Once again, it appears that you are looking for pretty-printed output, since for 2D Input there's little difficulty.

I'll leave aside the approach of building it with the mouse using palettes (or command completion for the Greek), and then conversion to Atomic Identifier via the right-click menu. You've been shown that in another recent thread.

We can construct TypeMK (the stuff that atomic identifiers are made of) for this.

Download typemk.mw

Presumably your question is about the pretty-printing of 2D Math output.

This was done in Maple 16.02, but may work in your Maple 13.
 

Download verbar.mw

@mapleatha 

In 2D Input mode you can enter A=B=C , or A+lamda I = A+ 4I = B , say. Then right-click on it and choose the context-menu action 2-D Math -> Convert To -> Atomic Variable in the menus that pop up. That turns it into a name which pretty-prints as output like the original input. In Maple 13 it is called an Atomic Identifier, I believe.

You can also create 2D Math expressions which do not execute, and you can also intersperse those within paragraphs of text, say. That is possible in Maple 13 too, I believe.

In a Document in Maple 2017 you could also enter such a thing in 2D Input, and then hover the mouse cursor near its end to reveal a round toggle button that can be used to disable execution of the line.

In this was you can create quite a variety of expository mathematical formulas which don't necessarily have to parse and evaluate to valid Maple language constructs.

In the example Document below I used the right-click conversion to the inputs assigned to foo and bar, and toggled the Q+R+S to non-executable. This was in Maple 2017.3.

Download 2datomic.mw

Here are some examples executed in Maple 13 (including convert-to-atomic-identifier on the rhs of the assignments to foo and bar).

The left-alignment below is an artefact of inlining into Mapleprimes; the items were centered in Maple 13's GUI.

Download 2dm13.mw

Using Maple 2017.2,

restart;

assume(nu > 2, beta > 0, lambda > 0, delta > 0, y >= 0):

S:=dsolve(beta+y+(D(h))(y) = nu*((lambda+beta+y)^2-delta*h(y))^(1/2)):

subsindets(simplify(S),RootOf,u->map(simplify,u));

[edited: I see that the OP has since indicated he is using 2016.2]

For Maple 2016.2 you could try instead,

subsindets(simplify(simplify(S),size), RootOf,
           u->map(uu->simplify(simplify(uu),size),u));

The syntax to load the package is,

   with(simplex)

and not,

   with simplex

as your Comment indicates.

Note the there should be no space between the "h" of "with" and the opening round bracket.

The round brackets are required, since here they denote a function call to the `with` command, and they are not merely separators.

Since the problem appears to be with just the pretty-printing of those names then you should be able to get by, say by avoiding that. (You don't need them beautiful for some purpose, do you?)

If you don't want to have to temporarily switch typesetting level then you could lprint or sprintf or print (or suppress output).

This has been reported as a bug on this site before, btw.

Consider your first example. It is not working for the reason you think, I suspect. What seems more likely is that plot3d is receiving as its first argument the list of three scalar expressions in x and y that is returned by the evaluation of se(x,y) where x and y have no assigned values. In this way that call plot3d(se(x,y),x=0..2,y=-2..3) matches a valid and documented calling sequence of the plot3d command.

For your second example plot3d(td(x,t),x=0..2,t=0..3) your should first execute the call td(x,t) and see what it returns. That is what you are passing to the plot3d command here.

The plot3d command, like most Maple commands, follow the so-calling standard evaluation rules of evaluating arguments before they are passed to the procedure.

A procedure (of say two arguments) which returns a list of three elements is not one of the valid calling sequences of the plot3d command. An unevaluated function call, like say the single right-quoted call 'td(x,t)' , which might evaluate to a 3 element list when x and t take on values, is also not a valid calling sequence of the plot3d command.

For Question 1:

Depending on your specific architecture hyperthreading may or may not interfere with  the efficiency of Grid computations.

You could see what happens if you disable hyperthreading in your machine's BIOS.

