Comment #5 on issue 1280 by mattpap: integrate(1/((a-x)*(b-x)), x) is
giving too complex results (probably correct)
http://code.google.com/p/sympy/issues/detail?id=1280
I fixed this in polys12. The problem was with initial preprocessing of the
input fraction in apart() (deg(p) < deg(q) after preprocessing didn't hold).
In [1]: var('a,b,c')
Out[1]: (a, b, c)
In [2]: f = (-2*a*b*x - b**2 - a**2*x**2 + a*c**2*x**2 + 2*b*x*c**2 +
4*b*c*x**2 + 2*b*x**3 + 2*a*c*x**3 + a*x**4)/(b**2*c**2 + b**2*x**2 +
a**2*c**2*x**2 + 2*c*x*b**2 + 2*a*b*x*c**2 + 4*a*b*c*x**2 + 2*a*b*x**3 +
2*c*a**2*x**3 + a**2*x**4)
In [3]: apart(f, x)
Out[3]:
2
1 1 b
─ - ──────── - ────────────
a 2 2
(c + x) a⋅(b + a⋅x)
In [4]: factor(_) == factor(f)
Out[4]: True
In [5]: apart(f, x, full=True)
Out[5]:
2 2 ⎛ 2 3⎞ 2 2 ⎛ 2 3⎞
b⋅a - c⋅b c⋅⎝- b + a ⎠ b⋅a - c⋅b b⋅⎝- b + a ⎠
───────────── - ───────────── ───────────── - ─────────────────
2 3 2 3 2 3 ⎛ 2 3⎞
- b⋅a + c⋅a - b⋅a + c⋅a - b⋅a + c⋅a a⋅⎝- b⋅a + c⋅a ⎠ 1
───────────────────────────── + ───────────────────────────────── + ─
2 2 a
(c + x) ⎛ b⎞
⎜x + ─⎟
⎝ a⎠
In [6]: factor(_) == factor(f)
Out[6]: True
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