@Zeineb I said tab_err:= Vector.... You have tab_err:= array....

@DarkMath To me, a true functional is something akin to Maple's D command: It takes a procedure (function) as its argument and returns a procedure. It's easy to do the same thing with your integrals. Then you could do away with the need to pass in the r and pass in the shift.

f:= g-> 
    local _r, r; 
    subs(__R= intat(g(_r), _r= __r), __r= r, __r-> __R)
:
f(sin);
       r-> -cos(r) 

f(sin)(r);
                            -cos(r)

f(sin)(r+eps);
                         -cos(r + eps)

@mmcdara 1@@0 evaluates to ()-> args. The 1 could be replaced by almost anything and it'd still work; the 1 just seems appropriate. The zeroeth iterated power of any function is the (multi-argument) identity function. 1 (or any number) can be considered a function in Maple that returns itself. Note that (f@@2)(x) returns f(f(x)) and generalize from there.

If that's not sufficient explanation, just ask again.

@abdulganiy The ability of display to handle legend must've changed recently. Here's a version of Tom's plot that should work for you:

restart:
B:= [
    [ 
        600*2^~[$0..4]+~1,    
        [2.87E-19, 7.94E-21, 7.94E-23, 1.03E-24, 5.91E-26]
    ],
    [
        2000*2^~[$0..4]+~1, 
        [3.30E-2, 5.37E-4, 8.47E-6, 1.33E-7, 2.08E-9]
    ],
    [
        [183, 365, 728, 1476, 2910],      
        [4.58E0, 7.54E-8, 2.20E-11, 4.95E-14, 9.15E-15]
    ],
    [
        [1621, 3020, 6166, 12022],      
        [2.95E-3, 8.51E-6, 3.39E-8, 2.51E-10]
    ]
]:
plot(
    (`[]`~@op@(log[10]~)~)~(B),
    legend= ["BFFM", "BNM", "BHM", "ARKN"],
    color= [red, gold, blue, black],
    symbolsize= 15,
    axes= framed, 
    symbol= [box, circle, solidbox, solidcircle],
    style= "pointline",
    labels= (typeset@log__10)~([NFE, `Max Err`])
);

@Jean-Michel Collard 

I have considered everything that you've posted to be appropriate material for MaplePrimes. However, you consistently (well over half the time) put your contributions in the wrong places. When I have suggested to you the correct placement (without any tone of reprimand), you have responded with stubborness and refusal. I would call that "roughness".

This is not a "chat room". It's a repository of technical and scientific information whose contributions will be used for reference for many years to come. Correct placement of the material helps with that.

@Carl Love And here is how you would correct the syntax on what you were trying to do. But note that this is not the preferred way to integrate a numeric ODE solution:

g:= 9.81:  h:= 0.1:  rinit:= 0.1: tinit:= 5:
dsysA:= {
    diff(r(s), s) = sqrt((g*r(s) + h)^2 - 1 + 1/r(s)),
    r(0) = rinit
}:
dsnA:= dsolve(dsysA, numeric, abserr= 1e-6):
rA:= s-> `if`(s::numeric, eval(r(:-s), dsnA(s)), 'procname'(args)):
rA(0.1);
                       0.429604957845729

t:= s-> tinit + 
    int(p-> (g*rA(p) + h)/(1 - 1/rA(p)), 0..s, numeric, epsilon= 1e-6)
:
t(0.1);
                        4.89144148361160

@Jean-Michel Collard I don't have direct access to users' email addresses. But any user here can contact another user via email by using the More => Contact Author menu in the bottom right corner of any message. I just used this method to send you one, which you can reply to via normal email.

If you send me an email, there's a good chance that I'll do one of these things:

1. Say that the material should be discussed on MaplePrimes.
2. Edit the material such that it'd be appropriate for MaplePrimes and return it to you so that you can post it.
3. Edit the material, return it, and suggest that I post it.

As the second-highest-ranking Moderator here, I request that you respect my decision on what material is appropriate for MaplePrimes and whether it should be added to an existing thread or made into a new thread.

@tomleslie My guess is that those two numbers were deemed outliers and not wanted for this plot.

It is obvious to me that whoever designed the syntax of animate intended this syntax for the plot under discussion:

plots:-animate(plots:-arrow, [<cos(t), sin(t)>], t= 0..2*Pi);

This solves the problem in the same manner as Robert Lopez's Answer. There is no difference between arrow and PlotVector with respect to this premature evaluation issue. There are numerous good reasons why one of these plot commands may be preferred over the other, but premature evaluation is not one of those reasons.

Maple offers many ways to change the order of evaluation of expressions. Among these ways, the unevaluation quotes are usually the most difficult to use and to understand. Although it's not always possible to avoid their usage, I think that it's best to avoid them when possible. In this case, the method for avoiding them has been intentionally built into the syntax of animate.

The failure to display the worksheet in the Question is due to a bug in MaplePrimes. It's not your fault, there's no neec to be sorry. The bug only affects the display of the worksheet, not its ability to be downloaded.

@Jean-Michel Collard You asked:

• Edgardo: Any idea to implement 2-spinors in the Physics package?

You should ask that as a new Question thread.

@Jean-Michel Collard You wrote:

• What you wrote is the link to all my "questions". With that I can't reply to Carl.

I realize that you've already found it and made your Reply; however, for future reference, from that link to your Questions you can click on the title line of any individual Question and that'll take you to that Question with all of its Answers and Replies. So Kitonum's original link works also.

@Prakash J "...for the curve is convergence" doesn't quite make sense in English. Do you mean initial conditions such that the curve has a horizontal asymptote, i.e., such that its limit at infinity exists and is finite?

@Robert Jantzen To attach a worksheet (or a few other file types), use the thick green up arrow on the toolbar. Worksheets cannot currently be displayed inline, but they can be attached for downloading.

I guess that you intended to attach a worksheet but then didn't do it.