Mixed Forms: set_comp, comp

[gh-mjungmath]

In the upcoming changes we want to allow mixed differential forms, among other things, being made immutable (see #30181, #30261).

However, the current implementation would not support that behavior properly, namely:

sage: M = Manifold(2, 'M')
sage: A = M.mixed_form()
sage: a = M.diff_form(2)
sage: A[2] = a
sage: A[2] is a
True

If A would be set immutable and a is not, this would contradict the behavior of an immutable element. Even if a would automatically be set immutable as soon as A had been set immutable, this might happen not on the behalf of the user.

I'd propose a similar approach as I had done in #30208 for bundle connections, and as it is already known for tensor fields, namely by introducing methods set_comp and comp (add_comp would not be necessary). Then each instance representing a homogeneous component is bound only to the mixed differential form.

As always, suggestions and opinions are welcome.

[mkoeppe]

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[git]

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

​69f7bb5

Trac #30272: new standard name for homogeneous components (without tests)

[gh-mjungmath]

First approach.

What I did:

• homogeneous components are bound to mixed form and a priori detached from other instances; in particular

  sage: A[0] = f
  sage: A[0] is f
  

yields False now.

• components are only initialized on demand (not on initialization of the mixed form)
• by default, homogeneous components are named according to the mixed form's name: A = A_0, A_1, ...
• set_comp method similar to tensor fields

I tried to maintain as much backwards compatibility as possible. For example, even if copies now, the names are still applied if A[:] = [f, omega, eta] syntax is used. But the long-term idea is to favor set_comp(i)[:] = ... syntax instead of omega[:] = ... plus A[i] = omega syntax.

Comments are appreciated.

[git]

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

​27aa360

Trac #30272: doctests added

[gh-mjungmath]

Here we go, that should be it. Please take a close look whether this is (at least) halfway consistent and transparent to the user.

In a next step, mixed forms will be equipped with an immutability switch.

[gh-mjungmath]

If desired so, I will squash the commits for final merge.

[egourgoulhon]

LGTM.

[vbraun]

Merge conflict

[git]

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

​89dc552

Trac #30272: merged

[egourgoulhon]

When clicking on the new branch, one gets a huge diff, which seems to be the whole 9.4.beta3 w.r.t 9.4.beta2. Wouldn't it be better to merge the previous ticket branch into a clean 9.4.beta3?

[gh-mjungmath]

That's odd. For me the branch against the current beta looks just fine:

[tscrim]

Replying to egourgoulhon:

When clicking on the new branch, one gets a huge diff, which seems to be the whole 9.4.beta3 w.r.t 9.4.beta2. Wouldn't it be better to merge the previous ticket branch into a clean 9.4.beta3?

That sometimes happens with the trac git helper. You don't have to worry too much about it as long as it pulls okay (a la comment:21).

[egourgoulhon]

Replying to tscrim:

Replying to egourgoulhon:

When clicking on the new branch, one gets a huge diff, which seems to be the whole 9.4.beta3 w.r.t 9.4.beta2. Wouldn't it be better to merge the previous ticket branch into a clean 9.4.beta3?

That sometimes happens with the trac git helper. You don't have to worry too much about it as long as it pulls okay (a la comment:21).

Indeed, this seems erratic: it looks good now, while the branch has not been changed.

[vbraun]

[release@zen Sage]$ sage -t --long --warn-long 49.3 --random-seed=0 src/sage/manifolds/differentiable/mixed_form.py  # 4 doctests failed
 
Running doctests with ID 2021-06-29-21-56-39-c62006fe.
Git branch: develop
Using --optional=build,dochtml,fedora,pip,sage,sage_spkg
Doctesting 1 file.
sage -t --long --warn-long 49.3 --random-seed=0 src/sage/manifolds/differentiable/mixed_form.py
**********************************************************************
File "src/sage/manifolds/differentiable/mixed_form.py", line 90, in sage.manifolds.differentiable.mixed_form.MixedForm
Failed example:
    A.display_expansion() # display expansion in basis
Expected:
    A = [x] + [x*y dx] + [x*y^2 dx/\dy]
Got:
    A = x + x*y dx + x*y^2 dx/\dy
**********************************************************************
File "src/sage/manifolds/differentiable/mixed_form.py", line 113, in sage.manifolds.differentiable.mixed_form.MixedForm
Failed example:
    B.display_expansion()
Expected:
    B = [x] + [x*y dx] + [x*y^2 dx/\dy]
Got:
    B = x + x*y dx + x*y^2 dx/\dy
**********************************************************************
[...]

[gh-mjungmath]

Ah damn, I mis-resolved the merge conflict.

Let's wait for #30473 anyway.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​da8893f	Use sage.typeset.unicode_characters in TensorProductFunctor and SignedTensorProductFunctor
​2a23cb5	Unicode symbol 2202 (partial) for the text display of coordinate frames
​5d096f1	f-string for unicode_symbol in TensorProductFunctor and SignedTensorProductFunctor
​76c2fd5	Use Unicode symbol for the Riemann sphere example
​5167e6c	Use Unicode symbol for default text display of RealLine
​332410b	Use unicode_otimes in TensorProductFunctor and SignedTensorProductFunctor
​f5d15d2	Merge branch 'public/manifolds/unicode_art' of git://trac.sagemath.org/sage into Sage 9.4.beta4.
​d87d09b	#30473: fix doctest error in DiffMap.pullback
​d62adad	merge unicode
​f1e7ef8	Trac #30272: remove set_name_comp + fix doctest

[git]

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

​91fc96f

Trac #30272: minor doctest fix

[gh-mjungmath]

Ready for review again.

[egourgoulhon]

The patchbot reports doctest failures that all pertain to the dependency #30473. They are all fixed in the latest version of that ticket. But I don't think it necessary to merge it here to move on.