@Markiyan Hirnyk With the third version, the final set does contain the correct residue. The problem is that it contains three other numbers as well.

@Christian Wolinski This works:

roots(denom(Pf));

This doesn't work (it gives empty output):

roots(denom(Pf), z);

Based on ?roots, I don't understand why the latter doesn't work. According to my reading, the two should be equivalent. Here's the relevant help:

• The call roots(a) returns roots over the field implied by the coefficients present.  For example, if all the coefficients are rational, then the rational roots are computed.  If a has no roots in the implied coefficient field, then an empty list is returned.  This assumes that a is a univariate polynomials.•
• The call roots(a, K) computes the roots of a over the algebraic number field defined by K. Here K must be a single RootOf, or a list or set of RootOfs, or a single radical, or a list or set of radicals.  For example, if I is given as the second argument, then roots looks for the roots of a over the complex rationals.
• The calls roots(a, x) and roots(a, x, K) are equivalent to the above if a is univariate in x. Otherwise, it treats the other indeterminates in a as parameters, and finds all roots as above and ignoring symbolic roots.

@Markiyan Hirnyk For the sake of readability, the the last three lines of output are

           Pfs:=            []
           ANS:=           {}
           ANS2:= {}, k = 2^(1/4)*(-1)^(3/8)

@Markiyan Hirnyk What are the empty words? Did I accuse you of trespassing the copyright law? No.

So what does this undocumented command do?

@Markiyan Hirnyk If you want to confirm its existence and the existence of its copyright notice, then do

interface(verboseproc= 2):
print(`evala/toprof`);

or

showstat(`evala/toprof`);

See ?option and ?interface.

@Markiyan Hirnyk The error message is due to the non-existence of command split in modern Maple.

@Christian Wolinski You are obviously a master Maple coder and master algebraist. Why don't you get modern Maple? Become a beta tester and you can earn a copy for finding a few bugs. Otherwise, what would it take for you to get modern Maple?

@Markiyan Hirnyk The fact that it prints with the body elided (or redacted) proves that it has option `Copyright...`. See ?option.

@Christian Wolinski There is no command split in modern Maple. Perhaps you mean factor?

@Mariusz Iwaniuk 

Okay, change +a to -a and change the assumption to a < 0. Then it works.

@vv Sorry about that. That's why my final animation seemed slower. The moral of the story is that I should use restart before testing!

@Markiyan Hirnyk I did comment on the purpose of parameter mu in my code below.

@Markiyan Hirnyk The parameter mu is the number of iterations between frames. In other words, every point makes mu micro-movements between frames.

@vv Try reducing the number of frames (the second parameter) from 600.

Did you change the number of starlings (points)? That hasn't worked well for me either. At 3000, they all get stuck.