The error message means rhs was passed a number and not an equation, suggesting sigma[qq] is not an equation. You have not given all the code, so you will need to upload your worksheet using the green up-arrow in the Mapleprimes editor for some more specific help.

It works in 1-D without the extra parentheses, which are not in your code region versions. 

CP2 := (X, Y) ->local  x,y; {seq(seq([x, y], y = Y), x = X)};

Edit: The code edit region codes and 1-D codes should work identically. 2-D has not kept up with recent additions to the Maple language, so my workaround is just to use 1-D (or in this case leave out the local declaration and ignore the warnings)

If you remove the 0.00005..0.00015 from the plot, you see the curves are all close to 1-eta, and there was nothing to see in the vertical range you specified. Of course I can't comment on why the parameters don't give what you were expecting.

There was earlier comment on related issues here and here. The conclusion seems to be high Digits (pehaps 40) are frequently required. If you have a nice matrix (normal or perhaps even just diagonalizable), you can just do the function on the eigenvalues and bypass Maple's routine. But in your case you have a non-diagonalizable matrix (JordonForm not diagonal). Then the general algorithm is much more complicated and involves an interpolating polynomial though the eigenvalues, and I'd guess this leads to numerical issues. In Horn and Johnson's discussion of this (Topics in Matrix Analysis, ch 6), they use Lagrange-Hermite interpolation for their discussion of the analytical case, but that would not be a good way to do it numerically - not sure of the method Maple uses. Both the nature of the function and the nature of the matrix mean this is a difficult problem numerically.

You didn't upload your worksheet (using green up-arrow in the Mapleprimes editor) so it's hard to tell. For me in Maple 2023 it is working. I changed some "." to "*" ( as shown in red), though thay didn't seem to be a problem. The plot looks correct, the Gibbs oscillations always need lots of terms to be less prominent.

Download fourier.mw

Edit - I realised your output is the general formula for any N. Do you really want that? Usually the sum you get when asking for a specific numberof terms, say fourier_f(5), is what is expected. If you don't need the general formula, add rather than sum is better.

Download fourier_with_add.mw

Download Quiz1.mw

The BellmanFordAlgorithm can do a whole row of the matrix at a time if you supply a list as the last argument, leading to a much faster result.

[Edit - newer version using topological order added]

Download longest_paths_in_a_DAG.mw

If you upload your worksheet (green up arrow in the Mapleprimes editor) then we can run the code without retyping it in.

In your first procedure, the wiggly line on line 2 tells you there is a syntax error there, which is that it is seeing you want m as a local even though you used it already in the first line. Your first line should be U::Matrix and not U::Matrix(m).

In the second procedure A:=Matrix is not correct and should be removed. In both cases, the Dimension command is in the LinearAlgebra package and so should be LinearAlgebra:-Dimension (and since it returns two things the second version uses it correctly)

You should assign the procedure to a name, for example fillme:=proc(A)

Here's a small step in the right direction.

Download inverf.mw

The following parameters make it positive semidefinite:

My procedure was pretty ad-hoc, using Satisfy and just adding conditions until it worked.

positivedefinite.mw

@mmcdara - I think you needed C[1]<=0, but in 2015 it didn't lead to a solution even when I made that change, 2023 just gave one solution when solving the conditions. Since the matrix is symmetric, the discriminants of the quadratics have to be positive anyway, and the signs of the coefficents can be used to test for two positive roots. But I don't really see why your method gave a different result.

@sursumCorda I'd be suspicious of the deprecated linalg routine. All principal minors (of all sizes) need to non-neg, so perhaps systematically working through these would be a better method. 

Use datasetlabels = contents for this, but it isn't pretty.

The short answer is that there is no obvious way to do this. You can certainly make subsets and two-element subsets as you have described if you are using labeled structures (and exponential generating functions). But the OEIS series you gave is for unlabelled graphs, so I don't see how it could arise from labelled structures. The combstruct package takes a grammar and then enumerates for either labeled or unlabelled structures but not for a mixture.

I don't really understand the functorial composition. But as far as I can see, there doesn't seem to be a simple way that its generating function is related to the generating function of the operands, and the basis of the combstruct package is that the grammar translates directly to operations on generating functions.

(If your object is just to calculate the numbers in the OEIS series, that can be done through Polya counting and can be programmed in Maple.)

For consistency in the A and nA labels, use MathML for both, so set A:=`#mo(A)` (or use mi for both A and nA if you want italics). I also added padding=10 to StyleVertex so the lines don't touch the labels.

For the weight locations you could use GetVertexPositions and then programmatically adjust the locations for the colored edges to have the same y value as the corresponding uncolored ones, and then save with SetVertexPostions. But that is a lot of work, and for me the weights look OK already.

Arbrepondéré.mw

Perhaps could be done in fewer steps, but this works.

Note: I scaled the result arbitrarily to make it simpler, under the assumption that it is was intended to be equal to zero, but you can leave that out.

Download dchange.mw

Well, all but 2 are random...

Download GivenDet.mw