I don't understand what distinguishes f from the members of F. Isn't f being treated identically to the members of F? So why not just put f in F? If you plan to treat f later as distinguished, just put f in a distinguished position in F, such as first or last, and extract it later.

Your usage of D is highly suspicious. Are you aware that D has a predefined meaning as Maple's differential operator? that D[i] means the derivative with respect to the ith variable of a multivariate function (thus implying that there are two (as yet unnamed) independent variables in your differential equation, making it a PDE, not an ODE)? that you have a variable named Dy where you may have meant D(y), which would make y the dependent variable of the differential equation? that the superscript (2) means not squaring but a double application of the operator? that the y in the first term of your ode1 is being treated as a coefficient of the differential operator rather than its argument?

You should upload your complete code as a downloadable worksheet. However, I can guess what most of the variables are/should be defined as. Let me know if I have this right.

ode:= (D@@2)(y) - epsilon*(1-y^2)*D(y) + y = 0;
eord:= 1;

Good point: Come to think of it, in 16 years of Maple usage, I've never used programmatically the output of the with command. I don't see any use for it other than possibly as a reference for the spelling of the command names, which could just as well be found on the package's help page. Anyway, as suggested by taro, you can use a colon (:) to suppress the displaying of the return value of any command.

@Mac Dude 

In Standard, you can easily make an array plot without using plots:-display. Like this:

P1:= plot(x, x= -2..2):  P2:= plot(x^2, x= -2..2):
_PLOTARRAY(Matrix(2,1, [P1,P2]));

(This only works in the Standard interface. In Classic, plots:-display actually does a significant amount of recomputation to make an array plot. I don't know how this will work with plots automatically sent to files with plotsetup.)

I hope that you can make good use of that.

@Mac Dude 

I've been working on it, but it will be a big job to adapt this to the moderm plot structures and to the Standard GUI. The examples which produce an empty plot in the Standard GUI will produce a correct plot in the Classic GUI. Some examples with fancy tickmarks will give errors in either GUI.

As far as I can see, your expression Branch1Cons doesn't contain any arctan functions, or, indeed, any inverse trigonometric functions at all. So what's the point of all those arctans in the substitution list?

The error I was tracking down was ultimately caused by this plotting difference between Standard and Classic. Execute the following line in both:

plot(x, x= -10..10, view= setattribute(-10., "a banana") .. 10.);

In Classic, it's just the normal expected plot. In Standard, it's an empty pair of axes. This was very hard to track down because of the weird way that negative floats with attributes print (on don't print) in Standard. Try this in both Standard and Classic:

x:= setattribute(-23., "a banana");

This works as far as the kernel is concerned, but it prints nothing in Standard. Even lprint(x) shows nothing.

I decided that this wasn't worth a separate Question, because I doubt that there's any workaround. But if someone finds one, I'd be grateful. This situation breaks the logarithmic plotting package that I have posted (14 years ago) on the Maple Applications Center. That package relies on creating plots with attributed floats in the VIEW.

@acer Thanks for the Answer. I am actually facing another issue, but I believed it was the above because I blindly believed that setattribute worked on software floats like it used to. Something goes terribly wrong now. I'll ask another Question.

@tomleslie 

Thanks for the Answer. No, you're not missing anything. The Answer to my Question, as it's stated, is as simple as you say. But it doesn't get to the bottom of my issue, for which I'll need to ask another Question. It seems that something bizarre happens in Maple 18 when setattribute is applied to any float---hardware or software---and then that float is made the return value of a procedure, an operation that definitely worked in Maple 9.5 and earlier. According to ?setattribute, the command is supposed to work on floats.

@sourav 

This code is a disaster waiting to happen, and I am wary of making little fixes to it while its overall disastrous structure remains. So I suggest that you rethink this from the very beginning. Nonetheless, I may be able to make a little fix to the for loop in question. T1 = 0.5, so in the first iteration of the loop, a*T1 = 0.5. The only statement in the loop is an assignment statement whose left side is ics[a*T1], where ics is a list. What do you mean by the 0.5 element of the list? Lists can only have positive integer positions. A list is like a group of people waiting in a queue (aka as a line). There's a first person in the queue, a second person, etc., but there's no 0.5 person.

@sourav Please upload your worksheet in a way such that I can download it to use it. Use the green up arrow on the toolbar in the MaplePrimes editor (last item in the second row).

@Peter Lang You wrote:

Mr. Carl Love, with your explanations about the fair use doctrine, if I understand it is allowed in a "slightly"way (how slight ?) to add comments (equations, formulas and drawings from the paper).

The criteria for determing whether a use is "fair use" (also called "fair dealing" in some countries) are detailed and well-established. There is a thorough explanation in this Wikipedia article. 

@MDD 

You wrote:

This example shows that in your implementation the coefficients are not unique.

Yes and no: The program strives to find nontrivial solutions by setting the free variables to 1 rather than 0. (I've already explained elsewhere in this thread why I do this.) So, yes, the coefficients are not mathematically unique; but, no, the coefficients returned by this program are unique because my program uses 1, and only 1, as the value for the free variables. So the program will never return a different answer.

I deduce that when the list of polynomials be linearly independent then the coefficients are unique.

That's mathematically obvious; it's not something inherent to my program.

The code fragment that you give works for me if I let z1=10 and T1=.5. So I need to see the rest of your code to figure this out. The error may be in g0 (if g0 is a procedure). 

@Peter Lang 

You're talking about a copyrighted paper that's already been published in an academic journal, right? Then your inclusion of some material from that paper in some comments in your program and your posting of that program here would almost certainly be considered "fair use" or "fair dealing" in any court in the free world. And who told you that you don't have the right to do this? the publisher? Don't believe them. They are legally allowed to tell you that you don't have the right when in fact you do, and they usually will tell you that. Don't ask the publisher for permission. The fair use doctrine applies even if (especially if) you don't ask permission.

If you're talking about something other than a copyrighted work that's already been published, the above doesn't apply.

I am not lawyer, so the above is not legal advice. Double check. If you're an academic, your institution probably has an officer who's qualified to advise you on this matter.

Did you recently escape from a totalitarian country?