Hi Travis, On 2015-11-06, Travis Scrimshaw <tsc...@ucdavis.edu> wrote: >> On 2015-11-05, Travis Scrimshaw <tsc...@ucdavis.edu <javascript:>> wrote: >> > I would then be advocating for using UniqueRepresentation if that was >> > the only issue. >> >> It really depends whether in comparing manifolds you would prefer to do >> *some* >> heuristics to detect homeomorphic manifolds, or prefer to consider >> manifolds unequal if they were created with different input data. >> > > IMO, such checks are too expensive to be done at creation. For example, you > want do so some tests over all n-spheres.
I did not say anything about whether the tests should be done at creation time or not. I was talking about "comparing manifolds", which obviously means "comparing manifolds AFTER creation"- If you want that two distinct homeomorphic manifolds may evaluate equal then you must not use UniqueRepresentation. That's all. > Granted, there are nice and well-defined inputs for 2d and 3d > manifolds, which would make good sense to do Cached/UniqueRepresentation > around these structures. For a general (topological) manifold where there > are not necessarily such nice inputs, what would you give as input data? Whatever you currently give. An atlas. A simplicial complex. A system of multivariate polynomial equations. Here is an example in terms of "polynomial equations" as input data. The first question is to you whether you want that the same set of equations yields identical manifolds or distinct manifolds. The second question is whether you want that the manifolds are identical if and only if the two systems of equations have the same solutions. It depends on your answers whether to use CachedRepresentation, UniqueRepresentation or nothing. Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
