       Re: Reduce command Mathematica

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• Subject: [mg128248] Re: Reduce command Mathematica
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 29 Sep 2012 02:57:14 -0400 (EDT)
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• References: <20120928024928.42056685E@smc.vnet.net>

```eqn = 2 n - Tanh[z] Tanh[2 n z] == 0;

Reduce[{eqn, Element[n, Integers],
Element[z, Reals]}, z]

n == 0 && (z == 0 || (z \[Element] Reals && z != 0))

eqn /. n -> 0

True

Or for a specific value of n, say n=2:

sol = ((Solve[#, z][] &) /@
With[{n = 2},
List @@
FullSimplify[
Reduce[{
2 n - Tanh[z] Tanh[2 n z] == 0,
Re[z] == 0}, z],
Element[C, Integers]]])

Reduce::ztest: Unable to decide whether numeric quantities
{Re[Log[-Sqrt[1/3 (2+Times[<<2>>])]]],Re[Log[Sqrt[1/3 (2-I
Power[<<2>>])]]],Re[Log[-Sqrt[1/3 (2+Times[<<2>>])]]],Re[Log[Sqrt[1/3
(2+I Power[<<2>>])]]]} are equal to zero. Assuming they are. >>

{{z -> (1/2)*I*
(-ArcCot[2/Sqrt] +
4*Pi*C)},
{z -> (1/2)*I*(Pi + 4*Pi*C)},
{z -> (1/2)*I*Pi*(-1 + 4*C)},
{z -> (1/2)*I*(2*Pi -
ArcCot[2/Sqrt] +
4*Pi*C)},
{z -> (1/2)*I*
(ArcCot[2/Sqrt] +
4*Pi*C)},
{z -> (1/2)*I*(-2*Pi +
ArcCot[2/Sqrt] +
4*Pi*C)}}

FullSimplify[eqn /. n -> 2 /. sol,
Element[C, Integers]]

FullSimplify::infd: Expression Tan[1/2 \[Pi] (-1+4 C)] Tan[2 \[Pi]
(-1+4 C)] simplified to Indeterminate. >>

FullSimplify::infd: Expression 4+Tan[1/2 \[Pi] (-1+4 C)] Tan[2
\[Pi] (-1+4 C)] simplified to Indeterminate. >>

{True, True, Indeterminate == 0, True, True, True}

Bob Hanlon

On Thu, Sep 27, 2012 at 10:49 PM, Oznur Oztunc <oznr83 at gmail.com> 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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