#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.11
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers: Travis Scrimshaw
Authors: Eric Gourgoulhon, | Work issues:
Travis Scrimshaw | Commit:
Report Upstream: N/A | 3a525002469e0ef676a0dcf48f8f7f8683b85853
Branch: | Stopgaps:
public/manifolds/top_manif_basics |
Dependencies: #18175 |
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Comment (by egourgoulhon):
In the above commit, I've
- renamed class `Manifold` to `TopologicalManifold`
- renamed function `manifold_constructor` to `Manifold`, i.e. to the name
by which it is imported
to the global namespace (IMHO, this makes the documentation more clear
for a beginner:
previously, `sage: Manifold??` was returning something like `def
manifold_constructor`...
Also the html doc looks better with a single name)
- renamed class `TopologicalSubmanifold` to `OpenTopologicalSubmanifold`,
to avoid any ambiguity with
embedded submanifolds of lower dimension
- revert the attribute `_open_covers` to a list of lists (instead of a set
of frozensets), mostly to
ensure the reproductibility of computations from one machine to another
one, i.e. this garantees
that `for ... in` loops are always performed in the same way (maybe this
is something to
be discussed further...). Moreover, the mathematical definition of an
open cover refers to an indexed family, which corresponds more to a list
than to a frozenset.
- removed the method `is_open()` from `AbstractSet` (where it was always
returning `True`!) and
implemented it in `TopologicalManifold`. Now it is on the same footing
as methods `superset`,
`union` and `intersection`, which are not implemented in the base class
`AbstractSet` but in each
of the subclasses `TopologicalManifold` and `ManifoldSubset`
- removed the (unused) argument `category` from `ManifoldSubset.__init__`
- added an example to illustrate the class `OpenTopologicalSubmanifold`,
as well as enough doctests
to get a full coverage
To answer to some of your questions in the code:
- I don't think that `ManifoldPoint` must inherit from
`AbstractNamedObject` since the name is
not essential in the definition of a point (it can have no name),
contrary to that of a subset.
Moreover, it would slower the creation of points, which can be a problem
(no such problem for
parent objects, which are not expected to be massively created)
- Yes, I think we need `list_of_subsets` to have something duplicable from
one machine to another one
(cf. remark above about `_open_covers`).
The test suite of `ManifoldSubset` and `OpenTopologicalSubmanifold` fails
because of the lack of a method `lift`. What this method shall be? I guess
we have to wait for the morphism ticket (#18725) to implement it.
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:89>
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