Changes between Initial Version and Version 1 of Ticket #18529, comment 40


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Timestamp:
11/03/15 10:37:17 (3 years ago)
Author:
egourgoulhon
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  • Ticket #18529, comment 40

    initial v1  
    1 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.
     1I'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. There is also the issue of endless loop mentioned in comment:39.
    22
    33For 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