In Maple 2019.2 a wrapping pair of (2D Input) single-bars | get parsed as a call to the LinearAlgebra:-Determinant command.

But a wrapping pair of (2D Input) double-bars will get parsed as a call to Norm, according to whether that currently has a binding to, say, LinearAlgebra:-Norm or VectorCalculus:-Norm (which use a different default norm).

I obtain these in 2D Input from the Operator palette.

So, can you get by using the double-bars? Making it work with the single-bars could involve some ugly setup code.

Download Norm_2D.mw

The single left-ticks denote names. The double-quotes denote strings.

Occurrences of cc within a name or a string do not get substituted just because cc has some value (whether a name, string, or whatever).

The commands sprintf and nprintf can be used to format (substitute) a value into a string or a name, respectively. But notice that the characters in a name get rendered in italic, while those within a string appear upright.

for c from 1 to 2 do
  sprintf("the power is %a",c);
  plot( x^c, x= -1..1, title=sprintf("the power is %a",c) )
end do;

for c from 1 to 2 do
  nprintf("the power is %a",c);
  plot( x^c, x= -1..1, title=nprintf("the power is %a",c) )
end do;

You can also use cat or || to concatenate strings or names. Notice that concatenating a string with an integer cc produces another string, and concatenating a name with an integer cc produces another name.

for c from 1 to 2 do
  cat("the power is ",c);
  plot( x^c, x= -1..1, title=cat("the power is ",c) )
end do;
for c from 1 to 2 do
  "the power is "||c;
  plot( x^c, x= -1..1, title="the power is "||c )
end do;
for c from 1 to 2 do
  cat(`the power is `,c);
  plot( x^c, x= -1..1, title=cat(`the power is `,c) )
end do;
for c from 1 to 2 do
  `the power is `||c;
  plot( x^c, x= -1..1, title=`the power is `||c )
end do;

You can also use the special term typeset within the context of most plotting commands to blend strings and math for titles, axis labels, captions, etc. See the Help page for topic plot,typesetting

for c from 1 to 2 do
  plot( x^c, x= -1..1, title=typeset("the power is ",c) )
end do;

Note that the examples above use quotes of some sort to delimit strings (or names containing spaces), and commas to delimit items in a sequence. This is to prevent ambiguity. Simply writing, say, title= the power is c in free form is not valid syntax of the language.

ps. I'm not sure where you saw such use of a period (dot) to denote concatenation. That has not been part of the language for 20 years now.

Here is one way, with a few additional items to also specify the view and tickmarks.

L := [1,2,2,2,3,3,4,4,5,5,6,6]:

Statistics:-Histogram( L, binwidth=1,
                       view=[min(L)-1..max(L)+1,0..0.3],
                       xtickmarks=[$1..max(L)] );

histo.mw

If you would like custom spacing between the column bars you could also use the ColumnGraph command. Eg,

with(Statistics):
L := [1,2,2,2,3,3,4,4,5,5,6,6]:
T := table(Tally(L,output=list),sparse):
S := {L[]}:
LL := [seq(i=T[i]/nops(L),i=min(S)..max(S))]:
ColumnGraph(LL, datasetlabels=none,
            offset=0.625, distance=0.25, width=0.75,
            view=[min(L)-0.625..max(L)+0.625,0..0.3],
            xtickmarks=[seq(i,i=min(S)..max(S))]);

Is this the kind of thing you want?

Download mapleprimes_ac.mw

See the command combinat:-numbpart for the number of partitions of an integer.

When you call fsolve on the multivariate system then it does use Newton's method. See below. You can choose any t value you want below (not just 0 or 1).

You can also obtain explicit solutions in terms of t, symbolically, using solve. These can also be evaluated at specific values of t.

Download RFs.mw

My usual experience is different from what you describe.

When the computational kernel crashes in the GUI then I am usually still able to save the worksheet by closing the GUI using the top corner icon (window decoration button from the OS, which often looks like an X). When I do this the GUI still offers me the choice to save the worksheet, even though the kernel has crashed.

Of course that doesn't include instances when the GUI itself has frozen. By far the most common cause of that is an attempt at printing an extremely large result.

The .m (dotm) structure does not support modules completely. (It never has and I doubt it ever will.) And objects are modules.

Trying to save an object to a single .m file is user-error, in my opinion.

Additionally, two MultiSets constructed with the same elements are still two MultiSets. The documentation states that explicitly. It also states that they can be compared directly with `=` under evalb.

But *nowhere* does it state that they are the same or identical and would therefore be treated as such under evalb when compared in any nondirect manner (ie. contained in any other structure).There is nothing in the Help page of evalb that suggests that, and it is a mistake to infer it.

The command DocumentTools:-Layout:-Equation will pick up and make use of the current typesetting level during its construction.

You can also override that by passing the option typesetting=extended to that Equation command.

(nb. I've also wrapped your argument to Table within a Textfield, which Maple 2019 seems to like, although Maple 2015 works without it. You can also give that Textfield the alignment=left option if you don't want it centered by default. So this attachment work in both versions.)

Equation_typesetting.mw

[edited] I am aware that the piecewise pretty-prints as 2D in regular output, regardless of the interface(typesetting) level. In the context of Layout:-Equation this just means that the naming of the permitted values for its typesetting option are somewhat misnamed. But the details above should still suffice to resolve the OP's question.

You can enforce runtime type-checking for assignments to locals of procedures. You can do this by setting the assertion level.

Note that type(y,integer) will not return true (below) while y is still unassigned.

Download local_type_assertion.mw

One additional problem here is that your original qN_ep doesn't guard against fsolve possibly returning NULL.

I'll answer the same way as your previous question, using operator form instead of the awkward/confusing multiple unevalution quotes.

I also reduce Digits from 100 to 20, since it produces similar plots but doesn't take as long.

NLPSolve_test_ac1.mw

There are two issues.

Your original call to plot3d suffers from premature evaluation. One way to deal with that is by using additional unevaluation quotes (as Carl and Kitonum showed). I find that approach slightly awkward and slightly confusing since, as you say, you don't understand just how it works.

Another way to deal with that evaluation issue for the plot3d call is to use operator form for its arguments. I show that in the attachment below. This also deals with the ugly and awkward need to keep unassigning epsilon,m,n, etc.

But you also asked about why the 2D plots differ between Maple 2017 and Maple 2019. In Maple 2019 the call to fsolve inside your qN_ep can return a value at which its expression is very close to zero (yet the expression's slope is also near zero). I suspect that what you want instead is the earlier root that passes through zero without small slope. See the attachment.

The plot3d call takes a while because you have Digits=100. I'm not sure that you need to set it so very high. Try it at 20.

plot3d_test_ac1.mw

In addition to what Kitonum has already mentioned, you might find the following of interest.

Download surd.mw

The typesetting level matters here.

Download inert_div.mw

The very first request's target (expected result) has the c4 factored out but not nurdel. That is not consistent with the later examples' expected results.

I am not seeing a consistent definition of how the OP expects the input expressions to be handled, so I don't see a common approach. Have I missed a consistent definition of the treatment?

Download collect_examples.mw