@emendes Sorry for the delayed reply. I didn't reply yet because I now understand even less than before! I'm trying to figure out how to ask you the right questions so that I can understand. Four things that will help:

1. If I ask you a question, please consider it word by word and answer it as precisely as possible. Please answer every question that I ask, even if you need to say "I don't know." Please indicate precisely which of my questions you are answering (perhaps by quoting it).
2. I know virtually nothing of the mathematics underlying your project, and please don't try to explain it to me. So, terms like "symmetric" and "dynamics" should not be used. I understand sets, lists, intersections, combinations, etc.
3. Please use the best English usage and spelling that you can manage.
4. Ask about small actual-use cases rather than contrived examples.

Here's why I now understand less:

1. abc is a set/list of exactly one copy of every possible 3-combo from parms.
2. conds takes as input an n-combo and outputs an n-combo.
3. You Search for the output of conds in abc. Because of point 1, it will necessarily be found exactly once! Where are these multiple copies that we're supposed to be removing?

Making the axes three different colors really helps with seeing the animation. Great idea; vote up.

@vv I was only referring to lines here because that's what the OP asked about. I am well aware that 2D objects (polygons) are laid down before 1D objects (curves). I mentioned that in the original post that I made about this topic nearly 20 years ago (in some other Maple forum). Indeed, I also covered 0D objects (points, text), which are laid down after 1D objects, and axes, which are laid down last. At the time of my original test, all objects of each dimension were laid down in reverse order. Apparently, that has changed for lines.

@acer Amazing timing difference between DEtools:-phaseportraint and odeplot + fieldplot.

Did you mean theta= 0..2*Pi rather than theta= 0..16?

@Kitonum All the extra lines are controllable. I find this a good compromise towards reducing extra lines:

axiscoordinates= polar, labels= [`\tr`,theta](t), axis[1]= [gridlines= false],
axis[2]= [gridlines= [subticks= 0], tickmarks= [subticks= 3]]

@nm People like you too; you've got a lot of Vote Ups. I will be very upset if you stop posting.

I've lost hundreds of reputation points in similar mysterious circumstances since about the 3rd week of January. When I look, it is not because of the withdrawal of vote ups from recent postings.

You may be referring to embedded assignment, due to my code. This is different than embedded code (code built in to embedded GUI components such as table cells). Regarding the former, I have done some small amount of efficiency testing, and I can find no significant difference in time or memory. When used judiciously, in well-formatted code, they can improve readability; if used haphazardly, they can decrease it. Let's consider my usage in this thread, which is limited to these two lines:

            
(i0:= map2(`~`[`=`], [r,theta](0), `[]`~(.75, Pi/8*~[$0..15]))), #inits
 linecolor= [seq(COLOR(HSV, .85*i/ni, 1, .85), i= 0..(ni:= nops(i0)-1))],

The first line sets the initial conditions; the second sets the colors of the corresponding trajectories. It's necessary in the second line to know how many conditions are in the first line. I could've hard-coded that in the second line, 16. But that's not robust if that number changes. The embedded assignments set up the automatic transfer of that information between the lines.

@Kitonum If you wish, the option axiscoordinates= polar can be added to any of your odeplot commands. This only changes the way that the axes, gridlines, and tickmarks are drawn; it doesn't change the curves.

You have extensively documented your problem except for the most important detail: Nowhere have you shown a complete plot3d command.

@emendes Sorry, I'm having some trouble understanding what you want to do. In particular:

• abc is a list (or set) of 3-tuples. Why 3?
• Is your exclusion criterion as I coded, i.e., nonempty intersection between a particular 3-tuple (as returned by conds(...)) and the tuples in abc?

Sets are far more convenient and a little more efficient than lists for this purpose, but if you need to use lists, that's fine.

If I understand you correctly, when a subset (or sublist) S is removed, one example should be put back. In other words, exactly one element of S should remain in the overall list. Is that correct?

And it should remain in its original position? (If no, then this can be easily achieved by replacing remove with selectremove.)

@vv You wrote:

• Please note that I have mentioned the sfloat->hfloat->sfloat conversion from the beginning.

You're right, and I apologize for not recalling that from my initial reading. No offense was intended, just ordinary academic discussion.

@Earl My mimimal understanding of the formula (which comes entirely from Weisstein, Eric W. "Gauss-Bonnet Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gauss-BonnetFormula.html) says that from the 2*Pi you must subtract the corner angles.

How do you account for the curvature at either cone's apex?

@AOdrzywolek @vv Both of you (VV and the OP) seem to be unaware of this paragraph from help page ?evalhf (where I've added the emphasis):

• The evalhf function converts all its arguments to hardware floats, computes the answer and converts the answer to a Maple float result. Hence the user never deals with hardware floating-point numbers....

In short, evalhf does not return hfloats, which is exactly what you seem to be trying to get it to do; rather, it returns sfloats.

If you want hfloats to write to your file, then put the code that creates and writes those numbers in a procedure with option hfloat. Do not use evalhf within this procedure, because even within such a procedure, evalhf still returns sfloat​​​​​​​s.