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MathGroup Archive 2002

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Re: Approximation of complex solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37428] Re: [mg37422] Approximation of complex solutions
  • From: BobHanlon at aol.com
  • Date: Mon, 28 Oct 2002 03:40:53 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 10/27/2002 7:53:03 AM, not at for.you writes:

>I would like to have mathematica attempt to find complex solutions to the
>equation:
>
>cos(cos(cos(cos x))) = sin(sin(sin(sin x)))
>
>It always tells me the variables appear to be related in a non-algebraic
>way.  Is there a way to have it approximate these solutions?
>

Clear[f];

f[x_] := Cos[Cos[Cos[Cos[x]]]] - Sin[Sin[Sin[Sin[x]]]];

Off[General::ovfl, General::unfl, 
    FindRoot::frnum, FindRoot::cvnwt];

Union[Select[Flatten[
      Table[{x, Conjugate[x]} /. 
          FindRoot[f[x], {x, xr + I*xi},
            WorkingPrecision -> 25],
        {xr, -Pi/2, Pi/2, Pi/16},
        {xi, Pi/16, Pi/2, Pi/16}]],
    Abs[f[#]] < 10^-15 &],
  SameTest -> (Abs[#1 - #2] < 10^-12 &)]


Bob Hanlon


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