Clemens Heuberger wrote:
> x = polygen(QQ)
> equation = -960000000*x^7 + 416000000*x^6 - 66400000*x^5 + 5600000*x^4
> - 280000*x^3 + 8400*x^2 - 140*x + 1 roots = equation.roots(QQbar)
> a_root = roots[-1][0]
> abs_root = abs(a_root)
[...]
> Is this expected behaviour?

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Well, QQbar has a number of well-known but not yet fixed efficiency
problems...
> I am intersted in the smallest root(s) in
> absolute value only, any suggestions for achieving that in less time?
You could perhaps compute a polynomial whose roots include the zÂ·conj(z)
for all roots z of equation (e.g., with a resultant), factor that
polynomial, and sort its root numerically while increasing the
precision until you can tell which of the factors correspond to
dominant roots. Or something like that :-/
--
Marc
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