Re: Reduce command Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg128248] Re: Reduce command Mathematica*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sat, 29 Sep 2012 02:57:14 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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][[1]] &) /@ With[{n = 2}, List @@ FullSimplify[ Reduce[{ 2 n - Tanh[z] Tanh[2 n z] == 0, Re[z] == 0}, z], Element[C[1], 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[5]] + 4*Pi*C[1])}, {z -> (1/2)*I*(Pi + 4*Pi*C[1])}, {z -> (1/2)*I*Pi*(-1 + 4*C[1])}, {z -> (1/2)*I*(2*Pi - ArcCot[2/Sqrt[5]] + 4*Pi*C[1])}, {z -> (1/2)*I* (ArcCot[2/Sqrt[5]] + 4*Pi*C[1])}, {z -> (1/2)*I*(-2*Pi + ArcCot[2/Sqrt[5]] + 4*Pi*C[1])}} FullSimplify[eqn /. n -> 2 /. sol, Element[C[1], Integers]] FullSimplify::infd: Expression Tan[1/2 \[Pi] (-1+4 C[1])] Tan[2 \[Pi] (-1+4 C[1])] simplified to Indeterminate. >> FullSimplify::infd: Expression 4+Tan[1/2 \[Pi] (-1+4 C[1])] Tan[2 \[Pi] (-1+4 C[1])] 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 >

**References**:**Reduce command Mathematica***From:*Oznur Oztunc <oznr83@gmail.com>