@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? 

This is known as the optimization version of the partition problem. It is known to be NP-hard. (See the Wikipedia article "Partition problem", especially the second paragraph.) It is usually formulated like this:

Given a list (or multiset) of positive integers, find a partition into two sublists such that the absolute value of the difference of the sums of the sublists is minimized.

I've thought about this problem (very casually) for several decades because of the following application, which used to be practical, but is somewhat obsolete now due to advances in audio playback technology. 

Problem/Application: You have a group of recordings of songs of varying lengths that you want to place onto both sides of a compact cassette tape. You can cut the tape to any length, but the length of the two sides is necessarily the same. You want to minimize the amount of blank (no music) time because it is annoying to have that silence while you're waiting for the tape player to switch to the other side.

@rlewis 

Have you clicked to "play" the animation? There is no way to do this programmatically; it must be selected by mouse by the end user. There are two ways (in the Standard GUI):

1. Right click on the plot to bring up the context menu. Select Animation, then Play.

2. Left click on the plot to select it. The animation controls will appear in the toolbar. The third tool from the left is the "play". It's a yellow triangle pointing right.

@tobbie247 

I don't know these methods. But it is clear that the numbers that you give are not solutions to the problem at hand:

Eqs:= [
     limit(numapprox:-pade(diff(f,x), x, [4,4]), x= infinity) - 1,
     limit(numapprox:-pade(t, x, [4,4]), x= infinity)
]:
eval(Eqs, [A= 0.742408087440, B= 0.943866213084]);

     [12.1675708991394, 1.28648179604728]

If the given A and B had been solutions, the returned numbers would be close to 0.

Perhaps if you present the original problem, someone here can try to solve it.

@Feenix 

My real name is Carl James Love.

@acer Acer,

After issuing the command readlib(realroot) (in Maple 16 or earlier, of course), is there some way to list all of the global names that are newly defined as a result of that command? In this case, that list would include zero_one, polyvariations, and midpoint.

@Carl Love 

Where does the procedure zero_one come from? It is not defined explicitly in your code proving1.txt. After running the code in Maple 16, this procedure exists. After running the code in later Maple, the procedure does not exist. The absence of this procedure is the reason for the error.

@Feenix Thanks. That's what I needed. So far I've been able to confirm what you report: The program works in Maple 16 and errors out in any later Maple.