Updates:
Cc: mattpap
Labels: Polynomial
Blockedon: 1949
Comment #4 on issue 2010 by asmeurer: Integration with the full Risch
Algorithm
http://code.google.com/p/sympy/issues/detail?id=2010
So there is a nasty bug from polys10:
In [1]: c
Out[1]: Poly(0*_t0 + (1 + x + x*(1 + x) - (1 + x)**2)/(1 + x)**2, _t0,
domain='ZZ(x,1 + x)')
In [2]: c.as_basic()
Out[2]: (1 + x + x*(1 + x) - (1 + x)**2)/(1 + x)**2
In [3]: c.as_basic().expand()
Out[3]: 0
In [4]: c.is_zero
Out[4]: False
It's hard to reproduce in the interpreter, but it doesn't happen in polys11
because that seems to have disbanded the strange domain='ZZ(x,1+x)'. I
bisected it down to the new options manager. The incorrect result in [4]
was causing risch_integrate() to incorrectly report that some integrals are
non-elementary. For example, risch_integrate(diff(exp(2*x**2)*log(x)*log(x
+ 1), x), x) (this requires some other changes that I will commit very
soon). That domain stuff was also causing serious slowdowns in some cases,
where the size of the rational coefficients of a Poly would explode after
only a few iterations through some routine.
Therefore, I decided to go ahead and brave the merge into polys11. It was
very difficult, mostly because of the code that was moved into different
files, but I managed to complete it. The merge commit is at
http://github.com/asmeurer/sympy/commit/9b252e90bd4454f6bd2e27ed3e6e4b0d99a719e0.
The changes there should be useful for whenever you cherry-pick the
remaining poly-related commits from integration3 over polys11, since most
of them are in code that is now in a new file.
The good news is that, with those other changes I mentioned,
risch_integrate(diff(exp(2*x**2)*log(x)*log(x + 1), x), x) now works.
Also, I can now take advantage of some of the other fixes in polys11, like
Poly.mul_ground(). And judging the fixes I had to make, it was going to be
a tough merge whether I waited or not.
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