Revision history [back]

Hi all,

I'm new to Sage, transitioning from Mathematica --- so let me know if I'm doing something weird! I am interested in defining functions on a Tangent space (i.e. $f : TM \to \mathbb R$, the natural space of solutions for a Boltzmann equation). To do this, my first attempt is this:

E.<x,y,z> = EuclideanSpace()         # Define the spatial Euclidean Space
TE = E.tensor_bundle(1,0)     # Tangent bundle on the Euclidean space
TE_manifold = E.total_space() # Gets the tangent bundle as a manifold?
display(TE_manifold) 

This outputs "9-dimensional differentiable manifold TE^3". I would expect the dimension to be 6; tangent bundles normally have double the dimension to my understanding. Is this the expected behavior? Digging into the source code for total_space(), I found that the dimension is being computed as TE._rank * E._dim, while I would expect that should be TE._rank + E._dim.