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http://wiki.axiom-developer.org/309PartialFractionWithUnknownConstants/diff
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This example is from Ulrich Schwardmann: Computeralgebra-Systeme, 
Addison-Wesley, 1995, p127f.
It tries to compute a partial fraction of a fraction with unknown constants.
The result is not the expected partial fraction decomposition, and does not 
seem to have any other senseful
interpretation (it is q/x).

Following is a verification of the partial fraction that macsyma computes.

\begin{axiom}
q:=(x+a)/(x*(x**3+(b+c)*x**2+b*c*x))
partialFraction(q,x)

(c-a)/((c^3-b*c**2)*(x+c))-(b-a)/((b**2*c-b**3)*(x+b))+((b-a)*c-a*b)/(b**2*c**2*x)+a/(b*c*x**2)
 - q

\end{axiom}

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