron/base.pyc in _acted_upon_(self, actor, self_on_left)
   3687             return self.translation(actor)
   3688         else:
-> 3689             return self.dilation(actor)
   3690 
   3691     def __neg__(self):
.....
ValueError: V-representation data requires a list of length ambient_dim

Depends on #28770

CC: @jplab @jiawei-wang-ucd

Component: geometry

Keywords: polytopes

Author: Jean-Philippe Labbé, Jonathan Kliem

Branch/Commit: a1072ee

Reviewer: Jonathan Kliem, Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/28724

[mkoeppe]

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 ```
 sage: b3 = polytopes.Birkhoff_polytope(3)
 sage: b3.ambient_dim()
-....:             9
+9
 sage: proj_mat=matrix([[0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0]])
 b3_proj = proj_mat * b3
 Traceback (most recent call last)

[jplab]

comment:2

Agreed, that would be nice to add this in the coercion.

[jplab]

comment:3

Are you on it? I could come up with something.

[jplab]

Author: Jean-Philippe Labbé

[jplab]

comment:4

Here's a first version.

I wanted to have a linear_transformation method for a while... That was a good timing to add it.

---

New commits:

755d5c4

First version of linear transformation

[jplab]

Commit: 755d5c4

[jplab]

Branch: public/28724

[tscrim]

comment:5

What happens when the linear transformation moves the polyhedron outside of the fields the backend can handle? Can you add such a doctest?

[kliem]

comment:6

Can you just initialize the new parent like this?

new_parent = par.base_extend(linear_transf.base_ring(), ambient_dim=new_dim)

This should automatically keep the backend if possible, but change it, if not possible.

[kliem]

comment:7

This does not work, when the matrix consists of floats.

Please apply the change I suggested, which fixes this, and add a doctest with floats.

However, this still does not work with sqrt5 for example, even with backend field or normaliz.

This is because coercion of parents does not work in this case. I'm trying to figure out what's going on there.

[kliem]

comment:8

I added #28770 as a dependency, because it would be nice to have doctest with a square root of something or so.

If you think this is unnecessary, feel free to remove it again.

[kliem]

Dependencies: #28770