On Sunday, December 28, 2014 5:26:40 AM UTC+1, Joy merwin monteiro wrote: > > Hello, > > a couple of things struck me when I was looking at the mail regarding a > proposed > group theory project by Vamsi. > > a) The manifolds in rn.py just need to setup a coordinate system, since > the parameterisation > is the identity map. How would one describe, say, Sn? >
Supposing you mean the N-sphere by Sn, a sphere cannot be mapped by one single patch. You need at least two. Patches are currently just containers, there is no way as of now to define coordinate transition functions between overlapping patches. Anyways, I don't think that a manifold should be represented by its embedding into the Euclidean space (in the case of Sn, a map from one vector of Sn to a vector in R_(n+1) ). Once you have a coordinate system on a patch, you can define your own function mapping its coordinates to the Euclidean space. > b) can we simply do plot(manifold) to visualise it? > > Visualizing a manifold depends on the embedding you choose. A plot is basically a projection from the manifold to 2D or 3D Euclidean space, so as soon as you have a map to do that, you can plot the manifold. > Since this seems to be of a more elementary nature as compared to the > LieGroup thing, > I think it will be a good exercise to write sn.py in the nature of rn.py > which implements > S1 and S2. It should also help me get a better hang of the code. > As there are currently no ways to define transition functions among patches, defining S1 and S2 is identicaly to define R1 and R2. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/bb2d9d8c-d45e-4466-8c5a-b65b4dd23b8d%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
