List Assignment for Bundle Connections

[gh-mjungmath]

Bundle connections were implementet quite superficially (by me). In this ticket, I want to improve the assigment behavior of bundle connections.

First of all, the methods set_connection_form and add_connection_form now return the corresponding connection 1-form ready for further assignment.

The main improvement in this ticket is to allow list assignments:

sage: M = Manifold(2, 'M', start_index=1)
sage: X.<x,y> = M.chart()
sage: E = M.vector_bundle(2, 'E')
sage: nab = E.bundle_connection('nabla')
sage: e = E.local_frame('e')
sage: nab[e, :] = 0  # set all entries to zero
sage: nab[e, 0, 0].display()
connection (1,1) of bundle connection nabla w.r.t. Local frame (E|_M, (e_1,e_2)) = 0

For details see the documentation, which I have also improved.

[gh-mjungmath]

Last 10 new commits:

​fe43915	Trac #30191: code improvements + in ZZ check removed again
​461ff65	Trac #30191: != [] removal reverted
​af5af8f	Trac #30191: elif reverted + in ZZ check for automorphismfield_group
​f0c6ee8	Trac #30191: minor fix
​f1221da	Trac #30191: minor fix
​a042313	Trac# 30191: wrong indentation reverted
​4cc92e9	Trac #30191: comp check unified to if comp
​f98a47b	Trac #30191: unused ScalarField import removed
​9c5a25b	Trac #30208: assigment for bundle connections
​fa87f4b	Trac #30208: documentation improved

[git]

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

​4f0c279

Trac #30208: Merge branch 'develop' into bundle_connection_extension

[tscrim]

Misindent:

-            sage: M = Manifold(2, 'M')
+             sage: M = Manifold(2, 'M')
             sage: X.<x,y> = M.chart()
             sage: E = M.vector_bundle(2, 'E')

Also in add_connection_form and set_connection_form, you need to deprecate the form input (or keep it with a default of None).

[git]

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

​41983da

Trac #30208: form input deprecated

[gh-mjungmath]

Is this suitable?

Addendum: Do you think this attempt is better than the one before?

[tscrim]

You should make it a standard deprecation using from sage.misc.superseded import deprecation. Also, there will need to be separate deprecations for each of the two methods.

My (not so well informed) opinion is that both approaches seem natural. So I don't really can't make a comparison about which is better.

[gh-mjungmath]

Replying to tscrim:

You should make it a standard deprecation using from sage.misc.superseded import deprecation. Also, there will need to be separate deprecations for each of the two methods.

I will change this. Thank you.

My (not so well informed) opinion is that both approaches seem natural. So I don't really can't make a comparison about which is better.

I thought this approach is more natural in terms of the "immutability" discussion we had months ago. The connection forms are now somehow fixed and clearly bound to the connection. Furthermore, it is much closer to the implementation of AffineConnection.

Eric, what do you say?

[tscrim]

Replying to gh-mjungmath:

Replying to tscrim:

My (not so well informed) opinion is that both approaches seem natural. So I don't really can't make a comparison about which is better.

I thought this approach is more natural in terms of the "immutability" discussion we had months ago. The connection forms are now somehow fixed and clearly bound to the connection.

A few months ago seems like a lifetime now. Although I think it was more than a few months, but I don't quite remember the outcome of that conversation...

[gh-mjungmath]

Replying to tscrim:

A few months ago seems like a lifetime now. Although I think it was more than a few months, but I don't quite remember the outcome of that conversation...

And still, time flies...I think the outcome was #28562.

[git]

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

​f9cb6c1

Trac #30208: deprecation warning

[tscrim]

LGTM.

[gh-mjungmath]

Thank you for the positive review. Besides, I am still curious what Eric has to say about these changes.

[gh-mjungmath]

Sorry, I have found some severe flaws.

[gh-mjungmath]

I have sensed something really odd, and I have no idea where this might come from:

sage: M = Manifold(3, 'M', start_index=1)
sage: X.<x,y,z> = M.chart()
sage: E = M.vector_bundle(2, 'E')
sage: e = E.local_frame('e') # standard frame for E
sage: nab = E.bundle_connection('nabla', latex_name=r'\nabla')
sage: nab[e, :] = 0
sage: nab[e, 1, 2][:] = [x*z, y*z, z^2]
sage: nab[e, 2, 1][:] = [x, x^2, x^3]
sage: nab[e, 1, 1][:] = [x+z, y-z, x*y*z]
sage: vframe = X.frame()
sage: e[1][[e, 2]]
0
sage: om = nab[2, 2]
sage: om(vframe[1])
Scalar field connection (2,2) of bundle connection nabla w.r.t. Local frame (E|_M, (e_1,e_2))(d/dx) on the 3-dimensional differentiable manifold M
sage: e[1][[e, 2]]
Scalar field connection (2,2) of bundle connection nabla w.r.t. Local frame (E|_M, (e_1,e_2))(d/dx) on the 3-dimensional differentiable manifold M
sage: e[1][[e, 2]] is om(vframe[1])
True

What the...?

Addendum: I think the problem comes from the unique zero scalar field. Somehow it gets altered via __call__ of TensorField. It has therefore nothing to do with this ticket. I have opened another ticket #30239.

[git]

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

​c34e481	Trac #30191: remove in ZZ check
​65dff3d	Trac #30191: Merge branch 'develop' into conversion_attributeerror_fix
​acc407c	Trac #30191: try-except block for zero check
​0d27b57	Trac #30191: unnecessary comment block removed
​f94bcbe	Trac #30191: if blocks rearranged
​28dec69	Trac #30191: doctest errors fixed
​6a55a0b	Merge branch 'conversion_attributeerror_fix' into bundle_connection_extension
​bb476e2	Trac #30208: minor fix

[gh-mjungmath]

I have uploaded the fix of a minor mistake.

[git]

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

​a77aebc

Trac #30208: copy_from reverted to recover old behavior

[git]

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

​934a439

documentation slightly improved

[tscrim]

While this was already there, so I am not going to stop a positive review, but I really dislike doctests like this:

            sage: nab._new_forms(e)  # random
            dict of forms

It is only # random because of the print order, but you can easily make it print in a fixed order by

sage: d = nab._new_forms(e)
sage: [d[k] for k in sorted(d)]

By marking it as # random, it can take any output, so it can mask bugs.

If you don't want to change this, you can just ignore and set a positive review. If you do change, you can just set it to a positive review after you run the doctest on the file.

[git]

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

​d3c8cab

Trac #30208: random doctest removed

[gh-mjungmath]

Very good point. Thank you Travis. I've changed it.

[gh-mjungmath]

I'm just thinking about whether the list assignment via copying is the right way to do. The Python documentation says:

Assignment statements in Python do not copy objects, they create bindings between a target and an object.

I suggest, we remove the __setitem__ method again, and encourage the use of set_connection_form(i, j).copy_from(omega) instead. If that meets with your approval, I will open a ticket for that and apply the same changes for mixed differential forms.