Is it possible to represent a partial differentiation without specifying what the derivative is acting upon? This would be handy in manipulating vector fields symbolically. For ex., suppose we have a vector field Y = y * d/dx and we'd like to compute the pushforward of Y by some diffeomorphism F. Can one express "d/dx" in the usual mathematical partial differential notation and in a way that Sage can handle?
This is implemented in SageManifolds, see for instance here for an example of vector field on the sphere S^2 (in the section "Module of vector fields" of the worksheet).
SageManifolds is not fully implemented in SageMath yet, so you have to install it according to these instructions. Note that SageManifolds is installed in the SageMathCloud (see here for some SMC example including vector vectors fields on S^2).
Asked: 2016-04-19 00:53:11 +0100
Seen: 805 times
Last updated: Apr 19 '16
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
There is a differential forms package now, which might have some useful stuff?
Thanks. I'll have a look at the package. For now, I have resorted to positional notation, i.e., representing the field by its vector of coefficients. So Y = y*d/dx above becomes [y,0], etc.