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2013-04-01 11:03:04 -0500 marked best answer Coordinate Transforms

You can define functions to act as transformations:

T(r,theta) = (r*sin(theta), r*cos(theta))

and then just use them as normal functions: T(2,pi/2)

Also, you can pass an arbitrary 3d transformation to 3d plots using the transformation keyword. See the examples in the plot3d documentation. See also the builtin Spherical and Cylindrical transformations, or even the spherical_plot3d or cylindrical_plot3d functions.

It would be cool to have a transformation module that defines a bunch of transformations for convenience.

2013-03-31 13:04:28 -0500 asked a question Coordinate Transforms

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.


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