One scenario in which the derivatives appearing in the prettyprinting of a "Vector" do not get formatted in dot-notation is when it is handling a VectorCalculus:-Vector. I don't see mention of that package in your Question.

If you are using the global constructor :-Vector when you use the shortcut <...> (by virtue of not having loaded VectorCalculus, say) then it seems to work OK in Maple 2016.2. See attachment.

If you do indeed want VectorCalculus loaded and/or want its results to be prettyprinted with dot-notation, then you could get dot-notation for its "Vector" results by wrapping them in the command :-Vector(...) . That would give you the BasisFormat(false) appearance. I don't see any easy way to get the dot-notation displayed in the BasisFormat(true) style in Maple 2016.2.

usedot20162.mw

Your posted example suffers from computational issues (e.g roundoff error), rather than a display-driver problem.

Short workaround:

restart;
CodeTools:-Usage( plot(x->eval(evalf[20]((1-x)^(10^9))), 0..10^(-15)) ):
memory used=6.48MiB, alloc change=33.00MiB, cpu time=36.00ms, real time=39.00ms, gc time=0ns

Usually a more natural way to deal with such an issue is simply to raise Digits at the level at which you are calling plot. But, as seen at the end of the following code, there are some unexpected issues with that approach for your example as given.

(Link to the attached worksheet is at the end.)

plotprob.mw

The attached worksheet contains code (in its Startup Code Region) which will programatically embed an animation (or a sequence of plots) in a Plot Component along with control buttons.

It also provides an example using an option to automatically play the animation when embedding it.

I created this is Maple 2017.2, but it seems to work also in Maple 2015.2 (but it won't work in Maple 18.02 or older, as is).

embedanim01.mw

[edited] Here's a revision with a few more bells and whistles such `width` and `height` options, suppression of Table borders, scaling/zooming (useful for constrained 3D plots),  and examples with suppression of the button controls.

I removed use of the OrthogonalExpansions package, so someone without that could still run the sheet.

embedanim02.mw

I'm not really sure what you are trying to obtain.

But is it something like any of these (inside a plot call)?

labels=["x",typeset(Beta[0]=2.345*10^(-``*9)/Unit(cm^3))]

labels=["x",typeset("y", [2.345*10^(-``*9)/Unit(cm^3)])]

labels=["x",typeset(Beta[0]=2.345*10^(-``*9)*Unit(cm)^(-``*3))]

Does the following call (which assigns to res) get you what you want?

Download latex16.mw

I have some evidence that the result might be approximately -1.413e14  (obtained in about 6 minutes on a fast machine). I have to rush off, but I'll try and upload details, after a few more checks, hopefully this evening.

There have been many reports over the years from Danish students who have encountered worksheet/document corruption problems. I assembed a list a while back, and added it here.

There appears to be at least two sorts of problem:
1) entire loss of content, with saved .mw file becoming all null characters.
2) chopped XML in the .mw file, where the GUI does an imcomplete job of closing all tags reasonably when re-opening. (This can often be ameliorated by editing with a separate program by an expert, to recover more from the trailing chopped portion.)

I have previously submitted the whole set of links as a bug report. I'll also submit this (and another from a week or so ago).

Mapleprimes seems to see such reports soon after the start each school year, as new students get their assignments.

I don't know whether there is one or more causes. Use of Danish characters seems a likely culprit, but clearly that is difficult for the students to avoid. But I have also noticed that many of the "repairable" chopped worksheets contain several very large images, constructed and edited inplace with the drawing canvas functionality of the GUI. I suspect that those large canvas structures may trip up the GUI when saving. It's unclear.

Here is a suggestion for the Danish students. First, turn off auto-save, but save frequently. Save each time to a new and distinct file name, where I mean distinct from all previously saved instances. Each time you save, double-check that the newly saved document is not corrupted, by doing by Close and then re-Open on it. I realize that this would involve a great deal more effort.