Hi,
In Sage 9.0.beta8 we have
sage: a = var('a')
sage: integrate(1/(x^4 + x^2 + a), x)
...
AttributeError: 'RootSum' object has no attribute '_sage_'
The same error occurs in Sage 8.9, but not in Sage 8.8 (and below). In Sage
8.8, we have instead:
sage: a = var('a')
sage: integrate(1/(x^4 + x^2 + a), x)
integrate(1/(x^4 + x^2 + a), x)
Note that RootSum is a SymPy object. Actually, in Sage 9.0.beta8, forcing
the algorithm to 'maxima' yields the same result as in Sage 8.8:
sage: integrate(1/(x^4 + x^2 + a), x, algorithm='maxima')
integrate(1/(x^4 + x^2 + a), x)
So it seems that since Sage 8.9, when integrate() is not capable to find an
answer via Maxima, it tries SymPy but is not capable to translate the
result back to Sage. I could not find a ticket about this. Shall I open one?
Eric.
PS: for the record, a primitive of 1/(x^4 + x^2 + a) is
sage: b = sqrt(1 - 4*a)
sage: f = sqrt(2)/b*(arctan(sqrt(2)*x/sqrt(1 - b))/sqrt(1 - b) -
arctan(sqrt(2)*x/sqrt(1 + b))/sqrt(1 + b))
as we can check:
sage: diff(f, x).simplify_full()
1/(x^4 + x^2 + a)
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