symbolic sums of roots

[kcrisman]

See ​this sage-devel discussion, where it is pointed out that both Maxima and Sympy can return solutions to integrals using a symbolic sum of roots, e.g.

sage: f=1/(x^4+x^3+1)
sage: fm=f._maxima_()
sage: fm.integrate()
'integrate(1/(x^4+x^3+1),x)
sage: fs=f._sympy_()
sage: fs.integrate()
RootSum(229*_t**4 + 6*_t**2 + _t + 1, Lambda(_t, _t*log(-37785*_t**3/3547 - 5496*_t**2/3547 + 12979*_t/3547 + x + 691/3547)))

(Thanks to mmarco for this.)

Perhaps this shouldn't be the default return for integrals but it certainly could be useful.

[mmarco]

The object itself can be created in pynac using algebraic numbers. The problem is to handle it then. I posted an example in the sage-devel discussion.