ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 14 Aug 2021 12:45:22 +0200Is 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?https://ask.sagemath.org/question/56534/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/**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). Wed, 07 Apr 2021 20:09:41 +0200https://ask.sagemath.org/question/56534/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/Answer by mjungmath for <p><strong>Reasons for asking:</strong> 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). </p>
https://ask.sagemath.org/question/56534/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/?answer=58459#post-id-58459It might be of your interest that Matthias Koeppe is currently working on a refinement of the manifold's subset implementation. The full meta-ticket can be found in [#31740](https://trac.sagemath.org/ticket/31740).Sat, 14 Aug 2021 12:45:22 +0200https://ask.sagemath.org/question/56534/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/?answer=58459#post-id-58459Answer by eric_g for <p><strong>Reasons for asking:</strong> 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). </p>
https://ask.sagemath.org/question/56534/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/?answer=56547#post-id-56547This is not implemented yet. The current functionalities for submanifolds are described in
[[1]](https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/topological_submanifold.html),
[[2]](https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/differentiable_submanifold.html), [[3]](https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/pseudo_riemannian_submanifold.html), [[4]](https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_submanifold_Kerr_slicing.ipynb) and [[5]](https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Notebooks/SM_Schwarzschild_horizon_degen.ipynb).
You are very welcome to contribute to SageMath by implementing the requested functionality; please visit https://sagemanifolds.obspm.fr/contrib.html and https://trac.sagemath.org/ticket/30525.
Thu, 08 Apr 2021 10:03:23 +0200https://ask.sagemath.org/question/56534/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/?answer=56547#post-id-56547Comment by perfectly_odd for <p>This is not implemented yet. The current functionalities for submanifolds are described in
<a href="https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/topological_submanifold.html">[1]</a>,
<a href="https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/differentiable_submanifold.html">[2]</a>, <a href="https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/pseudo_riemannian_submanifold.html">[3]</a>, <a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_submanifold_Kerr_slicing.ipynb">[4]</a> and <a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Notebooks/SM_Schwarzschild_horizon_degen.ipynb">[5]</a>.</p>
<p>You are very welcome to contribute to SageMath by implementing the requested functionality; please visit <a href="https://sagemanifolds.obspm.fr/contrib.html">https://sagemanifolds.obspm.fr/contri...</a> and <a href="https://trac.sagemath.org/ticket/30525">https://trac.sagemath.org/ticket/30525</a>.</p>
https://ask.sagemath.org/question/56534/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/?comment=56571#post-id-56571Thanks, @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!Fri, 09 Apr 2021 01:36:30 +0200https://ask.sagemath.org/question/56534/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/?comment=56571#post-id-56571