Comment #3 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Excellent! Thanks for the information. So I guess what we need to do is:
1. Implement the Viete formulas in the polys somewhere.
2. Put in a check somewhere in RootSum to see it the function inside the
Lambda is a rational function in the dummy variable (this means some
RootSum functionality won't work with a Python lambda, so maybe we should
not allow those or issue a warning).
3. If it is a Lambda, apply these formulas. Actually, do you always get
symmetric polynomials? What if you have something like r**2*log(x - r).
And I just randomly chose log(x - r). As you know, it could be any
log(S(x, r)), where S is a polynomial in x and r.
4. Make RootSum.diff apply the derivative to the Lambda (another thing that
won't work with Python lambdas), and then when it creates a new RootSum, it
will apply the check from step 2.
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