kiraMou

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restart; with(plots); a := .8; N := 4; for k to N while k <> j do t[k] := sinh(x[k]+I*a)^N*(product(sinh(1/2*(x[k]-x[j]-(2*I)*a)), j = 1 .. N))/(sinh(x[k]-I*a)^N*(product(sinh(1/2*(x[k]-x[j]+(2*I)*a)), j = 1 .. N))) end do

.8

 

4

 

-1.000000000*sinh(x[1]+.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[2]-.8*I)*sinh((1/2)*x[1]-(1/2)*x[3]-.8*I)*sinh((1/2)*x[1]-(1/2)*x[4]-.8*I)/(sinh(x[1]-.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[2]+.8*I)*sinh((1/2)*x[1]-(1/2)*x[3]+.8*I)*sinh((1/2)*x[1]-(1/2)*x[4]+.8*I))

 

-1.000000000*sinh(x[2]+.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[2]+.8*I)*sinh((1/2)*x[2]-(1/2)*x[3]-.8*I)*sinh((1/2)*x[2]-(1/2)*x[4]-.8*I)/(sinh(x[2]-.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[2]-.8*I)*sinh((1/2)*x[2]-(1/2)*x[3]+.8*I)*sinh((1/2)*x[2]-(1/2)*x[4]+.8*I))

 

-1.000000000*sinh(x[3]+.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[3]+.8*I)*sinh((1/2)*x[2]-(1/2)*x[3]+.8*I)*sinh((1/2)*x[3]-(1/2)*x[4]-.8*I)/(sinh(x[3]-.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[3]-.8*I)*sinh((1/2)*x[2]-(1/2)*x[3]-.8*I)*sinh((1/2)*x[3]-(1/2)*x[4]+.8*I))

 

-1.000000000*sinh(x[4]+.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[4]+.8*I)*sinh((1/2)*x[2]-(1/2)*x[4]+.8*I)*sinh((1/2)*x[3]-(1/2)*x[4]+.8*I)/(sinh(x[4]-.8*I)^4*sinh((1/2)*x[1]-(1/2)*x[4]-.8*I)*sinh((1/2)*x[2]-(1/2)*x[4]-.8*I)*sinh((1/2)*x[3]-(1/2)*x[4]-.8*I))

(1)

list4 := fsolve({t[1] = -1, t[2] = -1, t[3] = -1, t[4] = -1}, {x[1], x[2], x[3], x[4]}); list4 := fsolve({t[1] = -1, t[2] = -1, t[3] = -1, t[4] = -1}, {Im(x[1]) = .5 .. 1, Im(x[2]) = .5 .. 1, Im(x[3]) = -1 .. -.5, Im(x[4]) = -1 .. -.5})

``


Download system.mw


 

Download system.mw

 

Solving a system of equations

I want to solve the following system (please see the code) for small even N=4,8,16. They said that the roots lie on the lines Im x_i = ±π/2 and they are symmetric with respect to the imaginary axis. For N=4, I tried with fsolve directly but the roots are:

 x[1] = -3.799588601-1.570796327*I,

 x[2] = -3.799588601-1.570796327*I,

 x[3] = .1196098914-1.570796327*I,

 x[4] = 1.110549099-1.570796327*I

these solutions are not valid because half of them should have +π/2 as an imaginary part, and they should be mutually distinct and also symmetric with respect to the imaginary axis. Therefore, for N=4  I am expecting solutions of these form :

x[1] = a_1-I* π/2,

x[2] = -a_1-I* π/2,

x[3] = a_1+I* π/2,

x[4] = -a_1+I* π/2,

I tried with fslove({system}, {Im(x[1]) = .5 .. 1, Im(x[2]) = .5 .. 1, Im(x[3]) = -1 .. -.5, Im(x[4]) = -1 .. -.5}) but it does not work! I do not know what should I do to make Fsolve locate the wanted solutions. Thanks in advance!

 

I am not familiar with mathematica syntax. I have this code which is written .np and I would like to translate it efficiently to Maple syntax.I tried FromMmaNotebook but it is not helpful for me. I would be grateful if you would give me a little help me translate the code. I attached the code as diagon.txt (you can change .txt with .nb)

Thank you in advance!diagon.txt

 

Hey!
I am using the solve function and I get the following form of the result :

rootsq0 := {z = 9.096986124+3.141592654*I}, {z = 1.138376998+3.141592654*I}, {z = .3074241220+3.141592654*I}, {z = .5854971300+3.141592654*I}, {z = -2.519351300+3.141592654*I}, {z = -5.138371980+3.141592654*I}, {z = -1.759344122+3.141592654*I}, {z = -0.9698634104e-1+3.141592654*I}

I want to convert rootsq0 into a list [9.096986124+3.141592654*I, 1.138376998+3.141592654*I, ...]. So, I would like to remove {} and z=. Any suggestions are welcome! :)


 

Download analy_numer.mw

 

 

Hello,
I am trying to compute the convolution integral numerically and compare the result with the analytic result. My numerics is giving terrible results:

Hey everyone,

f_1 and f_2  are satisfying the set of non-linear integral equations I have attached to this message.
I know that I need to solve them numerically by iterations. Probably, the first guest of the function f_1 and f_2  is the driving term. a is just a parameter which can be fixed (I guess smaller than \pi/4). * is the convolution product and k is the momentum space parameter. I learnt that in order to solve them I should solve them in the Fourier space. I know also that I need to discretize these function in the “real ” space between {-L,+L} before applying the FFT or one of its relatives. Thank you for any suggestions or leads.

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