@dharr The (poorly named) display command is not needed to display an unaltered already-existing-in-memory plot. You could simply use 

plt0;

or even just

%;

@Joe Riel The above can also be done via subs:

om:= kernelopts('opaquemodules'= false):
Statistics:-Visualization:-VennDiagram:-GenerateSize:= subs(
    "%.2f%%"= "%.0f%%", 
    eval(Statistics:-Visualization:-VennDiagram:-GenerateSize)
);
kernelopts('opaquemodules'= om):

An easier way: Using the same a,

simplify(sum(a(2*k-1) + a(2*k), k= 1..infinity));

This works because simplify will already know from the summation limits that k is a positive integer.

@Blanc In mathematical English, the term for a quotient of polynomials is rational function, not "rational fraction". The use of "fraction" perhaps led to some initial confusion regarding this Question. The "simple elements" of the decomposition are called (unfortunately) partial fractions. If a field of coefficients is specified (or implied), and all of the denominators are irreducible polynomials (or powers thereof) over that field, then it's a full partial-fraction decomposition.

@Blanc Here's a simpler procedure. It doesn't need the add or op or to treat irreducible denominators as special degenerate cases.

If you want to replace the general-case ​​​​​​Factor that I used by one of the more specific factorization procedures (Berlekamp, DistDeg, Sqrfree), some very minor syntax changes might be needed, which I could provide. Each of those has its own help page.

Download ModParfrac.mw

@salim-barzani Obviously you've been posting nearly identical Questions under different usernames, the other name being @SSMB.

If some of your variables and parameters can be assumed to be real, it would make what your asking for easier.

Please post your algorithms as Maple code. I'm particularly interested in your set-partioning algorithm. (And your green-bordered example clearly shows that it's a multiset algorithm, which is significantly more difficult to do efficiently.) I'm not interested in the user-interface portions of your code, i.e., the parts the accept input from a user and display the output in a Maplet.

This should be a Question, not a Post. And since it contains the entire informational content of your previous Question, plus some additional (and very relevant) information, that previous Question should be deleted.

Do you understand that phi >= 0 does not imply sin(phi) >= 0, and that it's this latter inequality that allows for simplification under the square root? Here's your latest expression:

B:= sin(phi)^(13/4)*2^(3/4)*sqrt(cos(phi)^(5/2)*sqrt(2)
    /(sin(phi)*cos(phi))^(5/2))*a^2/(4*x^2) 
    + sin(phi)^2/(2*x^2)
:
simplify(B) assuming sin(phi) >= 0;
                               2 / 2    \
                       sin(phi)  \a  + 1/
                       ------------------
                                 2       
                              2 x        

@nm I think that you're losing the 2nd solution by using remove_RootOf. Use allvalues instead.

I'm on my phone at the moment, so I can't check this in Maple.

The last two commands used in your attached worksheet are eval and limit. The eval is "applying a substitution" and the limit is "applying the limit to get the exact answer" (the two things you asked for in your title). Both commands were successful; so I don't know what you're asking about.

If I've misinterpreted something, please post a worksheet where the final result is incomplete or incorrect. And please make it so that I don't have to enter formulas from the paper.

When asking a Question here, it's always best to post a worksheet whose final result is incorrect, incomplete, or gives an unexpected error message.

@C_R You wrote:

• I had 3+ Maple seesions runing when I observed this and only one was affected.

You say that only one "session" was affected. But are all worksheet tabs open within that one session also affected? If you are seeing the problem, please check by opening a new or existing worksheet in the same session, to see if it inherits the problem.

@nm I use strictly worksheet mode and 1D Maple Input, so 2D Input or document mode is not the cause of the problem. I suspect that Windows has something to do with it. As stated, it only happens to sessions that have been open for a long time. Personally, I never shut down my computer or Maple unless some crash or mandatory system reboot forces me to: so I don't shut it down for loss-of-kernel crashes.

Yes, I have that problem exactly as you describe, and I've had it for years. It seems to happen much less with Windows 11, but it's not completely gone. As you said, it only happens when Maple has been open for some time (I'd guess 3 or more days). It's something that affects the GUI display only: the kernel does not "see" any of the altered characters, and the display of all open worksheets is affected. The errors are not saved in the worksheets.

There are several other characters affected this way, such as + (plus) and - (minus). Notice the + replaced by C on the 2nd line of your output. The minus sign gets replaced by K. I think that all the new characters come from an upright sans-serif font.

For Maple 2025, in its new GUI, I've only noticed this bug when using zoom-factor 150% (Ctrl-4). Do you notice it at other zoom factors?

Since it's a nuisance for me to shut down my whole Maple session, I've learned to read the altered characters as they are. There's a one-to-one correspondence between the new characters and the ones they've replaced, and the alterations are always the same.

I haven't reported this bug because I don't know how to reproduce it, and I fear that my report would thus be essentially ignored.