@nm 

Auto save is on 7 min.  I do not think that it is related to it because I can see when autosave is working and has finished.

@mmcdara 

Before running the 6 hours test I tried the other idea somehow: f1-f2 until f5-f1. The equations to be Fsolved became bulkier than the original ones.

Not a single root with

T := Isolate([seq(F[i], i = 1 .. 5)], [x1, x2, x3, x4, x5],maxroots=1,mthd=RC): j := nops(T);

I canceled after 6 hours.

@acer 

The ghost image was caused by an error of mine: p1 should have been removed from the display statement.

For the rest I can work around.

The loss of the red color of the cube is still an open point but not a road block at the moment.

Thank you
 

@acer 

Ok, it seems that the effect of jagged shading can be dampend by finding forgiving plot options. However "closed" surfaces (I mean generated over 2 Pi) show the artefact even with no color (context pannel No color, Light 4 and Transparency 0.25). If this is not a graphics card artefact, it is perhaps a numerical artefact (hardware floats?). Or a Maple algorithm could be improved in the respect. Neighboring facets of a continuous surface should not show such discontinuities.

I think I can work around this this time.

The more severe mudding: Rotating the plot reveals structures that should simply not be there. It looks like as if plots:-sphereplot (here sphere moved to 0.9)  has generated structures out of the plot range and hiden them by making them fully transparent. Plot with the option transparency let them appear again. Could this be?

PS.: I forgot to mention. Also in  https://www.mapleprimes.com/view.aspx?sf=305936_Answer/multiple_animations_02.mw a cube lost completely its red color.

@Hullzie16 

Interesting way to remove brackets from expressions. I will see if I can make use of it next time I want Maple to generate code from Maple expressions.

@acer 

Its clear now what's happening.

Thank you for all the details!

Maybe the data structure to construct a matrix plays a role. Which one do you use?

@acer 

For some reason I thought the frames for the second animation call were set to 150. I was probably a bit overworked and annoyed by the upload problem.

I constructed the example upon your reply for discussion. Here is a corrected version (which is the second way I described above)

multiple_animations_02.mw

The example and the system of odes is simple but already shows what I expected: plotting a space curve with odeplot is much faster that using plottools. However, I am a bit surprised how fast it goes and I would for this example not write a procedure. The dependence of the cpu time on the number of frames and the integration time is instersting to observe. Its not excluded that the the third way will take more computation time than the second way if space curves are involved.

For complex and/or numerically demanding cases with long integration times one could think of reformulating at each time step IVP with dsol(timestamp).This does not work straight away with

(first time I am seeing dsolve solutions this way).

My question has somehow been answered: Try the second way and estimate computation effort and then decide to optimize with the thrid way. For that it would be good to be able to reformulate the IVP. This is the remaining question I have at the moment.

@acer

I wanted to attach an example with 3 plots to be displayed together (without letting the cube spinning for a moment). But I am getting this here

I had to delete the last plot structure and it worked.

And yes, I thought odeplot is in this sense optimized that the integration is done once or at certain points in time odeplot stores intermediate results and uses them as new initial conditions.

multiple_animations.mw

Uploading the code with the green arrow makes investigations easier.

Without knowing the pde and the initial/boundary conditions its difficult to tell. However, the error message gives already a hint that the timestep for sol2 is too large.

If you want to keep this time step you could try to play with with numeric methods and options. See ?pdsolve,numeric

@matmxhu 

It looks to me that the combination of commands have reveald a deficiency of a recently improved implementation. Here is the ouptut from Maple 2022, which shows that compactdisplay was not working at all on partial derivatives

I the past Edgardo Cheb-Terrab provided often swift fixes for the Physics package. This might change in the future. Better now to make MapleSoft formally aware of it: https://www.mapleprimes.com/scr/new

I hope the physics project will continue.

My best whishes for his future!

@dharr I could expand a bit on your idea. Works well for a single path

Remove

currentdir(); #some path
FileTools:-SplitPath(%);
remove(has,%,"Users");
FileTools:-JoinPath(%)

Replace

currentdir(); #some path
FileTools:-SplitPath(%);
subs("Users"="Utilisateurs",%);
FileTools:-JoinPath(%)

@MaPal93 

Partial derivative of a summation: why it is not just 2*`X__i`?
I am not sure I understand what you mean. Suppose n=3. Then A=X_1^2+X_2^2+X_3^2. For any i from 1 to 3 the derivative is always 2X_i, that is, for i=1 is 2X_1, for i=2 is 2X_2, for i=3 is 2X_3. Why their sum?

Answer: You are correct.

A := sum(X[i]^2, i = 1 .. 3);
seq(diff(A, X[i]) = 0, i = 1 .. 3);
                            2       2       2
                   A := X[1]  + X[2]  + X[3] 

               2 X[1] = 0, 2 X[2] = 0, 2 X[3] = 0

But you did not differentiate w.r.t. X__1, X__2, X__3. You differentiated with respect to X[i] over which Maple summs up.

Partial derivative of a double summation: how to define the nested structure of a double summation where j<>i?
I cannot see how B_wrong is calculated, and Sum it's just an inert form so not that useful. In any case, B_wrong is surely not correct since I never really included the j<>i constraint on the index (the summation over j has to skip j=i). How do I do this?

Answer: I misunderstood what you where after because in your worksheet

B__correct - B__wrong;
                               0

System of n equations: how to define and solve for it?
I wanna solve this generically. That is, if I have n+1 equations where n of them are functions of X_i (and X_j) and the last one of X_r, the output solution is X_i=... and X_r=...  

Answer: I do not think that this is possbile in generic way without letting solve know the number of equations and their structure. My trivial example worked. But this is an exception. There might be other examples which are equivalent to computing the inverse of a nxn matrix which could work. Before speculating too much I prefer to hear wheather Ronan's way suits you. Looks very promissing to me.