Coordinates.m

Andrew D. Lewis

16 August 1998

1 Changing coordinates?

In Coordinates.m I have a few functions for changing coordinates for some standard types of tensors.

2 The functions if Coordinates.m

Here’s what you get—not much at the moment. The coordinate notation in all these is the same. The original coordinates are named in x and the new coordinates (i.e., those to which you are transforming) are named in xp. In xofxp you put the components of x as functions of xp, and conversely for xpofx. Thus, you need to explicitly know the coordinate change and its inverse. When changing coordinates for covariant tensors, you need only xofxp. Optional arguments are in italics.

Deriv->{Explicit,Implicit} This is an option for certain function calls which differentiate. If you select Explicit, differentiation will be explicit (the default), and if you select Implicit, differentiation will be implicit.

TransformMetric[g,x,xp,xofxp,Deriv] This one changes the compo-

nents of a Riemannian metric g.

TransformOneForm[omega,x,xp,xofxp,Deriv] This changes coordinates

for a one-form omega.

TransformVectorField[X,x,xp,xofxp,xpofx,Deriv] X is a vector field.