I want to create a NxN circulant matrix of a system with fixed boundaries. This is an idea of what I'm trying to do (but it doesn't work):

> N := 8;

> A := Matrix(N, shape = Circulant[[2, VectorCalculus[`-`](1), ZeroVector[row](VectorCalculus[`+`](N, VectorCalculus[`-`](3))), VectorCalculus[`-`](1)]]);

>A[1,N]:=0;

>A[N,1]:=0;

In other words, I want to make a circulant matrix of the elements 2, -1, 0, 0, ..., -1 (with N-3 zeros). Then I want to set the top right and bottom left elements to zero (that's the fixed boundary portion). The first command almost works for N=4 -- except with extra square brackets in the matrix -- but doesn't work for N=8 or 16 (N is always a power of 2). The second and third commands seem to be bad syntax (I haven't really tried to figure them out yet).

I tried the following, but did not get 0. Why not?

>restart;

>b:=3*beta*Pi*(3-4*cos(z)+cos(2*z))/(16*z);

>-b+sqrt(b^2)

I know I can do this by hand, but this is part of a larger equation which I narrowed down to this issue.

I'm trying to create a matrix that mimcs the FFT equation as seen here. (Note that I don't want to do the transform, I just want the symbolic matrix of it.) I want to make the matrix in terms of the symbol omega, but I also want it to reduce correctly. Here's what I mean:

I used this post to figure out:

Student here. I'm having a real hard time with Maple's help. Can someone tell me how to create F, without having to type the whole thing in (like I just did) each time I change N. F is really just columns of omega raised to the (column-1)*(row-1) power

I also need help with the syntax for pulling out a column of F, and multiplying A (an NxN matrix) by that column,

A*F(column n):

>restart;
>N:=2^3;

>ω:=N->e

Hi. I need to plot a discrete set of points. I have the function, but the assignment is to print the points. I cannot figure out how to plot them correctly (yes, I've been reading the help). The points are created as values from functions and stored in arrays(?) (or, what I think Maple calls arrays), like this:

a := proc (t) options operator, arrow; (-1)*.12*t^4+12*t^3-380*t^2+4100*t+220 end proc
v := proc (t) options operator, arrow; (-1)*.48*t^3+36*t^2-760*t+4100 end proc