Fred wrote: << On 12/17/08, rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> wrote:
... Thereby reenacting one of my favorite denestings:
1/5 3/5 3/5 2/5 1/5 2/5 3/5 1/5 1/3 - 2 3 + 2 3 + 3 + 2 (3 - 2 ) = ------------------------------------- , 2/3 5
a major simplification that looks anything but.
Indeed! u := 3^(1/5); v := 2^(1/5); w := 5^(1/3); l := (u^3 - v)^1/3; r := (u + v^2 - v*u^3 + v^3*u^2)/w^2; evalf(l - r); # -.6607822845 ?!
Mathematica gives a different result: <<n[1]:= u = 2^(1/5) 1/5 Out[1]= 2 In[2]:= v = 3^(1/5) 1/5 Out[2]= 3 In[3]:= w = 5^(1/3) 1/3 Out[3]= 5 In[4]:= x = (v^3 - u)^(1/3) 1/5 3/5 1/3 Out[4]= (-2 + 3 ) In[5]:= y = (-u v^3 + u^3 v^2 + v + u^2)/w^2 2/5 1/5 3/5 2/5 1/5 3/5 2 + 3 + 2 3 - 2 3 Out[5]= ----------------------------------- 2/3 5 In[6]:= N[x-y] -16 Out[6]= -2.22045 10
--Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele