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MathGroup Archive 2006

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Re: Re: sorting list of roots af a transcendental function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65287] Re: [mg65263] Re: sorting list of roots af a transcendental function
  • From: János <janos.lobb at yale.edu>
  • Date: Fri, 24 Mar 2006 00:59:44 -0500 (EST)
  • References: <dvrcdq$a6i$1@smc.vnet.net> <200603231158.GAA07742@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Mar 23, 2006, at 6:58 AM, Roger Bagula wrote:

> Dule wrote:
>> Dear group,
>>
>> for calculating a model i need values for x which are given by the
>> transcendental function Cot[x] == x/a - a/(4*x). a is a parameter  
>> 0<a<200.
>> i obtained the roots with Table and FindRoot:
>> Table[FindRoot[Cot[x] == x/a - a/(4*x), {x, i}], {i, 1, 50}]]
>>
>> I have two questions:
>> 1. Is there a better way to do this?
>> 2. How can i construct a list, where the values for x, which appear
>> multiple are dropped?
>>
>> Thanks!
>>
>
> I have a similar question of my own:
> I want to get the weights where this equation has largest roots  
> equal to
> integers:g^3-g-w[n]=0
> for prime weights:
> w[n]=Prime[n]
>
> b = Table[Table[x /. NSolve[x^3 - x - Prime[n] - 1 == 0.x][[m]],  
> {m, 1,
>                  3}], {n, 1, 10}]
> MatrixForm[b]
> c = Table[{n, Max[Table[Abs[x] /. Solve[x^3 - x -
>      Prime[n] - 1 == 0.x][[m]], {m, 1, 3}]]}, {n, 1, 20}]
> ListPlot[c]
>
> This doersn't work: it doesn't see them as Integers:
> d = Flatten[Table[{n, If [IntegerQ[
>            Max[Table[Abs[x] /.
>              Solve[x^3 -
>                  x - Prime[n] - 1 == 0.x][[m]], {m, 1, 3}]]], Max[
>                    Table[Abs[x] /. Solve[x^3 - x - Prime[n] - 1 ==  
> 0.x][[
>      m]], {m, 1, 3}]], {}]}, {n, 1, 20}], 1]
>
> That is in:
> {{1, 1.6717}, {2, 1.79632}, {3, 2.}, {4, 2.16631}, {5,
>     2.43484}, {6, 2.5483}, {7, 2.74784}, {8, 2.83714}, {9,
>      3.}, {10, 3.21447}, {11, 3.27976}, {12, 3.4611}, {13,
>      3.5719}, {14, 3.62475}, {15, 3.72594}, {16, 3.86794}, {
>      17, 4.}, {18, 4.0421}, {19, 4.16331}, {20, 4.24028}}
>
> I want output ( integer weights separated out):
> { {3, 2},  {9, 3},  {17, 4}}

Here is a newbie approach:

In[1]:=
lst = {{1, 1.6717},
     {2, 1.79632}, {3, 2.},
     {4, 2.16631},
     {5, 2.43484},
     {6, 2.5483},
     {7, 2.74784},
     {8, 2.83714}, {9, 3.},
     {10, 3.21447},
     {11, 3.27976},
     {12, 3.4611},
     {13, 3.5719},
     {14, 3.62475},
     {15, 3.72594},
     {16, 3.86794}, {17, 4.},
     {18, 4.0421},
     {19, 4.16331},
     {20, 4.24028}};

In[2]:=
Select[lst,
   FractionalPart[#1[[2]]] ==
     0 & ]
Out[2]=
{{3, 2.}, {9, 3.}, {17, 4.}}





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