Thanks, Francesco.
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.
>
>
Yes, I noticed that the Patch class would not be able to do this. Hence, I
was thinking being able to represent
Sn consistently would be a useful use-case to add the required machinery,
if you think something like this makes
sense.
> 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.
>
I agree with you, this is probably the correct approach. Then the question
is, where would this function exist
within Sympy? Should a Manifold class, which would contain the patches,
contain an optional Embedding class/attribute
corresponding to each Patch?
>
>
> 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.
>
Agreed. Going back to my previous paragraph, what do you think is the best
way to handle such a map (and hence the
plotting capability)?
>
>
> As there are currently no ways to define transition functions among
> patches, defining S1 and S2 is identicaly to define R1 and R2.
>
>
Then, the only way to tell S1 and R1 apart would be to associate them with
a metric? Then again, where should this
metric be stored?
Thanks,
Joy
--
The best ruler, when he finishes his
tasks and completes his affairs,
the people say
“It all happened naturally”
- Te Tao Ch'ing
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