in mathematica 8: c = (1 + Sqrt[3] + Sqrt[2] 3^(3/4))^(1/3)/(Sqrt[3] - 1)^(1/6); FullSimplify[c] = (2*(7 + 3*Sqrt[3] + Sqrt[72 + 42*Sqrt[3]]))^(1/6) which has even fewer radicals than the one given just below. of course, one can always ask, what does "simplest" mean? bob --- Bill Gosper wrote:
Condensing a published value of Theta_4(0,-e^(-6 pi)), Corey's nascent denester uncovered this curious simplification: (1 + Sqrt[3] + Sqrt[2] 3^(3/4))^(1/3)/(Sqrt[3]-1)^(1/6) -> (1 + Sqrt[3] + Sqrt[2] 3^(1/4))^(1/2)/2^(1/6)
It also reduces the nesting depth of LambdaStar[5] := Sqrt[ModularLambda[Sqrt[-5]]]:
In[249]:= DenestRadicals[Sqrt[1/2 - Sqrt[Sqrt[5] - 2]]] [...] In[250]:= ToRadicals[%]
Out[250]= (1 - Sqrt[5] + 3 Sqrt[-2 + Sqrt[5]] + (-2 + Sqrt[5])^(3/2))/(2 Sqrt[2])
which canNOT be done by working outward from the innermost. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun