Updates:
Labels: -NeedsBetterPatch NeedsReview
Comment #12 on issue 2132 by mattpap: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
All problems from #10 and #11 were fixed:
In [1]: a = S("(1-5*x^2)/(x-2*x^3+x^5-1)")
In [2]: a
Out[2]:
⎛ 2⎞
-⎝1 - 5⋅x ⎠
─────────────────
3 5
1 - x + 2⋅x - x
In [3]: b = integrate(a, x)
In [4]: b
Out[4]:
⎛ 5 ⎛ ⎛ 2⎞⎞⎞
-RootSum⎝t - t - 1, Λ⎝t, t⋅log⎝x - t ⎠⎠⎠
In [5]: b.diff(x)
Out[5]:
⎛ 2⎞
-⎝1 - 5⋅x ⎠
─────────────────
3 5
1 - x + 2⋅x - x
In [6]: RootSum(x**5 - x + 1, sin)
Out[6]:
⎛ 5 ⎞
RootSum⎝x - x + 1, Λ(x, sin(x))⎠
In [7]: _.doit()
Out[7]:
⎛ ⎛ 5 ⎞⎞ ⎛ ⎛ 5 ⎞⎞ ⎛ ⎛
5 ⎞⎞ ⎛ ⎛ 5
sin⎝RootOf⎝x - x + 1, 0⎠⎠ + sin⎝RootOf⎝x - x + 1, 1⎠⎠ + sin⎝RootOf⎝x - x
+ 1, 2⎠⎠ + sin⎝RootOf⎝x - x + 1, 3
⎞⎞ ⎛ ⎛ 5 ⎞⎞
⎠⎠ + sin⎝RootOf⎝x - x + 1, 4⎠⎠
In [8]: a = RootSum(z**5 - z**2 + 1, Lambda(z, z*log(x - z)))
In [9]: a.diff(x)
Out[9]:
⎛ 2⎞
-⎝5 - 3⋅x ⎠
───────────
2 5
1 - x + x
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