       Re: Reduce command Mathematica

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• Subject: [mg128264] Re: Reduce command Mathematica
• From: Dana DeLouis <dana01 at me.com>
• Date: Mon, 1 Oct 2012 02:23:06 -0400 (EDT)
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```> Reduce[2 n - Tanh[z] Tanh[2 n z] == 0, z]

Hi.  I can't get this to work either.
Here's a technique when working with 1 equation, and 2 variables.
You are looking for the contour of 0.
(Mouse over the 0 line in the chart for confirmation)

equ=2 n-Tanh[z] Tanh[2 n z];

ContourPlot[
equ,{n,-2,2},{z,-3,3},

Contours->Range[-4,4],
CoordinatesToolOptions->Automatic,
FrameLabel->{"n","z"}
]

As you can see, the obvious solution is n=0.
But, there is also a solution near the top and bottom with  -.5 < n <+.5

Sometimes, putting further constraints works, but it doesn't work here:

Reduce[{equ == 0 , -1/2 < n < 1/2}, z, Reals]

<< No Luck >>

For example, if n = 1 / 4, then it won't catch the solution for z of Log[2+Sqrt]  :

equ /. {n -> 1 / 4,  z-> Log[2+Sqrt]}   //FullSimplify

0

Hopefully, someone can jump in with a better idea:

= = = = = = = = = =
HTH  :>)
Dana DeLouis
Mac & Mathematica 8
= = = = = = = = = =

On Thursday, September 27, 2012 11:06:13 PM UTC-4, Oznur Oztunc wrote:
> Hi,
>
> I have the following system.Why isn't Reduce able to find the solution? I have tried some command (Solve). But I can't be solve this equation.
>
> Reduce[2 n - Tanh[z] Tanh[2 n z] == 0, z]
>
>
>
> Regards, and thanks to all who will answer!
>
> =D6snur =D6stun=E7

```

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