ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 22 Nov 2018 08:31:44 -0600Tensor density in sagemanifolds?https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/Hello community.
I've just realized that within the class `TensorField` there are subclasses `DiffForm` and `MultivectorField`. I was wondering whether a maximal (i.e. rank $n$ in $n$ dimensions) differential form or multivector field are considered as tensor densities. I'm thinking in the Levi-Civita epsilon.
Well, more generally... Is there a way to assign a density weight to a tensor?Thu, 22 Nov 2018 02:30:38 -0600https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/Comment by eric_g for <p>Hello community.</p>
<p>I've just realized that within the class <code>TensorField</code> there are subclasses <code>DiffForm</code> and <code>MultivectorField</code>. I was wondering whether a maximal (i.e. rank $n$ in $n$ dimensions) differential form or multivector field are considered as tensor densities. I'm thinking in the Levi-Civita epsilon.</p>
<p>Well, more generally... Is there a way to assign a density weight to a tensor?</p>
https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44383#post-id-44383Btw, if you would like to implement tensor densities, please visit https://sagemanifolds.obspm.fr/contrib.html.Thu, 22 Nov 2018 08:31:44 -0600https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44383#post-id-44383Comment by eric_g for <p>Hello community.</p>
<p>I've just realized that within the class <code>TensorField</code> there are subclasses <code>DiffForm</code> and <code>MultivectorField</code>. I was wondering whether a maximal (i.e. rank $n$ in $n$ dimensions) differential form or multivector field are considered as tensor densities. I'm thinking in the Levi-Civita epsilon.</p>
<p>Well, more generally... Is there a way to assign a density weight to a tensor?</p>
https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44379#post-id-44379Yes I confirm that tensor densities are not implemented yet. In particular, the method `PseudoRiemannianMetric.volume_form()` returns a tensor field (a $n$-form), not a tensor density.Thu, 22 Nov 2018 07:16:29 -0600https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44379#post-id-44379Comment by rburing for <p>Hello community.</p>
<p>I've just realized that within the class <code>TensorField</code> there are subclasses <code>DiffForm</code> and <code>MultivectorField</code>. I was wondering whether a maximal (i.e. rank $n$ in $n$ dimensions) differential form or multivector field are considered as tensor densities. I'm thinking in the Levi-Civita epsilon.</p>
<p>Well, more generally... Is there a way to assign a density weight to a tensor?</p>
https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44373#post-id-44373I don't think this is implemented yet. To implement tensor densities I guess `TensorField` should become a subclass of `TensorDensity` (or `TensorDensityField`?) with weight zero, and probably much functionality could be moved to `TensorDensity` with the appropriate generalization (taking the weight into account).Thu, 22 Nov 2018 03:11:38 -0600https://ask.sagemath.org/question/44371/tensor-density-in-sagemanifolds/?comment=44373#post-id-44373