Comment #2 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
In this particular case, this is an application of Viete formulas. Take an
expression:
In [6]: var('r1:6')
Out[6]: (r₁, r₂, r₃, r₄, r₅)
In [7]: R = _
In [8]: sum(r/(x - r) for r in R)
Out[8]:
r₁ r₂ r₃ r₄ r₅
────── + ────── + ────── + ────── + ──────
x - r₁ x - r₂ x - r₃ x - r₄ x - r₅
and put it together. In the denominator you will get x**5 - x + 1 and in
the numerator there will be sums and products of roots. Take Viete formulas
and it will simplify to the result given by Maple (checked also in
Mathematica).
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