@mriedel It's not really another issue. It is the issue. The command residue works by simply calling series. Check out the simplistic code with showstat(residue).

@Markiyan Hirnyk It isn't possible for Maple to produce an animation without a fixed number of frames and hence cycling. So don't blame vv's code for this defect.

@mriedel Maple has no trouble converting r to algebraic form. What it has trouble with is simplifying that algebraic form to something which is recognized as a pole of the expression.

rr:= convert(r, radical);

     rr := 2^(1/4)*((1/2)*sqrt(2-sqrt(2))+(1/2*I)*sqrt(2+sqrt(2)))

evalf(residue(z^2/(z^4 + 2*z^2 + 2)^2, z= rr));

     Float(infinity)-Float(infinity)*I

I see in the MSE link that you have given a simplication r1 => r. I don't see a simplification r => r1, which is what is needed for residue to work.

@vv Vote up.

But I think that it'll be much smoother and much more like the original with much less reconfiguring of E and F. I completely removed the the line

if rand(1..10)()=1 then FE() fi;

and I got a fine animation for the 200 frames. So, I'd make the 10 much larger. I'd also set the maximum number of entries of E and F that can change on any iteration at about 1/3.

An alternative would be to change a very small fraction of E and F on every iteration. I'm implementing this idea right now.

@mskalsi Most of my worksheets are short, so I don't need to use the feature much. However, I have my global setting such that it always asks me to select a server, just in case.

@Markiyan Hirnyk Ah, I didn't know that, Vote up, because now Explore seems betters than an animation.

What do you want to know about cmaple? It's on-board help page is very thorough.

@Thomas Dean Yes, plot and plot3d commands (and maybe a few other plotting commands) use, when possible, something called evalhf instead of evalf. The evalhf tends to be 20-30 times faster. The h stands for hardware.

Here's how evalhf can be applied to the current example:

restart:
st:= time():
y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m):
f:= unapply(abs(y), m):
n := 500: ## sample size
M := <seq(2.*idx/n,idx=1..n)>: ## m
Y := map[evalhf](f,M)+~Statistics:-Sample(Normal(0,3), n)^+: ## signal + noise
time()-st;

restart:
y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m):
f:= (x) -> abs(subs(m=x,y)):
n := 500: ## sample size
M := <seq(2.*idx/n,idx=1..n)>: ## m
Y := map[evalhf](f,M)+~Statistics:-Sample(Normal(0,3), n)^+: ## signal + noise

                             0.062
Error, unable to evaluate built-in function `subs` in evalh

See? The evalhf is very restricted in the commands that it can use. They're listed at ?evalhf,fnclist.

@samira moradi Use command Export, ExportMatrix, or ExcelTools:-Export. They all get the job done one way or another.

@Thomas Dean The notation A:-B is definitely superior, more robust, and clearer to read, and less ambiguous than A[B]. It's a shame that the latter is emphasized in the help pages. There is a rare situation where A[B] is required: When B isn't literally the name of an export of module A but is an expression which evaluates to the name of an export.

I took your code, commented out most lines, and wrote under those lines my suggested improvements:

restart:
with(Statistics):
y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m);
## fix complex values
#f := (x) -> abs(evalf(subs(m=x,y)));
f:= unapply(abs(y), m);

n := 500;

## mean 1, std dev 0.5
#X := RandomVariable(Normal(1, .5)):
M := Sample(Normal(1,.5), n):
#Y := [seq(f(M[idx]),idx=1..n)]:
Y:= f~(M):

#A:=[seq(idx,idx=1..n)]:
#plot(A,M,style=point,symbol= circle, symbolsize= 1,title="Values of M");
Statistics:-Histogram(M, title= "Values of M", frequencyscale= absolute);
#plot(A,Y,style=point,symbol= circle, symbolsize= 1,title="Values of Y");
Statistics:-Histogram(Y, title= "Values of Y", frequencyscale= absolute);
plot(Y,M,style=point,symbol= circle, symbolsize= 1,title="M vs Y");
#DataSummary(M); DataSummary(Y);
DataSummary~([M,Y])[];
#Data:=Matrix(n,2,[seq([Y[idx],M[idx]][],idx=1..n)]):
Data:= <Y,M>^+:

plot(
     [[y, m, m= 0..2], Data], labels= ['y', m],
     style= [line, point], color= [red, black],
     symbol= point, symbolsize= 1
);

@Markiyan Hirnyk Sorry, you're right, I used the word hyperplane incorrectly. I meant a nontrivial affine subspace.

@Thomas Dean To generate the Data, I extracted the point data from the first plot and added a Normal(0, .1) to each second coordinate. Like this:

y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m):
P:= plot([y, m, m= 0..2]):
Data:= op([1,1], P):
Data[..,2]:= Data[..,2] + Statistics:-Sample(Normal(0,.1), op([1,1], Data))^+:

That's all there is to it.

@Ronan See ?use, ?object,operators, ?ProgrammingGuide,chapter09.

@Markiyan Hirnyk Agreed. In some ways Explore is better than an animation (flexibility). The animation is automatic and exportable.

@vv Iterator overwrites the same Array on each iteration rather than generating a new Array. So it seems likely that the indices would be returned in the same order on each iteration. Only a kernel programmer could say for sure.