Comment #13 on issue 2132 by asmeurer: Derivative of RootSum
http://code.google.com/p/sympy/issues/detail?id=2132
Good idea about just converting RootSum(..., sin) into RootSum(…, Lambda(i,
sin(i))).
It's good to see that you implemented an unevaluated form of RootSum; I was
going to suggest that. Shouldn't the keyword be evaluate=False instead of
auto=False, matching with other parts of SymPy? On the other hand, it
looks like auto transfers through after taking .diff, so maybe it matches
better with the auto option from polys. Also, I would
expect "evaluate=False" to not expand the Poly, which might not be what you
want (is there code that relies on the poly in RootSum being irreducible?).
It's your call on whether to call it auto or evaluate.
This just hangs, though it could just be the speed issue you were referring
to in comment 9:
In [8]: a = integrate((x**2 + 1)/(x**5 - x + 1), x)
In [9]: a
Out[9]:
⎛ ⎛
⎛ 2
3 4⎞⎞⎞
⎜ 5 3 2 ⎜ ⎜664778640
1337030496⋅t 28487726817⋅t 7986016426⋅t 121922573260⋅t ⎟⎟⎟
RootSum⎜2869⋅t + 692⋅t - 164⋅t - 25⋅t - 1, Λ⎜t, t⋅log⎜───────── + x +
──────────── - ────────────── + ───────────── - ───────────────⎟⎟⎟
⎝ ⎝ ⎝338491559
48355937 338491559 338491559 338491559 ⎠⎠⎠
In [10]: a.diff(x)
Based on the traceback when I keyboard interrupt, it seems to get stuck in
line 645 of rootoftools.py (though not in expand).
Other than that, this seems to work well.
On an unrelated note, how many more things do you plan on doing in polys11
until you rebase/merge with master and put it up for review? I would like
to release 0.7 soon after it gets merged in (along with a couple of the
Milestone-Release0.7.0 issues).
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