set_default_frame() too restrictive on parallelizable manifolds

[gh-mjungmath]

sage: M = Manifold(3, 'M')
sage: U = M.open_subset('U'); V = M.open_subset('V')
sage: c_xyz.<x,y,z> = U.chart(); c_uvt.<u,v,t> = V.chart()
sage: M.default_frame()
Coordinate frame (U, (d/dx,d/dy,d/dz))
sage: e = M.vector_frame('e'); e
Vector frame (M, (e_0,e_1,e_2))
sage: M.default_frame()
Coordinate frame (U, (d/dx,d/dy,d/dz))
sage: M.set_default_frame(c_xyz.frame())
Traceback (most recent call last):
...
ValueError: the frame domain must coincide with the 3-dimensional differentiable manifold M

In case of M=SU(2)=S^3 this can happen: it cannot be covered by one chart but is parallelizable.

However, due to the error message, the method default_frame is obviously intended to return the default frame which covers M if possible. This is not given in the above example.

[gh-mjungmath]

I see two options here:

1. One allows also frames defined on subsets for set_default_frame, even in the parallelizable case.
2. One overwrites the default frame for the first frame which covers M in case it haven't covered M before.

[gh-mjungmath]

I think, both options are reasonable. The first is, of course, more comprehensible for to user.

I don't see a third choice. If you have any ideas, I'd welcome them.

[egourgoulhon]

Thanks for handling this. In all the sage/manifolds settings, the "default frame" is initially set as the first frame defined on the manifold, usually (but not necessarily) the coordinate frame corresponding to the first chart defined on the manifold. For consistency among all kinds of manifolds, I would be inclined to keep this behaviour even for parallelizable manifolds not covered by a a single chart, such as S³. So I would vote for option 1 of comment:1. Moreover, although it is also quite natural, option 2 would perform a silent change of the default frame, which may surprise the end user.

In DifferentiableManifold.set_default_frame(), there is

        if frame._domain is not self:
            if self.is_manifestly_parallelizable():
                raise ValueError("the frame domain must coincide with " +
                                 "the {}".format(self))

which triggers the error reported in the ticket description. Maybe we can simply remove this...

[gh-mjungmath]

Replying to egourgoulhon:

Thanks for handling this. In all the sage/manifolds settings, the "default frame" is initially set as the first frame defined on the manifold, usually (but not necessarily) the coordinate frame corresponding to the first chart defined on the manifold. For consistency among all kinds of manifolds, I would be inclined to keep this behaviour even for parallelizable manifolds not covered by a a single chart, such as S³. So I would vote for option 1 of comment:1. Moreover, although it is also quite natural, option 2 would perform a silent change of the default frame, which may surprise the end user.

In DifferentiableManifold.set_default_frame(), there is

        if frame._domain is not self:
            if self.is_manifestly_parallelizable():
                raise ValueError("the frame domain must coincide with " +
                                 "the {}".format(self))

which triggers the error reported in the ticket description. Maybe we can simply remove this...

This is exactly what I meant by "The first [option] is [...] more comprehensible to user.". Thanks for pointing this out in such detail.

Vector bundles currently use option 1 as well, btw.

Then, I will take care of removing the corresponding error messages and adapt the documentation if necessary. This is good, because #30178 can then be kept.

[gh-mjungmath]

New commits:

​7f50b3d

Trac #30320: error messages removed

[gh-mjungmath]

Similarly for charts, btw, though more unlikely. I've removed that error message, too. Agreed?

[gh-mjungmath]

Is that good or some more work needed here?

[egourgoulhon]

Replying to gh-mjungmath:

Is that good or some more work needed here?

Yes it's good. Sorry for the delay.

PS: I've added the ticket to #30235, where it was missing.

[egourgoulhon]

Replying to egourgoulhon:

PS: I've added the ticket to #30235, where it was missing.

Btw, don't hesitate to add relevant tickets there.

[gh-mjungmath]

Replying to egourgoulhon:

Replying to egourgoulhon:

PS: I've added the ticket to #30235, where it was missing.

Btw, don't hesitate to add relevant tickets there.

Okay, sure. :)

Besides, you meant the metaticket #30525, right?

[egourgoulhon]

Replying to gh-mjungmath:

Besides, you meant the metaticket #30525, right?

Yes.