#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 tscrim):
Replying to [comment:96 egourgoulhon]:
> Replying to [comment:95 tscrim]:
> > 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.
But does it depend on the ordering of subsets that give the open cover, or
which open cover it takes? Does the API for that have any control over
what order it was given (rather than the order in which the open covers
were created)? What I'm getting at is that it shouldn't depend upon these
things, right? Or are you trying to put a total ordering on these vector
fields, and if so, why?
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:97>
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