## 21403 Reputation

15 years, 111 days

## hmm...

@Kitonum Your (edited) approach is smooth, yes, but it computes the contribution from x=5..infinity as this:

int((sin(t)^2)^exp(t), t = 5 .. infinity, method = _d01amc,  numeric);
-8
3.730510477 10

But that looks quite wrong. (It's very close to 3.73051*10^-8 which wolframalpha.com gave me, btw, which I find funny.)

Consider just this portion,

int((sin(t)^2)^exp(t), t = 5 .. 20, numeric);
0.04401097083

Shouldn't the integral for x=5..infinity be at least that much? It seems that the approach to force method=_d01amc neglects a significant portion of the integral from x=5..infinity.

However,

int((sin(t)^2)^exp(t), t = 5 .. infinity, numeric);
0.04401097083

I don't much like the look of that result 0.04401097083 for x=5..infinity, either, because it's the same as the result for x=5..20. I distrust it because of further missed portions like this:

evalf(Int(t->(sin(t)^2)^exp(t), 20.42 .. 20.425 ));
0.00006521564386

And so on, in ever-narrower bands around odd multiples of Pi/2. I haven't thought much about whether it converges. The total integral from x=5..infinity might be a great as 0.0441 or so.

What to do, then? If a function were devised to compute each contribution from a periodic subrange, then evalf/Sum might be able to tell whether their numeric sum converges quickly enough to validate. Umph.

@dnaviaux Yes, what Carl just showed is very close to something done at the start of the old link (which I had cited earlier in this thread).

For example, generating the name that displays as the Greek letter under the GUI's printf ,

nprintf("&#%a;",sscanf(03A9,"%x")[]);

Ω

# And that name is just this entity
StringTools:-Explode(%);

["&", "#", "9", "3", "7", ";"]


You can make procedures to conveniently apply all these conversions and manipulations.

The following three entity representations all get rendered as the Greek letter Omega under the (usual) print command in the GUI. Actually the first two render directly as italic, and last as upright Roman, under print. But only the middle one is displayed as you want under the GUI's printf.

&#x3A9;    &#937;     &Omega;

Lastly, I don't think that any of this material is documented in Maple's Help or manuals. But it can be useful.

## zoom...

Using either Explore (or plots:-animate) a polar plot can be zoomed dynamically.

For fun,

Explore(plots:-polarplot([seq([j, (2*j*Pi)/10], j = 1 .. 10)],
style = pointline, color = "green",
symbol = solidbox, gridlines, size = [500, 500],
coordinateview=[0..11*(1-0.9*(N-1)/(200-1)), default]),
parameters = [[N = 1 .. 200, width = 400]], frames = 300, width = 600):


Other options can be added to the Explore call, to animate or adjust the number of frames, etc. Or, zooming "out"...

Explore(plots:-polarplot([seq([j, (2*j*Pi)/10], j = 1 .. N)],
style = pointline, color = "green",
symbol = solidbox, gridlines, size = [500, 500]),
parameters = [[N = 1 .. 50, width = 400]], animate, frames = 600,
width = 600):


@mmcdara I don't have any strict preference about what you post.

I was responding to your query, "...why is the possibility of receiving a vote or being selected as the best answer (ok, this rarely happens) no longer proposed in my replies?"

The reason is because Replies cannot take on votes or thumbs-up, or be selected as best Answer (cup icon). Only Answers can get such things, via the current mechanisms of this site.

## close followup queries...

Please add very close followup queries to this topic here, as Comment/Reply, rather than start a separate Question thread without branching (close-referenceing links). It helps to keep the content together.

## +- in printf...

@dnaviaux This is why I added +- as an example in my Answer to one of your previous Questions.

## border...

@jalal You can turn off the rendering of the borders for the vertex labels. That should hide the ellipses, which are elongated around the accented labels.

For example, in Maple 2020, you could add this line (before calling DrawGraph),

StyleVertex(G, Vertices(G), border=false);

With that added in appropriately, I get this in Maple 2020.1,

## ok...

@dnaviaux You can construct a larger table of symbols, and use it with printf.

Eg,

Symbols:=table(["inf"=&#8734;]):

printf(" %s   %s\n", Symbols["inf"], "inf");
∞   inf


You could make the indices in the table whatever you choose, eg, "inf" or "infty" or  "\infty" or escaped "\\infty" or what have you.

