thank you very much.

Best regards

@Markiyan Hirnyk

Here's what i have:

LagrangeMultipliers(f(x, y), [ ], [x, y])

[2*Pi*_Z55, 2*Pi*_Z54], [(2/3)*Pi+2*Pi*_Z55, -(2/3)*Pi+2*Pi*_Z54], [-(2/3)*Pi+2*Pi*_Z55, (2/3)*Pi+2*Pi*_Z54], [4*Pi*_Z49-Pi, 2*Pi*_Z47], [4*Pi*_Z48+Pi, 2*Pi*_Z47], [2*Pi*_Z51, 4*Pi*_Z52-Pi], [2*Pi*_Z50, 4*Pi*_Z53+Pi], [2*Pi*_Z45+Pi, 2*Pi*_Z46+Pi]

But i want it for x=0..2Pi and y=0..2Pi. How can i do that?

How can i use this command wihout constraints? I only find examples in the documentation using constraints g(x), h(x), etc?

Thank you in advance.

@acer 

The visualization of the discontinuities is also very interesting.

Thanks a lot for helping me solving this problem!

@_Maxim_ 

In other words, i have to find the discontinuities in the graphic. I'll try to visualize the situation in 2 dimensions.

img049.pdf

Sorry, I meant: How can i find the intervals on the z-axis I_j as shown in my picture?

@_Maxim_ 

Here is my original matrix

M := `<|>`(`<,>`(2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0), `<,>`(-1, 4, -1, 0, -1, 0, 0, 0, 0, 0, -exp(-I*x)), `<,>`(0, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0), `<,>`(-1, 0, 0, 4, -1, 0, -exp(I*y), -1, 0, 0, 0), `<,>`(0, -1, 0, -1, 4, -1, 0, 0, -1, 0, 0), `<,>`(0, 0, -1, 0, -1, 4, -1, 0, 0, -1, 0), `<,>`(0, 0, 0, -exp(-I*y), 0, -1, 2, 0, 0, 0, 0), `<,>`(0, 0, 0, -1, 0, 0, 0, 2, -1, 0, 0), `<,>`(0, 0, 0, 0, -1, 0, 0, -1, 4, -1, -1), `<,>`(0, 0, 0, 0, 0, -1, 0, 0, -1, 2, 0), `<,>`(0, -exp(I*x), 0, 0, 0, 0, 0, 0, -1, 0, 2))

i´m trying now to bring lambda_1=2 in my graphic which already contains all the other 9 eigenvalues we were talking about. And after that my program has to calculate the spectrum of my matrix. I found the command GraphSpectrum but i don't think that this would help.

Thank you very much (all of you).

How can i plot all 11 eigenvalues in one graphic? lambda_1=2 (double) and the others 9. I plot the 9 eigenvalues with the command from vv3082. Once i plot all the eigenvalues i have to determine the spectrum. The spectrum is given by the union of all intervalls (sepectral bands) on the z-axis.  Here´s what i have:

R := proc (i) options operator, arrow; RootOf(_Z^9-28*_Z^8+328*_Z^7-2088*_Z^6+(-2*cos(y)-2*cos(x)+7852)*_Z^5+(28*cos(y)+28*cos(x)-17768)*_Z^4+(-152*cos(y)-152*cos(x)+23632)*_Z^3+(408*cos(y)+408*cos(x)-17232)*_Z^2+(-12*cos(x)*cos(y)-540*cos(y)-540*cos(x)+5844)*_Z+32*cos(x)*cos(y)+256*cos(y)+256*cos(x)-544, index = i) end proc; plot3d([seq(R(i), i = 1 .. 9)], x = 0 .. 2*Pi, y = 0 .. 2*Pi)

?Between 5 and 8 you can see a sort of an arrow in the middle of the surfaces?

Thank you in advance.

@vv

Alright, so i can plot them all with the same command as you did for the first two eigenvalues?

@Kitonum 

okay but my parameters x and y are defined on the interval [0,2*Pi]. Any idea? More precisly, i have to plot the eigenvalues lambda_k(x,y) with implicitplot.

Thank you again