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Is there a way to define a submanifold of a Euclidean space by providing a list of implicit constraints, instead of by declaring a separate manifold and explicitly defining the embedding?

asked 2021-04-07 20:09:41 +0200

perfectly_odd gravatar image

Reasons for asking: My ultimate goal is to be able to integrate vector and form fields on surfaces defined by constraints in a 3D Euclidean space. A simple example would be the sphere (x^2 + y^2 + z^2 = R^2).

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answered 2021-04-08 10:03:23 +0200

eric_g gravatar image

This is not implemented yet. The current functionalities for submanifolds are described in [1], [2], [3], [4] and [5].

You are very welcome to contribute to SageMath by implementing the requested functionality; please visit https://sagemanifolds.obspm.fr/contri... and https://trac.sagemath.org/ticket/30525.

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Thanks, @eric_g---looks like you got to all three of my submanifold-related questions. Apologies for being repetitious; I just wanted to make sure I wasn't missing something obvious.

Also, those last two references (Jupyter notebooks for Kerr / Schwarzschild spacetimes) look pretty cool. Thanks for sharing!

perfectly_odd gravatar imageperfectly_odd ( 2021-04-09 01:36:30 +0200 )edit

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Asked: 2021-04-07 20:09:41 +0200

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Last updated: Apr 08