Fellow geometry enthusiasts:  I am studying a particular geometry and I would like to change from one set of coordinates to a new set that makes the metric unimodular (i.e. it's determinant is one). The components of the metric are rather complicated functions of the coordinates, so I don't know how to solve the system of linear first order PDEs that I get from the Jacobian. Is anyone aware of any software that can give me the new coordinates in terms of the old ones given the Jacobian of the transformation? I have Maple 18, but I have not been able to find this capability in Maple.
What is some good free software for doing physics calculations?  I'm mainly interested in symbolic computation (something like Mathematica, but free).
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