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These are replies submitted by Alger


Yes, it is less time and memory consuming to use Eignevectors(V) and apply sqrt to the result than using MatrixPower. Thank you.

I corrected also the repetition in matrix inversion.

But, I should give high Digits for large value for N in this case also to get accurate results.

I will also investigate the position of the command Digits in the code.

When you have time, please give me other ideas to improve the computation.

Best regards




Maple 18 gives the same error. 

Maple 15 gives the solution with no problem.

@Alejandro Jakubi 

Yes, I think the two environnements are differents (Maple and Matlab).

I use generally Maple for symbolic calculations (I appreciat it) and Matlab for numerical calculations. From the answers, I think it is simple to continue to do that.

I wanted to do all my calculations by Maple.

Thank you

@acer Thank you acer

Yes, it is what I want. It work well.

Thank you again


@Kitonum Thank you

But, I am interesting in the polar plot as given in:




Now, I do not know if it is possible to correct the axis as explained in my above post.



When we plot(cos(theta),theta=0..2*Pi), theta vary from 0 to 2*Pi in the X axis and cos(theta) vary from -1 to 1 in the Y axis.

When we plot the function cos(theta) with polar coordinates as:



The X axis and Y axis varies from -6 to 6. These axis represent the function R+cos(theta).

Is it possible to remove theses axis which correspond to R+cos(theta) and replace them with new axis X and Y where origines are at the radius R.

From the polar plot, I want to get in the figure, 0 replaced by -3, 2 by -2 and 4 by -1, to get the variation of cos(theta) between -1 and 1.

I hope it is clear now.



Is it possible to get on the axis of ordinate only the magnetude of the function cos(theta) and not R+cos(theta) ?

Thank you

@Carl Love 

Yes, this is what I want

Thank you


Yes your first code do the work (sorry). I have not understand the effect of the frequency.

I am very happy, thank you 

@acer : Thanks for the answer:

I want to plot a function where the axis of abscisse theta is the radius R (for example cos(theta)). As in the figure below in red.








@Kitonum Thank for the answer.

But, I want plot the function cos(theta) where the axis theta of the function is represented by the contour (perimeter) of radius R (not inside the circle). I do not know if my explanations are good.


Thank you

The command

plots:-matrixplot( Y, heights=histogram, gap=0.5,
                   orientation=[-55,55,0], labels=["","",""] );

 is what I want.

@Markiyan Hirnyk 

I have Maple 18 and I can not find the command.

dataplot does not exists in Maple 18

@Markiyan Hirnyk @Carl Love 8142: Thank you

Yes, OrthogonalExpansions package can be used to determine 2D Fourier series coefficients. Now, I can read the help from Maple18.

From DiscreteTransforms, are matrices (3) and (4) represent the coefficients of 2D Fourier expansion ?  The matrices are the Fourier transform and we need to do an inverse Fourier transform to get the coefficients ?

Can you help me to plot the 2D Fourier expansion function issued from Discrete Transforms with the original function f(x,y).

Thank you

I am using OrthogonalExpansion currently. It can not give the Fourier expansion from 2D Fourier transform.

I want to use 2D Fourier transform to obtain the coefficients of the 2D Fourier expansion of a surface as done in for curves.


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