Comment #27 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Now it can:
In [1]: f = 161*z**3 + 115*z**2 + 19*z + 1
In [2]: g = Lambda(z, z*log(-3381*z**4/4 - 3381*z**3/4 - 625*z**2/2 -
125*z/2 - 5 + exp(x)))
In [3]: RootSum(f, g)
Out[3]:
⎛ ⎛ ⎛ 2
3 4 ⎞⎞⎞
⎜ 3 2 ⎜ ⎜ 125⋅z 625⋅z
3381⋅z 3381⋅z x⎟⎟⎟
RootSum⎜161⋅z + 115⋅z + 19⋅z + 1, Λ⎜z, z⋅log⎜-5 - ───── - ────── -
─────── - ─────── + ℯ ⎟⎟⎟
⎝ ⎝ ⎝ 2 2
4 4 ⎠⎠⎠
In [4]: _.diff(x)
Out[4]:
⎛ x 2⋅x⎞ x
-⎝4 - 6⋅ℯ + 5⋅ℯ ⎠⋅ℯ
───────────────────────
⎛ 2⋅x 3⋅x⎞
7⋅⎝1 - ℯ + ℯ ⎠
(the same result is produced by Mathematica).
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