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

*To*: mathgroup at smc.vnet.net*Subject*: [mg65294] Re: [mg65263] Re: sorting list of roots af a transcendental function*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 24 Mar 2006 00:59:55 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

{#[[1]], x/.#[[2]]}&/@ Select[ Table[{n, ToRules[ Reduce[x^3-x-Prime[n]==1, x, Integers]]}, {n, 1, 20}], Length[#]==2&] {{3, 2}, {9, 3}, {17, 4}} Bob Hanlon > > From: Roger Bagula <rlbagulatftn at yahoo.com> To: mathgroup at smc.vnet.net > Subject: [mg65294] [mg65263] Re: sorting list of roots af a transcendental function > > 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}} > >