Partial fraction decomposition over the reals or complex
I am trying to get partial fraction decomposition (for integration) but over the complex numbers. For example, the denominator (x^2+1)*(x^3-2) should produce five fractions. I have experimented a bit with coercion but didn't manage to get anything. For example:
f=x^3-2 R=CC['x'] ff=R(f) factor(f); factor(ff)
x^3 - 2 (x - 1.25992104989487) * (x + 0.629960524947437 - 1.09112363597172*I) * (x + 0.629960524947437 + 1.09112363597172*I)
so far so good (except for decimals). But
1/(x^3 - 2), and
Traceback (click to the left of this block for traceback) ... AttributeError: 'FractionFieldElement_1poly_field' object has no attribute 'partial_fraction'
On the other hand,
(0, [0.209986841649145/(x - 1.25992104989487), (-0.104993420824573 + 0.181853939328620*I)/(x + 0.629960524947437 - 1.09112363597172*I), (-0.104993420824573 - 0.181853939328620*I)/(x + 0.629960524947437 + 1.09112363597172*I)])
which is correct but not exact. Is there a command to get an exact decomposition over C, or am I stuck with having to set and solve a linear system?