Updates:
Status: Started
Comment #4 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
1. I started implementing this.
3. I'm aware of the fact that the lambda can be an arbitrary expression.
The example you gave can be done by Mathematica and Mathematica's docs
state that if lambda is a rational function, then RootSum will always get
simplified. More experimentation should reveal the nature of RootSum for
arbitrary rational functions (a proof would also be nice).
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