Re: Mathematica plaintext output
- To: mathgroup at smc.vnet.net
- Subject: [mg107403] Re: Mathematica plaintext output
- From: Simon <simonjtyler at gmail.com>
- Date: Thu, 11 Feb 2010 08:09:32 -0500 (EST)
- References: <hl0le4$r88$1@smc.vnet.net>
When the radical form of the solution is too complicated (or unkown/
nonexistent), Mathematica uses Root.
To quote from the Documentation Center:
For linear and quadratic polynomials f[x], Root[f,k] is
automatically reduced to explicit rational or radical form.
For other polynomials, ToRadicals can be used to convert to
explicit radicals.
So, in this case ToRadicals works just fine:
In[1]:= Eigenvalues[{{1,2,3},{2,6,4},{3,4,5}}]//ToRadicals
Out[1]= {4+(6 2^(2/3))/(17+I Sqrt[143])^(1/3)+(2 (17+I
Sqrt[143]))^(1/3),4-(3 2^(2/3) (1-I Sqrt[3]))/(17+I Sqrt[143])^(1/3)-
((1+I Sqrt[3]) (17+I Sqrt[143])^(1/3))/2^(2/3),4-(3 2^(2/3) (1+I
Sqrt[3]))/(17+I Sqrt[143])^(1/3)-((1-I Sqrt[3]) (17+I
Sqrt[143])^(1/3))/2^(2/3)}
Simon
On Feb 11, 6:16 pm, nevjernik <hajde... at mijenjamo.planetu> wrote:
> Maybe this is trivial one, but I don't know how to interpret output of
> following:
>
> In:
> Eigenvalues[{{1, 2, 3}, {2, 6, 4}, {3, 4, 5}}]
>
> Out:
> {Root[12 + 12 #1 - 12 #1^2 + #1^3 &, 3],
> Root[12 + 12 #1 - 12 #1^2 + #1^3 &, 2],
> Root[12 + 12 #1 - 12 #1^2 + #1^3 &, 1]}
>
> WolframAlpha gives reasonable solutions:
>
> lambda_1 = 4+(6 2^(2/3))/(17+i sqrt(143))^(1/3)+(2 (17+i
> sqrt(143)))^(1/3)
> lambda_2 = 4-(3 2^(2/3) (1-i sqrt(3)))/(17+i sqrt(143))^(1/3)-((1+i
> sqrt(3)) (17+i sqrt(143))^(1/3))/2^(2/3)
> lambda_3 = 4-(3 2^(2/3) (1+i sqrt(3)))/(17+i sqrt(143))^(1/3)-((1-i
> sqrt(3)) (17+i sqrt(143))^(1/3))/2^(2/3)
>
> And below that, there is "mathematica plaintext output":
>
> {Root[12 + 12 #1 - 12 #1^2 + #1^3 & , 3, 0], Root[12 + 12 #1 - 12 #1^2
> + #1^3 & , 2, 0], Root[12 + 12 #1 - 12 #1^2 + #1^3 & , 1, 0]}
>
> Ok, it is obviously some plaintext output of result, but how one can
> deal with it in mathematica?
>
> Thanks
>
> --
> ne vesele mene bez vas
> utakmice nedjeljom