#18529: Topological manifolds: basics
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Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.0
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers: Travis Scrimshaw
Authors: Eric Gourgoulhon, | Work issues:
Travis Scrimshaw | Commit:
Report Upstream: N/A | c38ae80cbd8032cf7041259284b6f646265d1e42
Branch: | Stopgaps:
public/manifolds/top_manif_basics |
Dependencies: #18175 |
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Comment (by egourgoulhon):
Replying to [comment:95 tscrim]:
> Sorry for the delay in getting to this.
No problem.
>
> The `set` of `frozenset`s will have a faster lookup as manifolds get
larger. I think this is still valid mathematically because the indexed
family does not have to be ordered as far as I know. So it would be more
like a `dict`, but I don't think we care about the indexing; if we did,
then we should go to a `list`. For the doctests, we can just do a `sorted`
or we have an internal method which returns it in a canonical way (i.e.,
ordered via its string representation).
It is not only a matter of doctests, but of reproductability of real
computations. For instance the comparison of two vector fields on non-
parallelizable manifolds makes use of 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.
>
> `lift` can just be a method that creates the corresponding point in the
ambient manifold, and similarly for `retract`. Once we have #18725, we can
convert it to a `@lazy_attribute` which is set to the morphism (note that
this does not change the API).
>
OK, thanks.
> I don't reall agree with comment:92. I feel that this only removes a few
docstrings, adds some internal complexity, and increases memory usage
(although since we aren't really using this for `TopologicalPoint`, the
memory usage is less of a concern). In principle, it is a mixin class, but
it just acts like an ABC. So it is perfectly valid to override its
`_repr_`.
OK, I will revert to the previous version.
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:96>
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