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