The usual way to get math output is to use a Mathematical Expression component (also called a Math Container) and set the expression property:

DocumentTools:-SetProperty("MathContainer0", expression, ifactor(2600))

MathExpression.mw

I don't know much about this, but I understand from the wikipedia page that we just multiply the series by the appropriate root of unity. The following code is not very robust because it looks only at the first term of the series that puiseux outputs. If this is what you want, then it could be improved.

Edit: turns out each term gets a different phase factor, corrected in later post.

Download testWorkSheet.mw

The easiest way to get material onto this site is to upload a whole worksheet file using the green up-arrow. Other comments below.

Download unappply.mw

So you want a random one of the permutations of 3 letters, which can be done without generating them all as follows:

Download random.mw

I did it in exponential form, looking for exact roots and then finding numerical values for them.

Edit: I redid it in cartesian form. Earlier exponential form below

Your error message for RootFinding:-Isolate symbolic coefficients are not supported, {f, i, k} means you need to give values to f,i,and k or use solve for symbolic solutions.

Download solvecartesian.mw

[Exponential form: Download solve.mw]

The proposed solution satisfies the PDE:

Edit: you had some strange 2-D code that wasn't working correctly (no sqrt) so I originally thought it was not a solution.

solution_pde_check.mw

In general, plots:-display can combine various plots,so it can be done this way.

pde.mw

You write your application in Maple using embedded components that you interact with only by usng those components - say by pushing the button. Your plot would be produced in a plot component. Then you just open it in Maple Player and it works in exactly the same way.

You do not need to upgrade Maple to use the latest Maple Player. Maple Player is free.

But I don't think it is available for the ipad; the documentation says Mac, Windows and Linux.

I changed pi to Pi (pi has no special meaning in Maple), and sin(2*x) to sin(2*x[i])

The whole x array (each entry multiplied by 2) was being passed to sin.

 Asst_2_Q3bcd.mw

Download pseudospectrum.mw

Here's one way to do it. I'm assuming a list of lists is OK.

(Worksheet not displaying right now.)

Download powers.mw

powers:=proc(p,x,y)
 local pow:=(term,x,y)->[diff(term,x)/term*x,diff(term,y)/term*y];
 if type(p,`+`) then
   map(pow,[op(p)],x,y)
 else
   [pow(p,x,y)]
 end if;
end proc:

Here's one way to do it.

pointplot.mw

The loop can be done more elegantly generating the sequence (in 1-D) with a for loop

pts := [(for i from 0.1 to 0.9 by 0.1 do
         val := FirmModelPartial1(i, 0.2, 0.1)[3];
         if type(val,numeric) then [i, val] else NULL end if end do)];

but I can't remember if this was possible or not in Maple 2021.

Maple got stuck on the solution with arbitrary constants for longer than I was willing to wait. The equation is separable, and I'm guessing evaluation of the integral needs some appropriate assumptions about the values of the constants. So you can make progress for some specific values of the constants, for example if they are all 1:

Download dsolve.mw

I don't know, but since sqrt(q*conjugate(q)) = abs(q), you can use evalc(abs(q)). evalc assumes all the variables are real, which is equivalent to your assumptions on x and t.

abs.mw

I'm assuming by e^(n*t) you wanted exp(n*t). To evaluate the integral you need to apply some appropriate assumptions, which will depend on the particular function f you choose. So I used Int within the transform procedure, and then value on the result outside the transform procedure, with some assumptions that may or may not be what you want, but they make the exp argument negative so the integral doesn't go to infinity.

Download elzaki.mw