Hi sage-dev,
There is an ongoing discussion at #18529
<http://trac.sagemath.org/ticket/18529> about defining __eq__ for manifolds
and whether one should
use UniqueRepresentation (which implements equality by id). If anybody has
any opinion on this,
she/he is welcome to join the discussion.
The context is as follows:
- Manifolds are parents, whose elements are points.
- Manifolds are characterized by a user-defined atlas, which is a list of
coordinate charts defined on the
fly by the user, along with transition maps. "Defined on the fly" means
that charts are added to the
atlas during the working session. In particular, the atlas is not set at
the manifold construction.
- Two points are declared equal iff they have the same coordinates in the
same chart.
- Mathematically speaking, two manifolds are equal if they have the same
maximal atlas, not the
same "user-defined" atlas. Now maximal atlases cannot be represented in
the computer.
- One needs fast equality check for manifolds, since
(i) they are used as dictionary keys (for instance as the domains in the
dictionary of the restrictions of
some field)
(ii) check of chart equality involves comparison of chart domains, which
are manifolds (as open subset
of a manifold), and charts are massively used as keys in the
dictionary of coordinate expressions
of scalar fields
In the current branch of #18529 <http://trac.sagemath.org/ticket/18529>,
the manifold class inherits from UniqueRepresentation, so that
equality is by id and is therefore fast.
Examples of use corresponding to #18529 branch are here
<http://sagemanifolds.obspm.fr/doc/18529/reference/manifolds/sage/manifolds/manifold.html>
(they are rather primitive since there are
neither scalar fields nor continuous maps in #18529).
Thanks for your feedback.
Eric.
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