In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)",
Root[#^4 + 1 &, 2];
actually has three arguments, as can be seen from
% // InputForm
(* Root[1 + #1^4 & , 2, 0] *)
This is well explained in 34764. However,
((zj /. (sol[[1]] // N))[[1, 1, 1, 2, 2]]);
where sol is defined here, has only two arguments.
% // InputForm
(* Root[..., 2] *)
What criteria does Root use to determine the number of its arguments? Note that both instances of Root were generated by Solve.
FullForm? $\endgroup$ – xzczd Dec 30 '16 at 17:39Root[]related fun: if the associated polynomial equations are sufficiently complicated (e.g.Solve[{x^3 y - x y^3 + x^2 z^3 + y^5 == 1, x^5 - x^2 y^3 + y^2 z == 1, x y^2 + y z^3 + x^2 y^2 + z^2 == -1}, {x, y, z}, Reals]),Root[]takes a more elaborate form, having lists of polynomials as its first argument and a list of (apparent) indices as the second argument. $\endgroup$ – J. M. will be back soon♦ Dec 30 '16 at 17:46