@mmcdara 

Edit: This is essentially the answer from Kitotum posted before (appart from simplify that works equally well in this case). I did not see Kiotums answer because the browser page was not updaetd. I leave it here as a variant and for the records.

Correct remark.
I can only think of this approach with basic commands

expr := n*x^n - 2*n*x^(n - 1) + x^n;
fct := x^(n - 1);
fct*collect(simplify(expr/fct), x);

Any factors fct can be factored out and the remaining expression can be further formated (with collect in this case).

@sursumCorda 

That's an intersting question beyond assumptions and RootOf with index=real[]. Consider branching it off.

@Carl Love 

I went back to the other question and executed the help page as described.
-> no warnings

but after clicking the restart button and again execution the warning appears again.

The restart button also works for int_warning_2D.mw

Clicking restart before executing a document works also.

With Maple 2018 I get the integral evaluated with MeijerG.

With Maple 2019 the warning appears after clicking restart (probably the version when the warning was introduced)

@dharr 

I have tired also evala and substitution into the original problem. Here are some other attempts that do not yield the exact solution (which you have probably seen).

I hope someone from Maplesoft can shine more light onto this.

Excellent curve sketching by the way!

@sursumCorda @dharr

The fact that I cannot find a trace on index=real[n] in the official documentation of Maple let me assume that this is Maples way of defining internally the n-th entry in an ordered list of the real roots. Normally the user should not see this and indeed using the explicit option (without parametric) cases in this forum I re-run with Maple 2022 provided clean analytic output without RootOf.

So I do not think this is a real bug in the sense of a wrong solution. I would rather call it an unintended output of solve for some combinations of options and assumptions.

At least I found an error on my side in introducing the extra roots: I included negative values for b which are not part of the original problem b>0. Doing it correctly:

-(_Z^6*sqrt(3) + _Z^7 + 11*_Z^5*sqrt(3) + 2*_Z^6 - 5*_Z^4*sqrt(3) - 18*_Z^5 - 144*_Z^3*sqrt(3) + 4*_Z^4 + 39*_Z^2*sqrt(3) + 251*_Z^3 + 981*_Z*sqrt(3) - 66*_Z^2 + 873*sqrt(3) - 1698*_Z - 1512)*(_Z - 1);
solve({%, 0 < _Z});

gives only one solution.

Interestingly Maple knows that index=real[4] is the only valid solution and can in some instances provide an exact answer. On the other hand there seems to be no direct way to evaluate output with a RootOf expression with index=real[]. Internal information of the solution must have been lost in the output.

@dharr 
If I understand correctly index=real[4] is unexpected. Indeed I could not find anything in the help system altough it has been mentioned in this forum (searchable with: index AND real).

Since index=positive integer did not match I tried (on the factored expression in my worksheet solve_RootOf.mw)

-(_Z^6*sqrt(3) + _Z^7 + 11*_Z^5*sqrt(3) + 2*_Z^6 - 5*_Z^4*sqrt(3) - 18*_Z^5 - 144*_Z^3*sqrt(3) + 4*_Z^4 + 39*_Z^2*sqrt(3) + 251*_Z^3 + 981*_Z*sqrt(3) - 66*_Z^2 + 873*sqrt(3) - 1698*_Z - 1512)*(_Z - 1);
RootFinding[Isolate](%);

which returned the supposedly correct solution at postion 4
[_Z = -2.437068349, _Z = -2.283792841, _Z = -0.07778113818, _Z = 1.000000000]

I tested the other 3 solutions with the inital expression expr and all evaluated expr to zero.
Can we realy assume that expr has only 6 solutions (Is there a fundamental theorem for multivariate polynomials that states the number of roots? I.e. 3+3 or 3*3 in this case of maybe 12 because there are two RootOf with index=real[4])?

Just for completeness:

(solve(expr = 0, [a, b], useassumptions, parametric) assuming (0 <~ (a, b)))

returns the same expression with the bad roots. So useassumptions in combination with allsolutions is maybe a combination of options MapleSoft want's to have a look at.

Download solve_parametric.mw

@sursumCorda 

I am sorry, I can't relate https://www.mapleprimes.com/questions/235749-Better-Way-To-Remove-Entries-In-Piecewise#answer292495 to this quesion and the transformed minus sign. I also cannot spot any substantial changes in the expressions in both pdf files.

@acer Thank you for answering all my questions and the procedure that reveals the name of the procedure that issued the warning. The procedure worked well on a few examples with the exception of e^2 and du/dy warnings. My interpretation is that those warnings are not using the WARNING function.

@sursumCorda 

printing (via printpreview) or exporting your file on my machine is still fine.

I guess the print error has something to do with the print driver (assuming that everyone is using Maple 2022. There have been substantial improvements with the introduction of the print layout mode). On my machine I used the Adobe print driver

confirmed_2.pdf

I can't reproduce this with Maple 2022.2. Which version do you use?

Untitled_(16).pdf

@WhiteNoise 

the complicated formating works in almost all instances. If for some reasons the user has defined a name kOmega (which is unlikely I have to admit) the output will not be as intended.

Can you provide Maple code that crashes?

I have an open question about volume integrals that I would like to at least ask without the need of getting an answer right away:
Is it possible to compute the moment on inertia about an arbitrary oriented axis? A stopped at the point where I could not manage to define the domain of a cylinder.

Maybe such an example fits better in the “Physics Courseware Support: Mechanics”.

@Thomas Richard 

Thank you!
With AllSolutions it becomes a question of equaltiy of integrals where I am stuck:
 

Can someone help?
 

Download Equality_of_Elliptic_expressions_02.mw

What you indend to do sounds intersting.

Could you give or refer to examples of what the final result you want might look like?

I didn't find anything useful that matched the keywords in your question.