@vv You asked:

How have you included the gif file? In my case a single frame was copied this time.

Steps:

1. Left click on the animation to select it. It doesn't matter if the animation is actually playing at the time.
2. Right click on the animation to bring up the context menu.
3. Export as GIF.
4. Upload to MaplePrimes the same way you would upload any plot: with the green uparrow.

@tomleslie The GAMMA function is spelled all uppercase, so your point 2 doesn't apply.

@acer Thanks for that Explore. What is the purpose of the paradoxical clause

if true or del > 0.0?

And what is the purpose of the argument xx, which corresponds to no parameter of Starlings?

If you look up "flock of starlings" or "starlings murmuration" on YouTube, you'll understand why I named it Starlings. That's the effect that I'm trying for. As you may have guessed, I've redone the computations in 3D. I will post that soon.

@abcd No, I find nothing inappropriate about that. I'm just curious about why people change their account name. Your reason seems totally legitimate. There's a certain very frequent poster here who has changed about a dozen times. Also, it would never occur to me to use anything other than my real name, yet it seems that most people are more creative.

@abcd And what about marc sancandi? (Not sure if I spelled that correctly.)

@abcd 

From my previous example, note that A[2,1] doesn't work either. So, if you want to use a Matrix, then you need

userData[1, thisNode+1]

not

userData[thisNode+1, 1].

Applying convert(..., Matrix) to a 1D list creates a 1 x n Matrix, not an n x 1 Matrix.

@w-Teilchen It's not fixed in the current version, even if you use:

with(Physics):
Setup(redefinesum= true):

Why do you say that the given solutions are not real? Whether they are real or not depends on r. Do you have any assumptions for r that you forgot to include?

@Markiyan Hirnyk 

convert(2^(1/4)*exp((1/8)*(3*Pi*I)), RootOf):
allvalues(%):
expand(residue(z^2/(z^4+2*z^2+2)^2, z = %)):
evalf(%);

     0.117223193780180 - 0.0083307958818396*I

@Markiyan Hirnyk Replace roots(denom(Pf), z) by roots(denom(Pf)). However, Christian has already done the equivalent.

What's the point of me "seeing" the long sets of algebraic numbers? I already told you that the set contains the correct residue.

@Christian Wolinski 

roots(denom(Pf));

and

evala(Roots(denom(Pf)));

produce identical output. And that output has the roots expressed in terms of RootOfs.

@Christian Wolinski My _EnvExplicit is unevaluated. And the RootOfs are not all converted to radicals.

@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)