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MathGroup Archive 2006

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Re: sorting list of roots af a transcendental function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65275] Re: sorting list of roots af a transcendental function
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Thu, 23 Mar 2006 06:58:40 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <dvrcdq$a6i$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <dvrcdq$a6i$1 at smc.vnet.net>, Dule <dule23 at gmx.de> wrote:

> 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?

Yes. Have a look at the RootSearch package by Ted Ersek:

  http://library.wolfram.com/infocenter/MathSource/4482/

This package returns all the roots over a specified range as a list of 
replacement rules (see also the more primitive RootsInRange function 
that appeared in "Finding Roots in an Interval" in The Mathematica 
Journal 7(2), 1998).

> 2. How can i construct a list, where the values for x, which appear 
> multiple are dropped?

Using RootSearch you will not get multiples. The simplest way of 
removing repeated entries from a list is to use Union

  Union[{a,b,c,a}]

  {a, b, c}

If entries are not exactly the same then you can use the SameTest option 
for Union.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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