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

[jipilab]

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

[jipilab]

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

[jipilab]

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

[tscrim]

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

[gh-kliem]

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.

[gh-kliem]

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.

[gh-kliem]

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.

[gh-kliem]

Three more things.

• is_zero catches too many matrices. A 2-by-2 zero-matrix should not change ambient dimension, if it acts on a Polyhedron in ambient dim 2. if it acts on a polyhedron of dimension 3 it should throw an error.
• (Optional) Are you happy with the error message thrown, if the dimension of the matrix does not fit? If not you should take care of it.
• Currently, you implemented left action (and I don't know, what a right action should be). You should probably check, whether self_on_left is False.

[gh-kliem]

I applied those small changes as suggested above.

The matrix acts on the right now, by action of the transpose on the left.

---

New commits:

​0346231	First version of linear transformation
​e80556c	small changes
​1e68f1e	more consistent behaviour for empty matrix

[embray]

Ticket retargeted after milestone closed

[gh-kliem]

One probably should not return anything, if self is on left.

[git]

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

​eca962b

matrix must act from the left; improved documentation

[gh-kliem]

New commits:

​a521ca7	First version of linear transformation
​9385b30	small changes
​1a01fe3	more consistent behaviour for empty matrix
​7a694a0	matrix must act from the left; improved documentation
​a1072ee	give a error message if self on left; better error check for zero_matrix

[gh-kliem]

Bots are pretty much green. Some pyflakes warning, which I fixed in #28880 already (which is green botwise).

[jipilab]

Looks good to me.