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. |

| 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. There is also the issue of endless loop mentioned in comment:39. |