To get optimum value (maximum) of 3 variable p, q and w. Where p and q are from the function E1(p,q) and w from the function M1(p,q). The algorithm to obtain the optimum value is described below:-
step 1: Initialize w = c = 20

step2: Evaluate E1(p,q) by substituting w in it.

step3: Find optimum value of p and q from function E1(p,q) using NLPsolve or any other optimiztion method.

step 4: Substitute q optimum value into function M1(p,q) and evaluate it.

step 5: find optimum value of w from optimizing function M1(p,q).

step 6: substitute optimum value of w to E1(p,q) and evaluate it.

step 7: do step 3

step 8: do step 5 and 6

step 9: stop the loop when (w final - w previous) <0.05

I have done this through NLPsolve but it is showing error "Error, (in int) integration range or variable must be specified in the second argument, got 5000 = -3500 .. 1500*p+q-100000"

I am attaching the worksheet below. Please see the numerical analysis part below in the sheet. maple_question.mw

Is there a command to generate a second-difference matrix of size n by n?

This matrix has 2s on its main diagonal and -1 above and below each main diagonal element.

I currently have a document in which controls and a plot are displayed "inline".  I need more controls and more control over where they appear.  Ideally I need my code to display a window in which the controls are laid out and in which the plot can be displayed.  Is this possible with Maple (I know it can be done with other products)?

This is really a question on getting index positions of a sub list from the main list.

Have a list of Vertices and a list of populations for each vertes.

Then from the Neighbours list I need the respective positions in the Vertex list to sum to corresponding values from the population list.

2nd Question  Can the population values be displayed near its vertex or in the vertes circle? e.g y=5

Download Q_23-12-22_Test_Graph_indices_.mw

with(ImageTools);
U1 := Read("C:/Users/S/Desktop/StarPicture.jpg"):

ttt0 := textplot([0 + 0.5, (5 + 0) - 0.5, " Star ", color = "blue", font = ["times", "roman", "bold", 40]]):
display(ttt0, U1, axes = none, size = [400, 160]);

This is the error I get:

Error, (in plots:-display) cannot display array with other plots

I can see Maple doesn't allow adding images to plots. But is there a way around that?

I want to be able to virtually have a white box that I can add plots to such as curves, text, and images at certain locations etc? I want to do that with actual Maple code in the worksheet, without having to mouse-clicking Menu, insert, etc.

Thanks

As we know, choosing different generators can all represent the same group. But how can I get the combination of these different generators by maple? For example, how do I get the following different combinations of generators of C₆?

How do I characterize this equation set? I think it has 6 solutions, equal in pairs, or 3 distinct solutions.

restart;

eq1 := x = (((72*5^(3/2)+270)*a^2-1344*5^(3/2)*a)*w+(9*5^(5/2)-1485)*a^2-2016*5^(3/2)*a-12544*5^(5/2))/(((288*sqrt(5)+216)*a^2-5376*sqrt(5)*a)*w+(36*5^(3/2)-1188)*a^2-8064*sqrt(5)*a+6272*5^(3/2)):

eq2:= a^3 = -(128*5^(5/2)*w)/9+(1600*w)/3+(544*5^(3/2))/9+15200/27:

eq3:=1+w+w*w = 0:##   or w = (sqrt(3)*%i)/2-1/2;

for s1 in [solve(eq2,a)] do
    for s2 in [solve(eq3,w)] do
        subs(a=s1, eq1):
        subs(w=s2,%):
        lprint("sol",simplify(%));
    end do;
end do;
 

Thermal_Stress_Distribution.mw

Download Thermal_Stress_Distribution.mw

The loop for HFS _data_2 and SFS_data_2 and the loop for HFS _data_3 and SFS_data_3 do not seem to be terminated. I do not know what it is the issue here. Anyone who can help this?

Negativity_(v12_beta_gamma_mu).mw

Thank you in advance,

simplify(sqrt((x^2 + y^2)/x)/sqrt(x^2 + y^2)) assuming x>0, y>0

is not sqrt(1/x), why?

Warning, data could not be converted to float Matrix

If we have two univariate polynomials $f(x)$ and $g(x)$ such that

$gcd(f(x),g(x))=1$

then we know there exist two other polynomials $a(x)$ and $b(x)$ such that $a(x)f(x)+b(x)g(x)=1$. For example, if $f(x)=x^3−1$ and $g(x)=x^2+2$, then we can set

$a(x)=\frac{2x−1}{9}$, $b(x)=\frac{−2x^2+x+4}{9}$

Here the polynomials $a(x)$ and $b(x)$ are known as Bezout polynomials and they can be found using the extended Euclidean algorithm, which I know how to do using pen and paper, but not in Maple.

So my question is: in Maple, is there a way, given $f(x)$ and $g(x)$, to solve for $a(x)$ and $b(x)$?

Another training example (number 2 and last) for finding all solutions to a system of equations:

f1 := x3^2-0.1*x1^4-0.05*x2^4+1;
f2 := x1^3+x2^3+0.05*x3^3-1; 
f3 := -2*cos(3*x1)+2*cos(3*x2)-2*cos(3*x3)+1;

In my version, there are 116 solutions.
Is it so?

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

Download CD_ode.mw

I have been making animated 3d plots recently; the last time was perhaps three years ago, and I had some problems then.  If I recall correctly, I couldn't make an animated 3d plot that was plotted in non-Cartesian coordinates.

I am very happy to report that this works very smoothly now in Maple 2022, and it's pretty fast, too.  I have a fairly complex function to plot, involving piecewise polynomials on a tensor product grid in the xi and eta variables (actually, I let plot3d pick out the grid; it seems happier to do so) and then plot them on an elliptical base, in coordinates x = d*cosh(xi)*cos(eta) and y=d*sinh(xi)*sin(eta)  (d is just a numerical constant, giving the location of the foci at (d,0) and (-d,0)), for 0 <= xi <= xi[0] (the outer elliptical boundary) and 0 <= eta <= 2Pi.  The straightforward command works, and building a sequence of plots and using plots[display] works.  I put option remember into my procedure w(xi,eta) and because the sample points are consistent for the time-dependent function exp(I*omega*t)*w(xi,eta) the xi-eta grid needs only to be done once and then one can compute (basically) as many frames as one wants in rapid succession.

Works great.  Thanks, folks!

for k to nplots do
    t := evalf(2*Pi*(k - 1)/nplots);
    plts[k] := plot3d([(xi, eta) -> focus*cosh(xi)*cos(eta), (xi, eta) -> focus*sinh(xi)*sin(eta), (xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))], 0 .. xi[0], 0 .. 2*Pi, colour = ((xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))), style = surfacecontour, lightmodel = "none");
end do;
plots[display](seq(plts[k], k = 1 .. nplots), insequence = true);