Maple automatically transforms 1/2^(1/4) and 2^(-1/4) into 1/2*2^(3/4) .

That happens as a result of what's called automatic simplification, and cannot be avoid just by unevaluation. That is, it'd also happen for '1/2^(1/4)', ie. wrapped in single right-quotes (aka uneval quotes).

It should be possible programatically to turn it into an inert form and have that be displayed without the automatic simplification. Then you could get the output rendered as follows (or with 2^(-1/4) in the numerator):

Download inert_p_ex.mw

ps. Are you also wanting to simplify wrt that B^2 inside the square-root? Is B real?
Also, you have a term like e^(i*psi(x,t)), so is that deliberate that you don't use I and exp?

@salim-barzani Right the simplify command will not produce the results you want in Maple 2021.

That's why I showed you how it might be done using applyrule.

Is it the performance of the Maple GUI which is slow, or computation of results that is slow (even when run in both systems with all display of output results suppressed, etc)?

If it's the computation, then what computation?

@salim-barzani I've already showed you (above) that your given examples can be handled automatically by Maple 2024 by just the simplify command.

Such simplifications can also usually be restricted (eg. simplify(...,trig), etc) so that they don't alter other type of term.

You ask whether all your other Maple 2021 code (which you don't provide here) will run the ok in Maple 2024. It's likely that it will. But nobody can make such a prediction with 100% guarantee, without seeing the code.

Please put your followup examples on this here, instead of in wholly separate new Question threads,

@Ronan I added a response to your earlier Question thread on rotated text in a 2D plot.

@erik10 A terser variant on that is something like,

  Circle1 := ifelse(CircleOrNot="yes", circle(...), NULL);

or, when CircleOrNot is definitely assigned one of true or false,

  Circle1 := ifelse(CircleOrNot, circle(...), NULL);

@adam25185 Could you please upload and attach your full worksheet file, using the green up-arrow in the Mapleprimes editor?

@salim-barzani You're very welcome.

Please note that I put a line,

   indets(F, function)

into the sheet. That sort of thing can be useful, as a kind of check. In the original, it showed the long expressions that were just function calls of l and m.

You can also do it as,

   lprint(indets(F, function))

and get its result line-printed as 1-D code, if that helps diagnosis.

Please put your close followup queries here (or use the Branch button), rather than spawning another wholly separate Question thread for this.

You had a followup in which pointplot complained about non-numeric entries.
  Bifurcation_MaplePrimes_Oct_17.mw
The problem there is that not all the used entries of A (and L2) have (real,finite) numeric value as second element. Some have Float(infinity)+Float(infinity)*I, which your Maple 2018's pointplot doesn't like. Leaving the rest of your method the same, one possible adjustment is to replace non-numeric values by undefined as they occur.
  Bifurcation_MaplePrimes_Oct_17_ac.mw

ps. Another way to deal with such might be pare the final L2, right before calling pointplot. I didn't check which might be better, or add any bailout efficiencies. One you have it all working you might want to focus on its performance, and have it run under evalhf.

@WA573 I didn't at first understand that you were now wanting to deal with just this "new" example, and not the original example.

You can simply pass the explicit option to solve, to avoid any RootOf here.

Below I also show that you can verify the elements of those explicit solutions, after backsubstituting. (This simplification incantation is for this problem, not for all problems.)

Download ss_root_ac.mw

ps. The solve+allvalues approach given by mmcdara seems unnecessarily complicated, given that the introduction of RootOf can be avoided here.

I was only unsure whether you were still talking about this Question thread's original example, or just your issues with the followup example.

@WA573 It's not clear what you're now asking.

@Aixleft math If solving for {h, v1, t} then which of two solutions forms you might accept for positive t would depend on signum(g).

You've indicated in a followup Reply that you want positive t. Do you know anything about g?

@Michael 

1) I terminated my commands with a full colon in a few places, deliberately. I was trying to focus on the way the entries and procedure were displayed, without any distracting visual effects. This included:

   a) After definition of my variant on a procedure to read and then print a list of what changed in anames. That input line of code provides as much insight as would any displayed output of that same proc. I terminated that defining statement with a full colon to avoid such repetitious clutter.

   b) After my interface call. I set interface(verboseproc=2) higher than its default value of 1, so that procedures get displayed more usefully here. Note that here we want procedure bodies to be displayed in full even if they are read in from a dotm file or Library archive. When the interface command is used to set an option then its return-value is the old setting. I terminated that statement with a full colon so that you would not be distracted by that aspect.

   c) After my map[2] call. That call invokes printf on each entry in a list assigned to res. The printf effect is what I wanted you to see, ie. a plaintext display of your procedure, with line-breaking. But that printf display is a visual side-effect; the programmatic return-value from printf is NULL, and the return-value from that map[2] call is thus [] an emtpy list. I terminated my statement with a full colon so that you would not be distracted or thrown off by the output [] an empty list being printed at the very end.

2) Line-feeds are not part of a procedure structure, as stored by Maple. When a procedure is pretty-printed it gets displayed with some line-breaks, but not as many as you would like, it seems. There are a variety of ways to display the code of a procedure, and they display it in different ways. Not everyone else wants what you happen to want here, all the time.

ps. Here are some varieties of ways to display a procedure body. Since I'm doing it here on a proc that I define in the session (and not reading from Library archive or .m file) I don't need verboseproc=2.

Note that the first two examples below render differently in Maple 2024.1 than they do when the worksheet is inlined in this forum, ie. the outer procedure body may not get displayed with line-breaks. But your issue -- that the inner proc body is displayed in a single line -- is the same there.

Using lprint[2] is an alternative way to render display of the nested procedure with statement line-breaks and indentation.

Download disp_ex.mw

pps. Up until Maple 2018.2 the first example above would actually render with both inner and outer proc displayed with line-breaks (statement by statement), if one had the setting interface(prettyprint=1). But that no longer has that effect.

The %P modifier for printf was introduced in Maple 2019. The ability to add display a proc with line-breaks using lprint[2] was introduced in Maple 2019.

Starting in Maple 2022 the first example above even the outer proc would get less line-breaks during normal print rendering.

Also, since you're interpolating the data for the "density" plots then you might also want to use that same interpolating process for the contour lines (which then become smoother in places). It's just an idea.

For example,  Help_4_acc.mw