10 Feb
2011
10 Feb
'11
3:48 p.m.
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