Hi Aaron!
On Thu, Aug 5, 2010 at 2:01 PM, Aaron S. Meurer <asmeu...@gmail.com> wrote:
> (copied from issue 2010)
>
> I have ready in my integration3 branch a prototype risch_integrate()
> function, that is a user-level function for the full Risch Algorithm I have
> been implementing this summer. Pull from
> http://github.com/asmeurer/sympy/tree/integration3
This is just excellent!
I would like to invite everyone to try this. (Read Aaron's email above
for things to try and not to try yet.) So here are some tougher cases:
In [1]: risch_integrate(1/(x**8+1), x)
[hangs]
In [4]: cancel(risch_integrate(1/(x**9+1), x).diff(x))
Out[4]:
d ⎛ ⎛ 6 3 ⎞⎞ 3 d ⎛
1 + 3⋅──⎝RootSum⎝531441⋅t + 729⋅t + 1, Λ(t, t⋅log(x + 9⋅t))⎠⎠ + 3⋅x ⋅──⎝Root
dx dx
──────────────────────────────────────────────────────────────────────────────
3
3 + 3⋅x
⎛ 6 3 ⎞⎞
Sum⎝531441⋅t + 729⋅t + 1, Λ(t, t⋅log(x + 9⋅t))⎠⎠
──────────────────────────────────────────────────
It should be equivalent but it's a bit messy. Maybe we need to
implement some symbolic manipulation of RootSum().
In [18]: risch_integrate(sqrt(1+exp(x)), x)
NotImplementedError: Couldn't find an elementary transcendental
extension for (1 + exp(x))**(1/2). Try using a manual extension with
the extension flag.
[18] is probably not supported yet.
Otherwise it works great. I wasn't able to make it break.
Ondrej
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