@bernie Then you need a zip of aribitrary arity, like this:

N_aryZip:= proc(F, LL::seq(list), $)
local l,k, L:= [LL], n:= nops(L[1]);
     [seq(F(seq(l[k], l= L)), k= 1..n)]
end proc;

@Adri van der Meer These (the original equations, not the Maple code) are partial differential equations.

@Markiyan Hirnyk I was wrong, and I did not understand the question.

@abbeykabir The code is separating the real (Re) and imaginary (Im) parts of the roots. The real part is used as the x-coordinate of a point in the plot, and the imaginary part is used as the y-coordinate. The code (L-> [Re,Im]~(L)) ~ ([R1,R2]) is equivalent to the following:

F:= z-> [Re(z), Im(z)]:
[map(F, R1), map(F, R2)]:

As for a name for the plot, I'd call it a "plot of points in the complex plane".

@bernie You're right---the modification to noninteger values wouldn't work.

So, how about this?

Alist:= [seq(i, i= 1..10, 0.5)];
Xlist:= X1 ~ (Alist);
Flist:= zip(F, Xlist, Alist);

That will work no matter how the Alist is constructed.

@maplelearner I think that as long as the lower limit is greater than 0 and the upper limit is less than infinity, the evalf will work.

I think that the integral at infinity does not exist. Applying asympt to the inner integrand gives a leading term that is O(1/x^2). So the inner integral is O(1/y). So the outer integrand is O(1).

@acer A slight improvement: Increase numpoints for the default-method (rkf45) plot. There is obvious polygonizing for the first few steps unless you set numpoints to about 2^9 or higher.

@acer I note that the original post is 3-1/2 years old.

@Sujaan Kunalan The default method is Runge Kutta Fehlberg, abbreviated rkf45.

@abbeykabir Sorry, I don't understand it. Maybe someone else will.

Here's the only thing that I can think of to do with these 11 complex numbers: They can be plotted simply as points in the complex plane, with the numerator roots in one color and the denominator roots in another color.

@Gruyere I've noticed that you've spelled the variable name both broSet and brotSet, although it is consistently brotSet in "the entire code". If it is actually not consistent, that would cause the problem.

I am assuming that you are translating the problem statement from another language into English. But I am completely baffled by the translation. Try posting the problem statement in its original langiage.

@Oxtoto612 The circle-r is some bad character encoding for a right arrow, the right arrow meaning "approaches" in the sense of a limit. The expression in question means, in Maplese, limit(T(z)^r, r= infinity) = 0.

For some reason, this Question does not appear on the Active Conversations list (even in the long version of the list). This must be a bug in the MaplePrimes software. Maybe this Reply will cause it to appear.

Regarding your question: The numerator has 5 roots and the denominator has 6 roots. So now we have 11 complex numbers (one of which is also real, but that's irrelevant). What do you want to do with them? "Parametric plot" doesn't make sense in this context.

@Kitonum Yes, certainly simplify, expand, and combine slow things down significantly. I was just making two simple modifications to the existing code to make it work. All rational arithmetic and is done automatically, and procedure sqrt always simplifies square roots of perfect squares, so the types in your example work. But combinations of square roots that simplify to rationals are not necessarily done automatically (and, unfortunately, they aren't even necessarily done by simplify).