I've submitted a bug report against this.  (...noting that in some versions I couldn't interrupt the original example call.)

For such problems, it's not a bad idea to directly submit a report.

Does it switch back to 2D Output in the Help Examples if you toggle the input back to 2D?

@alexsid I see the same thing in Maple 2026 (and 2025) when running under the GNOME desktop management system (default) on Linux ubuntu 24.04 LTS.

I have (almost) trained my wrist to not slide the mouse pointer over to the right of Recent Documents, when the full list pops up, but instead use the arrow keys to move the highlighted selection up or down. Often it takes a few tries.

I'm a little slow and half figured it might be intentional. But now I'll submit a bug report.

You can pass a list of three items to plot3d, along with the option plotlist, to denote that it's not intended as a parametric plot.

This is documented in the 8th bullet point of the Description section of the plot3d Help-page.

Dr.D-N_ac.mw

Note that if you use a set rather than a list then its items may get re-ordered and subsequently no longer be correspond as intended to the colors (or other options) also supplied in lists. That might not happen in this particular example, due to a fortuitous set-ordering (lexicographic, etc). But in general it's not the case.

After a little investigation it seems that the situation might be slightly more complicated.

A routine in simplex is calling solve, and it is under there (SolveTools:-Tranformer) that Normalizer gets used for this example.

And there's some frontend in play. And the waters are muddy, as that SolveTools routine uses a custom variant of Testzero (not the default of leveraging current Normalizer). And that calls normal rather than Normalizer. And I find simplex:-do-pivot's use of series curious.

And I'm not yet completely sure that my success using a stronger Normalizer didn't just "luck out".

I will submit a bug report.

@nm It is slower to use allvalues on the result from PolynomialTools:-Split for this example, and Alfred specifically asked about factors in terms of radicals.

So constructing from the (optionally simplified) radical results obtained from your original solve(...,x,explicit) suggestion seems ok.

If this site does not like attachments with .flow as filename extension then the OP could zip up the file and try attaching that instead.

@Alfred_F One way,

P := x^4 - 12*x - 12;
R := simplify([solve(P, x, explicit)]);
Pf := mul(x - u, u = R);
simplify(expand(Pf));

You may also compare against, say,
     simplify(evala([solve(P, x, explicit)]))
which has rationalized denominators.

@sand15 I did not state that picking off the coefficient for a particular power was some easily done from Horner form.

What I wrote is that one can easily have both forms at hand. Having both at hand, each could be used for that to which it is individually well suited.

Your demonstration of difficulty in picking off a coefficient of a given power from the Horner form is quite beside the point. It's obviously not a good thing to do. But your doing that ill-judged action, right between a quote from me and a snarky personal comment about me, implies that I suggested doing that mis-judged approach. But I did not write or imply any such thing.

Let me finish off the sentence that you only partially quoted: "...even if one also uses the Horner form for computing values."

I began my paragraph by stating that one could easily have multiple representations at hand. That means having them each, in the same session, all avaliable for different calculations and queries. The Vector form and the expanded polynomial form can easily be used for picking off coefficients of particular powers even if one also uses the Horner form for the quite different task of computing values of the dependent variable from concrete values of the independent variable.

I didn't write -- anywhere -- about using the Horner form for picking off coefficients corresponding to particular powers of the independent variable. I only wrote of (and showed) using it to compute values. That is (obviously, I think) values of the dependent variable.

You appear to have somehow misinterpreted my statements as meaning the opposite of what I meant and feel to be their clear meaning. I understand that we all of us misinterpret or mis-phrase, from time to time. (I could find several places on this site where I've admitted to such.)  But I have trouble understanding the descent into sarcasm and personal attack.

I've changed your query from being a Post to being a Question.

Could you not supply a worksheet in which a specific and explicit example of such an H, and all the ensuing difficulties and situtations your mention?

@sand15 

Since it's come up in a few other postings, if I may I'd like to make a minor note about that typeset wrapping: it's not doing anything here, and in particular it's not protecting against further evaluation. The same effect would be attained in this example by using just,
    legend=['phi'(x), 'Predictor'(x)]
instead of,
    legend=[typeset('phi'(x)), typeset('Predictor'(x))]

Protection against, say, subsequent assignment to name x and full evaluation of the plot structure, could be had by instead wrapping with InertForm:-Display or the like.

Also, it's extremely easy to have at hand -- at the same time in a session -- all of these: Vector of coefficients, explicit form, Horner form. Examining the coefficients (by index of the Vector, or from power in the explicit form) is still just as easily directly possible even if one also uses the Horner form for computing values.

@Andiguys You can use the plots:-textplot command for that, the syntax of which you've been shown before (eg. here) and which is documented on its help-page. You can also add new line calls alongside those, and put it in a rectangle.

Download Graph_legend_error_ac2.mw

Or, more tersely, and without so much cruft, and with a linebreak between the label of axis[1] and the caption,

Download Graph_legend_error_ac3.mw

Or, lower right, and tighter together,

Graph_legend_error_ac4.mw

nb. The legend structure is always rendered outside the plot body (beyond the axes), and not "directly inside the plot", as you requested. That's why I've done it with rectangle&line&textplot instead of legend and legendstyle.

@dharr The OP has asked before about getting the prime notation in pretty-printing of expressions used in plots. (Others have asked it or similar questions too, eg here, and others)

The same underlying issue (that the setting/level is not being respected during the mark-up) affects titles, captions, textplots, labels, etc. Ie. anywhere that math can get marked up and displayed in a plot.

Your solution of InertForm:-Typeset (and another variant I've sometimes used of InertForm:-Display) has the benefits over Typesetting:-Typeset that:
1) it's a documented command
2) it doesn't have special-evaluation rules (and so directly handles this example in which the formula has been assigned to a name)

I'm going to submit a bug report against this somewhat long-standing issue.

@WD0HHU As was visible in the output shown in my Answer, I used Maple 2024.2.

I might have time to look at Maple 2025... later.

@WD0HHU Notice the Maple version in my posting. If your version is different then it's only helpful if you tell us what it is.