#18529: Topological manifolds: basics
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Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers: Travis Scrimshaw
Authors: Eric Gourgoulhon | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0fb39df7fafe7f0a765bf73b3f34a6cb41e65c40
u/tscrim/top_manifolds_refactor | Stopgaps:
Dependencies: #18175 |
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Comment (by tscrim):
Replying to [comment:68 egourgoulhon]:
> The refactoring with the new classes `AbstractObject`, `AbstractSet`,
`ManifoldSubset` and `TopologicalSubmanifold` looks good. It clarify
things, thanks! A suggestion regarding the naming: what about replacing
`AbstractObject`, which sounds too general, by `AbstractNamedObject`,
which would better reflect the class content?
That is okay with me.
> Regarding the separation manifold/structure, I am wondering how this
could fit with differentiable manifolds? Since the structure classes are
singleton, they store things like the differential order but not
properties specific to a given manifold, like the set of vector frames
defined on the manifold or its module of vector fields.
I wasn't imagining that they would be singletons, as they would carry
instance information like differential order.
> Then, how could one have a single class for all kind of manifolds? For
instance, the class `DifferentiableManifold` introduced in #18783 inherits
from `TopologicalManifold` and has the additional attributes `_frames`,
`_coframes`, `_frame_changes`, `_parallelizable_parts`,
`_vector_field_modules`, etc., which have no meaning for a topological
manifold. Besides, we don't want the user to write something like `v =
M.structure().vector_frame(...)` instead of `v = M.vector_frame(...)`, do
we?
Good point. Then rather these being instance objects, they should probably
be mix-in classes. This would help keep some separation of concerns, avoid
some redundancies, and make it easy to manage the distinction between the
full manifold and the submanifolds.
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:69>
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