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?
I don't think this is implemented yet. To implement tensor densities I guess
TensorField
should become a subclass ofTensorDensity
(orTensorDensityField
?) with weight zero, and probably much functionality could be moved toTensorDensity
with the appropriate generalization (taking the weight into account).Yes 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.Btw, if you would like to implement tensor densities, please visit https://sagemanifolds.obspm.fr/contri....