More functionalities for bases of free modules and vector frames

[egourgoulhon]

This ticket provides more flexibility in the choice of symbols and indices for ​bases of free modules of finite rank and, consequently, for ​vector frames on manifolds. In particular, the labels of the basis elements are no longer necessarily integers and can be customized, for instance:

sage: M = Manifold(3, 'M')
sage: e = M.vector_frame('e', indices=('x', 'y', 'z')); e
Vector frame (M, (e_x,e_y,e_z))

The symbol of each element of the basis can also be freely chosen, by providing a tuple of symbols instead of a single string; it is then mandatory to specify as well some symbols for the dual coframe:

sage: e = M.vector_frame(('a', 'b', 'c'), symbol_dual=('A', 'B', 'C')); e
Vector frame (M, (a,b,c))
sage: e[0]
Vector field a on the 3-dimensional differentiable manifold M
sage: e.coframe()
Coframe (M, (A,B,C))
sage: e.coframe()[0]
1-form A on the 3-dimensional differentiable manifold M

Besides, the slice operator is introduced for bases; it is now possible to write

sage: e[:]
(Vector field a on the 3-dimensional differentiable manifold M,
 Vector field b on the 3-dimensional differentiable manifold M,
 Vector field c on the 3-dimensional differentiable manifold M)

Internally, some refactoring of code has been performed. In particular, by renaming the FreeModuleCoBasis's attribute _form (the tuple containing the cobasis elements) to _vec, so that it matches the name of the FreeModuleBasis's attribute storing the basis elements, it has been possible to factor the method __getitem__ to the ABC Basis_abstract. Another improvement is getting rid of all methods _init_dual_basis in classes FreeModuleBasis, VectorFrame and CoordFrame thanks to the introduction of the class attribute _cobasis_class.

The functionalities introduced here provide a better user interface for #24623.

This work is part of the ​SageManifolds project, see #18528 for an overview.

[egourgoulhon]

New commits:

​a527e8e	First draft adding more flexibility in symbols of free module bases and vector frames
​2d43a23	More refactoring in vector frames
​0840d54	More work on vector frames
​01681b8	Add documentation for new options of vector frames

[git]

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

​9ddc467

Add method set_name to classes VectorFrame and CoFrame

[git]

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

​82c37b4

Cut long lines in src/sage/manifolds/differentiable/vectorframe.py

[egourgoulhon]

The above two commits add the method set_name to VectorFrame and CoFrame for even more flexibility (previously set_name was inherited from Basis_abstract and could not handle the domain name). This is required for #24623.

[tscrim]

Looks good overall. However, I do have one comment:

VectorFrame should process its arguments to ensure its unique representation, so this addition should not be needed (except the last bit of course):

         """
         from sage.manifolds.differentiable.vectorframe import VectorFrame
+        # Only tuples are valid entries for the unique representation of
+        # VectorFrame:
+        if isinstance(symbol, list):
+            symbol = tuple(symbol)
+        if isinstance(latex_symbol, list):
+            latex_symbol = tuple(latex_symbol)
+        if isinstance(indices, list):
+            indices = tuple(indices)
+        if isinstance(latex_indices, list):
+            latex_indices = tuple(latex_indices)
+        if isinstance(symbol_dual, list):
+            symbol_dual = tuple(symbol_dual)
+        if isinstance(latex_symbol_dual, list):
+            latex_symbol_dual = tuple(latex_symbol_dual)
         return VectorFrame(self.vector_field_module(dest_map=dest_map,
                                                     force_free=True),
                            symbol=symbol, latex_symbol=latex_symbol,
-                           from_frame=from_frame)
+                           from_frame=from_frame, indices=indices,
+                           latex_indices=latex_indices, symbol_dual=symbol_dual,
+                           latex_symbol_dual=latex_symbol_dual)
 
     def _set_covering_frame(self, frame):
         r"""

This probably means you need to implement a __classcall_private__/__classcall__ for that class. Note that __classcall__ is inherited, so you could define it in a base class.

[git]

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

​799066b

List entries of VectorFrame processed by __classcall_private__

[egourgoulhon]

Replying to tscrim:

Thank you very much for looking into this and for your comments.

VectorFrame should process its arguments to ensure its unique representation, so this addition should not be needed (except the last bit of course): This probably means you need to implement a __classcall_private__/__classcall__ for that class.

Thanks for the suggestion; this is done via __classcall_private__ in the above commit.

[git]

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

​da06d12

Small improvement in treatment of symbol attributes of free module bases

[egourgoulhon]

While working on #24623, I've noticed some issues regarding the naming of tangent space bases induced by vector frames. The above commit fixes this. It also removes unnecessary pieces of code in FreeModuleBasis.__init__ and FreeModuleBasis._new_instance.

[tscrim]

LGTM. Thank you.

[egourgoulhon]

Thank you for the review!