@MaPal93 I have solutions for your two questions above, but I don't have the patience to work through your long worksheet. Indeed, I've been ignoring your Questions, even though they're good Questions, for months because of this. If you make a version for me to work on, I will gladly answer those two questions. 

By a "version for me", I mean:

• Use colons to suppress all output that is not directly related to the fsolve problem.
• Use only one- or two-letter variable names for the decision variables and parameters of the equations passed to fsolve. No subscripts, no Greek letters.

@JAMET You still have a space after textplot. 

You wrote:

• I really have a hard nipple

I'm guessing that you don't really know what that means in English? It's a somewhat sexual thing. Perhaps you should try translating that again.

@mmcdara I agree with a lot of what you said. However, there is no ambiguity whatsoever in the meaning of denom(res) = 0, neither in Maple nor in mathematics. It means that both the real and imaginary parts are 0 (or, equivalently, the modulus is 0) regardless of the presence of the imaginary unit. There is no situation where it means that the real part is 0 and the imaginary part is unrestricted.

Also, there is only one equation here, not two. An inequation has a completely different algebraic status than an equation when solving a system of equations.

@mmcdara Your way is very likely better than the linear regression method that I used. I used it because the technique shown in my linked subsection of the Wikipedia page seemed almost identical to what the OP was already doing, except for the small change that I noted: replacing (i - 0.5)/n with (i - 0.3)/(n + 0.4).

Using the formulas for the maximum likelihood estimators given in the final section of that Wikipedia page, I get the same numbers as you did by using the equivalent Maple command.

k_hat:= fsolve(add(S^~k*~ln~(S))/add(S^~k) - 1/k = add(ln~(S))/n, k);
                     k_hat := 0.9301095062

lambda_hat:= (add(S^~k_hat)/n)^(1/k_hat);
                 lambda_hat := 129.944334168688

@Samir Khan I appreciate the great use of video/animation that you made in your Post. Vote Up!

@vv If there's a standard definition of ODE, it should be modified so that things that can't be put in that form (or the equivalent form for higher derivatives) are no longer considered ODEs.

@Ronan You can change the prompt (yes, that means the > ) with

interface(prompt= "(**)")

This is not a method of commenting out code. It's purpose is so that prompts that are accidentally transfered into the code by copy-and-paste operations will not be syntax errors because they will be read as comments.

Using Windows, I've never had a situation where the prompts get copy-and-pasted.

My preference is no prompt:

interface(prompt= ""):

I think that this is a clue to what's happening: There are numerous solutions that are exact duplicates.

invsol:= solve(sol=x+b, y):
nops([invsol]);
                               16
nops({invsol});
                               2

@charlie_fcl Are there really any problems? Or do you just get that warning message? A warning is not an error, and it may be innocuous.

@janhardo I don't know the exact relationship between the value of kernelopts(level) and the value that printlevel needs to set to to print at the corresponding level. It would require some experimentation.

@Mathrookie94 @acer Is it possible that the output is being affected by interface(displayprecision) set in an initialization file?

You can check by giving the command

interface(displayprecision)

from a command line. The response should be -1 if it hasn't been altered.

@lcz Note the need for nolist pointed out by @dharr . My Answer should be corrected to

op~(
    1,
    {entries}(
        ListTools:-Classify(
            g-> [seq](op(4, GraphTheory:-CanonicalGraph(g))), graph_list
        ),
        'nolist'
    )
)
 

@dharr Sorry that I forgot the nolist; I often do. I wish it were the default! I will correct my Answer.

And I retract my claim that the help page is incorrect.

And a Vote Up for @dharr!

@dharr Thank you for that example. My procedure for the canonical representative was based on the following paragraph from help page ?CanonicalGraph plus the somewhat obvious fact that there's a bijective correspondence between adjacency matrices and op(4, ...):

• Owing to graph symmetries, it is possible that CanonicalGraph may return distinct vertex orderings when invoked on two graphs G and H with identical vertex sets and edge sets. The representation is nevertheless canonical in the sense that if G and H are isomorphic, AdjacencyMatrix(CanonicalGraph(G))=AdjacencyMatrix(CanonicalGraph(H)).

Your example shows that this statement is wrong.
 

@dharr When there is a (reasonable) procedure to find a canonical equivalence-class representative, it is far more effcient to use ListTools:-Classify than to use ListTools:-Categorize. The former is O(n) and the latter is O(n^2), where n is the number of items being classified,