@Christian Wolinski Yes, I am working on it. I'm sure that you realize that it's difficult to exclude those undesirables from the indets. If you get to it before I do, then I think that he should select your Answer as Best.

The most important thing is that the OP learn to use indets rather than the details of this particular usage of it.

There have been numerous reports recently of this strange behavior, and the consensus has been that it's due to having a pirated copy of the Maple code.

@Joe Riel Yes, most associative operators should have a corresponding command with special evaluation rules akin to {seq, add, mul}. So that would include union, intersect, and, or. I don't include cat or xor because they have no possibility of internal simplification, so you might as well just apply their functional (prefix) forms to seq. 

@radaar Sorry for the delay in answering your memory question. I ran into a problem (a bug, I guess) specific to using Statistics:-Sample with Grid. I finally figured out a workaround for it, and I just Posted my version of your above code in the Posts section. Better yet, the solution is elegant, runs superbly fast, and uses an insigificant amount of memory. So, go read that Post.

The major problem with your code was that you were using Grid to do a small computation inside a large loop. Grid is very inefficient for small computations due to the overhead of initiating the kernels. The correct way is to make Grid:-Map or Grid:-Seq be the outer loop rather than be in the outer loop.

@JAMET The error is because the length of your major axis is less than the distance between the foci. Perhaps you meant 2*lma.

@nm Yes, I was aware of this when I posted the code. I was waiting for someone, mostly likely you, to notice ;-).

Actually, what stopped me was that in order to fix this properly, I need to know what the degree of the following is supposed to be:

diff(y(x), x) = y(x)^(1/2)  # (1)

Is it 1 or 2? Clearly, the degree of

diff(y(x),x,x) = diff(y(x),x)^(1/2) + y(x) 

is 2. But with #(1), I don't know if the y(x) is to be considered a "zeroeth-order derivative". If yes, then the degree of #(1) is 2; if no, then it's 1.

@ThU Perhaps I'm being naive, but I interpretted the Question to mean that the OP wanted the 2s to be placed in the algebraic exponents, while the minus signs were to remain in the arguments to exp. Your code doesn't separate the minus signs from the 2s. 

If I am indeed being naive about the OP's intent, then your method does seem like a reasonable way to get the desired result if you can get to the expression before it's entered.

@Guy1 To "vote up", you need to click on the thumb icon in the header of the Answer (upper right, under the timestamp). Please do that.

I added some significant details to the Answer, so you should reread it; specifically, I made a distinction between "merger of animations" and "animation of a merger".

I have no idea how or why this Answer got turned into a separate Question. I had nothing to do with it.  Unfortunately, I have no way to put it back where it belongs: an Answer to "Expand and negative exponent".

@Rouben Rostamian  Your choice of file extension, .maple, is a bit unfortunate because it's used for the "meta-worksheets" that were introduced a few versions ago. (These are collections of worksheets, variable assignments, and associated files.) The most commonly used extension for plaintext Maple code is .mpl.

@Oliveira See the help page ?worksheet,reference,initialization

@radaar The command map doesn't do multiprocessing. Why not try gradually increasing the value of numcpus as I suggested? Start with kernelopts(numcpus= 2).

@Thomas Richard Yes, I only used expand for pedagogical reasons. For practical coding, I'd use orthopoly:-T(5,x) to get the polynomial in place of expand(cos(5*arccos(x))).

@radaar Yes, using Grid:-Map will use a lot of memory. From your example worksheet, it doesn't seem like that will be a problem. Just increase the number of processors until you either run out of processors or memory. The memory usage should be roughly a linear function of the number of processors. If it isn't, there's likely some bug that'll require expert attention.

@nm Your Answer is okay for the n=2 case, but has no relevance to the other cases. That's fine, but I want to alert the OP not to try to apply your Answer to the other cases, because doing so could cause confusion.

I don't see how this Answer deserves a vote up, although someone gave it one.