#18529: Topological manifolds: basics
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Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers:
Authors: Eric Gourgoulhon | Work issues:
Report Upstream: N/A | Commit:
Branch: | f342e03e7008831c4789b94b03674c1a0cbbf3a6
public/manifolds/top_manif_basics | Stopgaps:
Dependencies: #18175 |
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Comment (by egourgoulhon):
I've already noticed some important loss of performance due to the
equality not being by id; I am afraid that for tensor computations this
will become much worse. Moreover, a sophisticated equality check (either
with `__eq__` or `is_isomorphic_to`) seems difficult to acheive: checking
the equality of the user-defined atlases is definitevely not sufficient to
assert the mathematical equality of two manifolds; one should compare the
maximal atlases instead, which is impossible. For example, if one first
construct S^2^ with an atlas of two stereographic charts and then another
S^2^ with an atlas of two polar charts, the two atlases differ, while both
objects represent the same manifold.
For the above reasons, I am considering to revert to the
`UniqueRepresentation` for manifolds. To solve the issue of the
redefinition by the end user disccused in comment:32, we could have some
handling of the cache in the function `Manifold`, so that
{{{
M1 = Manifold(2, 'M')
M2 = Manifold(2, 'M')
}}}
will construct two different objects. What do you think?
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:40>
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