Updates:
Labels: -Milestone-Release0.7.0 Milestone-Release0.7.1
Comment #4 on issue 1280 by asmeurer: 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 was implementing this in my branch when I found a bug in apart:
In [47]: print r
(-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 [48]: r
Out[48]:
2 2 2 2 2 2 2
3 3 4
-2⋅a⋅b⋅x - b - a ⋅x + a⋅c ⋅x + 2⋅b⋅x⋅c + 4⋅b⋅c⋅x + 2⋅b⋅x +
2⋅a⋅c⋅x + a⋅x
────────────────────────────────────────────────────────────────────────────────────────────
2 2 2 2 2 2 2 2 2 2
3 2 3 2 4
b ⋅c + b ⋅x + a ⋅c ⋅x + 2⋅c⋅x⋅b + 2⋅a⋅b⋅x⋅c + 4⋅a⋅b⋅c⋅x + 2⋅a⋅b⋅x +
2⋅c⋅a ⋅x + a ⋅x
In [49]: cancel(apart(r, x))
Out[49]:
2 2 2 2 2 2 2
3 3
-2⋅a⋅b⋅x - b - a ⋅x + a⋅c ⋅x + 2⋅b⋅x⋅c + 4⋅b⋅c⋅x + 2⋅b⋅x +
2⋅a⋅c⋅x
────────────────────────────────────────────────────────────────────────────────────────────
2 2 2 2 2 2 2 2 2 2
3 2 3 2 4
b ⋅c + b ⋅x + a ⋅c ⋅x + 2⋅c⋅x⋅b + 2⋅a⋅b⋅x⋅c + 4⋅a⋅b⋅c⋅x + 2⋅a⋅b⋅x +
2⋅c⋅a ⋅x + a ⋅x
In [50]: cancel(apart(r, x)) == r
Out[50]: False
In [51]: cancel(apart(r, x) - r)
Out[51]:
4
-a⋅x
────────────────────────────────────────────────────────────────────────────────────────────
2 2 2 2 2 2 2 2 2 2
3 2 3 2 4
b ⋅c + b ⋅x + a ⋅c ⋅x + 2⋅c⋅x⋅b + 2⋅a⋅b⋅x⋅c + 4⋅a⋅b⋅c⋅x + 2⋅a⋅b⋅x +
2⋅c⋅a ⋅x + a ⋅x
By the way, I was running into some problems implementing this
(automatically calling apart in integrate) in polys12 that didn't exist in
my branch, so I think we will have to postpone this issue (and if it always
requires my branch to work, then I don't hold much hope for the 0.7.1
release, as I don't think it will be ready to merge by then).
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