Re: Usage of #1

*To*: mathgroup at smc.vnet.net*Subject*: [mg96322] Re: Usage of #1*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 11 Feb 2009 05:23:53 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <gmrmdk$9uk$1@smc.vnet.net>

In article <gmrmdk$9uk$1 at smc.vnet.net>, Nandhini <nandhini.gopalan at gmail.com> wrote: > Im very new to mathematica. I have got a result where im getting > something like "Root[1+a #1+a^2 #1^5 &,1]. i wud like to know how else > i can write it. i dont want the #1 to b displayed. is tehre any > alternative. Plz help me out of this. A Root[poly, n] object is an exact representation of the nth root of the polynomial poly (written as an pure function, that is why you see the # character or Slot[]). Note that the polynomial expressed as a pure function in the Root[] object is the same as the original polynomial fed to the Solve[] function. To get the corresponding numerical values, one can use the N[] function, and, in some cases, one can try to get a representation with radicals by applying the ToRadicals[] function. For instance, In[1]:= Solve[x^5 + 2 x + 1 == 0, x] Out[1]= 5 5 {{x -> Root[1 + 2 #1 + #1 & , 1]}, {x -> Root[1 + 2 #1 + #1 & , 2]}, 5 5 {x -> Root[1 + 2 #1 + #1 & , 3]}, {x -> Root[1 + 2 #1 + #1 & , 4]}, 5 {x -> Root[1 + 2 #1 + #1 & , 5]}} In[2]:= % // N Out[2]= {{x -> -0.486389}, {x -> -0.701874 - 0.879697 I}, {x -> -0.701874 + 0.879697 I}, {x -> 0.945068- 0.854518 I}, {x -> 0.945068+ 0.854518 I}} In[3]:= ToRadicals[Root[#^3 + # + 11 &, 1] + Root[#^5 - 2 &, 3]] Out[3]= 1 1/3 (- (-99 + Sqrt[9813])) 4/5 1/5 2 1/3 2 (-1) 2 - (--------------------) + ------------------------- 3 (-99 + Sqrt[9813]) 2/3 3 Regards, --Jean-Marc