Is there something in sage that does the same thing that CoordinateTransform
and TransformedField
in Mathematica 9 ?
The idea is that CoordinateTransform
is given some coordinates, e.g. (r,th) and asked to transform them from "polar" to "cartesian", thus gives the expression of the cartesian coordinates in terms of the polar coordinates, e.g.
(x(r,th), y(r,th)) = (r*cos(th), r*sin(th))
Obvioulsly, it also works with other coordinates systems.
TransformedField
makes the transformation between a scalar, vector, or tensor field in, say, cartesian coordinates, to spherical coordinates.
These actions are not very complicated, nor difficult to implement when needed, but they are also very common.
Thanks.
references :
- http://reference.wolfram.com/mathematica/ref/CoordinateTransform.html
- http://reference.wolfram.com/mathematica/ref/TransformedField.html