Bill,
I tried it, but no go: Evaluation of Squint leads to an unsucessful evaluation of NSolve[q == 0,boa, WorkingPrecision -> 69] and "boa" is undefined at that point (* while inside the local variables definitions of Block *) This rather constricts my Mma 4.0 and it closes down. Does it really run ok on Mma8.0?
Wouter.
AARRGGHH!! I'm a careless idiot. This Squint[q_] := Block[{rts = #[[1, 2]] & /@ NSolve[q == 0, WorkingPrecision -> 69],boa, foos, S3 = Permutations[Range[3]]}, foos = InverseFourier[ rts[[#]]/Sqrt[5]]^5 & /@ (Join[{}, #] & /@ (Permutations[ Range[5]])); foos = (fifth[Together[#[[1, 2]]]] &) /@ Solve[0 == Rationalize[ Expand[Times @@ (# - Rest[foos[[Ordering[ Denominator[Rationalize[Plus @@ #, 9.^-69]] & /@ foos, 1][[1]]]]])]]]; boa = Rationalize[Plus @@ rts/5]; Evaluate[boa + foos.Select[ Exp[2*I*\[Pi]*Join[{}, #] & /@ Permutations[Range[4]]/5], MemberQ[Chop[#.foos + boa - rts], 0] &][[1]]^#] &] fifth[z_] := If[Sign[z] == -1, -(-z)^(1/5), z^(1/5)] should work as was advertised, but alas, I've found a screw case: Squint[9 - 84 x - 80 x^2 + 1024 x^3 - 256 x^4 - 1024 x^5] which should give radicals for Cos[2*Pi/41]*Cos[4*Pi/41] - Sin[5*Pi/82]*Cos[5*Pi/41], gives nonsense which is only a correct root for %@1 . I may have to abandon condensing all five roots into an f[Range[5]] and just return all five in a list. Apologies. And thanks for trying it! --rwg