@taro See ?substring.

@asa12 You have ended the genus command with a colon!! That's why you can't see the output. When I run your commands, I get that the genus is 2.

@Thomas Dean 

Ah, I will put the default axes in my maple.ini file.

The names p__1 and p[1] are distinct, and their subtraction should not be 0. There are a great many examples in Maple of names that are distinct but which print the same. This is an often-useful feature, not a bug.

The reason to use p__1 is that it's considered a completely separate symbol from p, whereas p[1] isn't a separate symbol. (Note that "symbols" is a subset of "names"; see ?name, ?type,name, ?type,symbol, and ?type,indexed.)

To see an example of what can go wrong if you try to use p and p[1] as separate variables, execute

p[1]:= 0;  p:= 1;  p[1];

@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.