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change of variables in PDE?


I hope this isn't too trivial a question...

I am trying to change variables in a PDE

f[x_,y_] -> F[X,Y]

where the new variables and functions are defined like, e.g.:

X = x^2 + y
Y = 2 + x y
F = x f

I would like Mathematica to recognize f and all of its partial
derivatives, applying the chain rule where necessary, etc. to a PDE
given in terms of f, x, and y, returning the PDE in terms of F, X, and
Y, with all derivatives fixed accordingly.

It seems that this would be a common request, and yet in all my searcing
I haven't found a way to do this. Is there a package anyone knows about
that does this?

Thank you,
Geoff Simms


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