@Rouben Rostamian  Many thanks. I followed your earlier instructions. At the end of the file, instead of guessing the variables, I included a SaveAll function (I believe @Carl Love is the author—the procedure follows after the text). After running make -f Makefile, a charsets.m file was created. In a Maple session, I executed read("charsets.m"); and then with(charsets); and this was the output:

with(charsets);
                 [cfactor, charser, charset, csolve, ecs, eics, ics, iniset, ivd, mcharset, mcs, mecs, pid, qics, remset, triser]

Although the source file contains many more defined procedures, how could the author determine which procedures are available and which are local? 

When I tried to use a function of the package with the given example but  I run into trouble.  Then I commented the last few lines (save, load help ...) and loaded the package again. 

read("charsets.txt");
with(charsets);
                 [cfactor, charser, charset, csolve, ecs, eics, ics, iniset, ivd, mcharset, mcs, mecs, pid, qics, remset, triser]
PS := [x1*x3-3*x2-1, -2*x4*x1-x3*x2*x4+2*x3, x2*x4^2-x4*x1+x3]:
charser(PS,[x1,x2,x3,x4]); 

But again it did not return the answer given by the author. 
 

Some questions:

1. Why does the author use charsets/index := proc(...) ... end proc;? Wouldn't it be better to write a module with the functions instead?

2. Some functions contain the statement options remember, system;. Would that cause any issues when converting to a module?

3. The author defined several procedures with names that clash with standard Maple procedures. Sometimes he uses the standard functions, and other times he does not. Would this also be a problem?

4. The author uses statements like "global charsets/@qs, charsets/@fact". What does this mean? Is there an alternative approach in newer releases?

5. The help file as it is can not be loaded into Maple 2024, correct? 

@Rouben Rostamian  Many thanks.  My ifst impression is that DifferentialPrem won't meet my needs, but I'll try a copule of examples to see how it goes.  
As for 2) here is the link: Charsets 

@acer Thank you for adding the details that you would eventually ask here in the forum.

[edit] Something odd is going on with this site. Yesterday, I could not send my reply to both of you since the site was down. I had the distinct impression that Carl answered first, hence my vote for his answer. Please tell me if I am wrong, and I will change it.

@Carl Love Many thanks. As usual, your answers are very clear and detailed. Thank you for your patience and help.

@acer Thank you very much for the thorough explanation. That was what I had in mind but I had no clue that freeze and thaw were available.    

@acer Many thanks.  Would you mind explaining what freeze does and why it is necessary?  

@ecterrab 

Thank you ever so much. Your explanation shed more light on a subject that I had been away from for decades.

Would you mind sharing your thoughts on the following PDE, based on what you wrote earlier, please?

PDE:=(sin(w)*alpha*b + alpha*y)*diff(H(x, y, z, w), x) + (x + z - b*sin(w))*diff(H(x, y, z, w), y) - c*y*diff(H(x, y, z, w), z) + (d*(y - x) + Gamma*y)*diff(H(x, y, z, w), w) = 0

My attempt by hand to find H led me to a quadratic function on x, y and z and a cos(w) that is almost a solution. 

@mmcdara Sorry for a late reply but I need to go through the material you sent me.  Thank you very much.

I already have the set of ODEs that was used to build the PDE.   What I need is the expression of u(x,y,v,w), which seems impossible to obtain in this case. (But your answer helped me gain insight into another problem). 

@mmcdara Thank you very much for the thorough explanation. The actual values for the parameters are {7, 1/10, 171/20, 1/10}. I have some questions, but I don't think sending them here is appropriate since they are mostly not Maple-related. If I may, I would like to contact you directly.

@ecterrab Many thanks.  One go is just what i need.   

@nm Just to report that I am experiencing the same issue while running Maple 2024 on a Mac.

@dharr Thank you ever so much.  With a bit of work I modified your answer to my needs (a related problem but in a completely different context). Without your answer I could not find a faster way to remove what i called twins.  

@dharr and @sand15 Sorry for the late reply. Many thanks for the asnwers. I need time to test the procedures using the real lists.  

@dharr Many thanks.  Yes, you were correct. The final list aligns with the one shown in the Maple worksheet. I have updated my question to reflect this. Indeed, it always involves a sequence of positive integers related to dynamic models, as I explained to @sursumCorda. The only challenge is that I don't have the list of twins for all the elements (models) in the list initially, as that would result in a huge list. Instead, I calculate it as I progress from one element to the next.

@sursumCorda The integer numbers represent dynamic models. Models 4 and 5 are transformed into model 1 via a symmetry operation. Therefore, there is no need to include models 4 and 5 in the final list.