You can also have more than one key index into the same value. Eg,

Symbols:=table(["inf"=&#8734;, "+-"=&#177;,
"plusminus"=&#177;]):

printf(" %s   %s\n", Symbols["inf"], "inf");
∞   inf

printf(" %s   %s\n", Symbols["+-"], "+-");
±   +-

printf(" %s   %s\n", Symbols["plusminus"], "plusminus");
±   plusminus


## mistake...

@Carl Love Your code does not account for the two choices for lowercase sigma, and so produces incorrect lowercase letters for tau to omega.

restart;
Greek_uppers:= [
"Alpha", "Beta", "Gamma", "Delta", "Epsilon", "Zeta", "Eta",
"Theta", "Iota", "Kappa", "Lambda", "Mu", "Nu", "Xi", "Omicron",
"Pi", "Rho", "Sigma", "Tau", "Upsilon", "Phi", "Chi", "Psi",
"Omega"
]:
Greek_lowers:= StringTools:-LowerCase~(Greek_uppers):
Greek:= table([
(Greek_uppers =~ [$145..145+16,$145+18..145+24])[],
(Greek_lowers =~ [\$145+32..145+32+23])[]
]):
Convert:= proc(x)
local r,q;
r:= irem(3*256+x, 64, q);
cat(StringTools:-Char~([192+q, 128+r])[])
end proc
:
Greek:= Convert~(Greek):

seq(printf(" %s  %s   %s\n", Greek[g], Greek[StringTools:-LowerCase(g)], g),g=Greek_uppers[18..24]);
Σ  ς   Sigma
Τ  σ   Tau
Υ  τ   Upsilon
Φ  υ   Phi
Χ  φ   Chi
Ψ  χ   Psi
Ω  ψ   Omega


## I know...

@student_1 Yes, I did in fact understand what you meant before. You can get that "legend" effect for the pointline style (as well as the particular placement), through a construction of the whole legend-thing via segments and textplots.

## not directly...

@student_1 Using various other symbols is easy and straightforward. See the symbols option in the plot,options Help page. Simply replace the symbol=solidcircle in the above code with your choices from the documented symbols.

Maple's legend and caption options don't support the location your last Reply's image shows. The inlined location of that "legend" in your image is possible if you programmatically build it up through use of carefully placed smaller plot segments and textplots. But those all have to be placed with some care/fiddling -- its construction and placement is not automatic.

 Just to be clear: when constructing the short line segments in such a construction the style=pointline could be used, or two segments with style=line and style=point could be overlaid. It's not difficult, but it is extra effort to set up.

If you have in mind such a specific kind of plot then it would have been more helpful and useful to have shown it when you first asked the original Question.

## version...

@snowman If you have an older version of Maple then you can specify that at in the header of your Question. That often saves time, avoiding back-and-forth fiddling.

I'd like to clarify that at no point have I suggested that dismantle produces the desired tree described by the OP. Some comments above seem to have confused that, and muddied distinctions between internal DAG structure and functional form.

I mentioned dismantle only because it uses a vertical rather than horizontal layout. I think that vertical layout can be a useful alternative.

The OP has now clarified the class of examples to be covered. Even for a meaningfully wider class the computations can be done easily with the op command (perhaps using lists as intermediate representation). This sort of thing has been done several times before. Using ToInert for the given task involves considerable unnecessary additional effort.

I don't recall anyone suggesting before that this functionality be made into a new command. That's a nice idea.

## not mine...

@mmcdara I didn't write that documentation phrase, so I cannot state what its author meant precisely.

I could suggest that the main difference is that ToInert produces something which can be programmatically manipulated, as opposed to dismantle which is more for a purely printing/display effect.

But I don't know what kinds of expression you wish to cover, and how. Certainly there is more work to be done in order to manipulate structures returned by ToInert. In many cases using op directly on the original expression seems simpler and easier. (Recall my response in another recent thread of yours, using both op(0,...) and [op(...)] .) But that won't serve for everything... It depends on what kinds of expression and structure are to be covered.

## simplified result?...

@nm That looks like showing the result of applying FullSimplify to the result from Rubi, rather than showing the result from Rubi. Are they the same?

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