#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
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 |
-------------------------------------+-------------------------------------
Comment (by egourgoulhon):
Replying to [comment:97 tscrim]:
> Replying to [comment:96 egourgoulhon]:
> > 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?
For this specific case (comparison), it depends on the open cover, not on
the ordering of the subsets in it.
> 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)?
No there is no control at the API level, because the API is `__eq__` (one
cannot pass extra parameters)
> What I'm getting at is that it shouldn't depend upon these things,
right?
Yes, in the ideal mathematical world. In the much less ideal symbolic
world, this is not so true... The argument goes as follows: in order to
have a pretty fast `__eq__` operator for tensor fields, the comparison is
not performed on all the subdomains where the tensor fields have known (or
computable) restrictions, but only on a single open cover, which is
mathematically sufficient. So one has to pick an open cover. By making
`_open_covers` a list, we ensure that the picked one is always the same.
The key point is that sometimes the comparison fails because of
simplification issues (no normal form for symbolic expressions), i.e.
`__eq__` returns `False` while the two tensor fields are mathematically
equals. This is not satisfactory but I guess this is inescapable when
dealing with symbolics. At least, by making `_open_covers` a list, we
garantee that the output of `__eq__`, whatever its mathematical relevance,
is consistent from one machine to the next one.
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:98>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
