Let me start by confirming that I have successfully used SageManifolds
to implement the several calculations I wanted to make using the Cartan
moving frames formalism. So first a big "thank you" for developing this
code!
> If you find some missing functionalities and you would like to
> implement them, please visit ...
Thanks for the invitation, but I'm a newbie at both Python and Sage...
I do however have some further questions, some of which likely reflect
my lack of comfort with (and ignorance of) object-oriented programming;
others may be in the category of feature requests for the future.
1. First and foremost, what is the proper way to manipulate the
components of both tensors and tensor-like objects such as the
connection, the connection 1-forms, and the curvature 2-forms?
A basic example would be how to set the mass to zero in the
Schwarzschild geometry *after* calculating the curvature. (I'm still
recovering from my shock at discovering that saying "m=0" is not
sufficient...) The best I've been able to come up with is to do
something like
object[1,2].expr().subs({m:0})
for each component of each affected object. Is there a better way?
A similar example would be how to apply simplifications to (all)
components of a given tensor or tensor-like object.
2. Is there a way to display (all) connection 1-forms or curvature
2-forms, ideally in a format analogous to that produced by
g.display_comp() or nab.display()?
(An answer involving a print loop is acceptable, although I can't get
the formatting right -- one entry per line, no extraneous symbols.)
3. Is there a way to specify the index labels on the connection 1-forms
and curvature 2-forms, analagous to index_labels on the connection?
(For that matter, is there a way to specify the labels on the metric?
I get an error when trying to set index_labels in that case.)
4. Can default (non-numerical) index labels be specified, rather than
repeating them in every display request?
Thank you,
Tevian
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