I am running

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)
%time abs_root.minpoly()

and am surprised that it takes approx. three minutes.


sorted(roots, key=lambda r: abs(r[0]))

then still takes 8 Minutes.

Is this expected behaviour? I am intersted in the smallest root(s) in absolute 
value only, any suggestions for achieving that in less time?



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