Comment #1 on issue 2448 by asmeurer: integrate hangs
http://code.google.com/p/sympy/issues/detail?id=2448
It doesn't hang for me. This is what I get. By the way, the problem is
not the extra symbols, but that the first integral is cos(x)**2 and the
second one is cos(x**2)**2 (due to the z in w).
In [1]: var('L r0 R0 z')
Out[1]: (L, r₀, R₀, z)
In [2]: Iz = (z, -L/2, L/2)
In [3]: integrate(r0**2*cos(z)**2, Iz)
Out[3]:
⎛ ⎛L⎞ ⎛L⎞⎞ ⎛ ⎛L⎞ ⎛L⎞⎞
⎜ sin⎜─⎟⋅cos⎜─⎟⎟ ⎜ sin⎜─⎟⋅cos⎜─⎟⎟
2 ⎜ L ⎝2⎠ ⎝2⎠⎟ 2 ⎜L ⎝2⎠ ⎝2⎠⎟
- r₀ ⋅⎜- ─ - ─────────────⎟ + r₀ ⋅⎜─ + ─────────────⎟
⎝ 4 2 ⎠ ⎝4 2 ⎠
In [4]: w = 2*pi*z/L
In [5]: integrate(r0**2*cos(R0*z)**2, Iz)
Out[5]:
⎛ ⎛L⋅R₀⎞ ⎛L⋅R₀⎞⎞ ⎛ ⎛L⋅R₀⎞ ⎛L⋅R₀⎞⎞
⎜ sin⎜────⎟⋅cos⎜────⎟⎟ ⎜ sin⎜────⎟⋅cos⎜────⎟⎟
2 ⎜ L⋅R₀ ⎝ 2 ⎠ ⎝ 2 ⎠⎟ 2 ⎜L⋅R₀ ⎝ 2 ⎠ ⎝ 2 ⎠⎟
r₀ ⋅⎜- ──── - ───────────────────⎟ r₀ ⋅⎜──── + ───────────────────⎟
⎝ 4 2 ⎠ ⎝ 4 2 ⎠
- ────────────────────────────────── + ────────────────────────────────
R₀ R₀
In [6]: integrate(r0**2*cos(w*z)**2, Iz) # hangs
Out[6]:
L
─
2
⌠
⎮ 2
⎮ ⎛ 2⎞
⎮ 2 ⎜2⋅π⋅z ⎟
⎮ r₀ ⋅cos ⎜──────⎟ dz
⎮ ⎝ L ⎠
⌡
-L
──
2
In [7]: %timeit integrate(r0**2*cos(w*z)**2, Iz) # hangs
1 loops, best of 3: 11.3 s per loop
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