@vs140580 You don't have to program it yourself by hand, for combinations or permutations. The combinat and Iterator packages already provide commands that do this (without constructing or storing the complete set at once). You seem to have trouble understanding that point.

@vs140580 I believe that we already (before) understood your point: You don't want Maple to compute all the permutations at once, because there would be too many to store at once in memory.

You have at least three choices in how to generate (iterate over) the permutations one at a time: write your own procedure, use the combinat:-nextperm command, or use the Iterator package appropriately.

In each of those three scenarios the complete set of permutations will not be constructed at any one time. The permutations get constructed/iterated-over, individually and one at a time. Your code could then manipulate or test each permutation, individually and one at a time.

Your request is quite common. That's why there are two ways already built into Maple for doing it.

@ogunmiloro Only you can state what are reasonable ranges for the parameters.

If you want the "best" parameter values then you probably would be better off doing global optimization rather than using the local optimization that Optimization:-Minimize offers here. You don't just want a relative minimum. The DirectSearch (version 2) package may be a decent choice, available from the Application Center for your Maple 18 I believe.

Also, global optimization becomes very time consuiming and expensive as the number of parameters grows. You have many parameters.

I hope that you understand that you (not us) are in best the position to state sensibly what might be reasonable ranges for the parameters.

Also, you still need to state what you want to happen if some parameter values cause the numeric solution to encouter an appararent singularity. You are in the position to judge that, not us. Do you want those parameter values to be accepted as possible candidates, or rejected outright? I'm guessing that you might want them rejected, but you have to judge.

@ogunmiloro You have not followed several of my suggestions, requests, and comments.

You did not change the C[C] (or C__C) used in the select call, to instead refer to one of the dependent variables of the DE system. And so, as I described would happen, you now get an error because there is no match and you are passing NULL to rhs. As I asked belore: which dependent variable of the DE system are you trying to access in computing the objective?

Also, you will need to accomodate the situation that the numeric solution encounters a singularity. How should the objective function behave in that case?

Also, you should probably supply ranges for the parameters in the Minimize call.

I have a version which computes a result from Minimize. But I made up the fixes for the issues I described. You need to figure out how you need these aspects to be adjusted, or else the results would be meaningless.

It might help if you uploaded and attach your document, so that we could see the original expression if it is significantly different (and don't have to type in either). It would also let us determine which version you're using.

You called simplify(..., symbolic) on something. Does that mean that you don't care about the branch cuts, or are not aware of the possible ramifications of doing so?

Do you have any objection to using a command or calling sequence which is not offered directly by the context-panel?

On Windows the 64bit Maple version comes bundled with the LLVM compiler, and usually the Compiler:-Compile command works "out of the box". In other words, you usually don't have to run the Compiler:-Setup command.

Is there a particular reason why you wanted to switch the external compiler from LLVM to something else like the Microsoft compiler?

Did you have a problem running Compiler:-Compiler with the default external LLVM compiler? (Perhaps you mistakenly thought that you had to run Setup?) Or do you need to use the inmem=false option? Or some other reason?

note: I changed your Post into a Question.

@Carl Love I read that part and had the same question, and I was planning to submit a bug report.

@Carl Love The instructions to find the maximum and saddle-point are weird. It suggests rotating the 3D plot, presumably so that the x- and y-values could be approximately read off of the axis tickmarks.

It seems strange to me that students might be studying extrema and saddle-points and not be looking at computing the stationary points' approximations.

@Carl Love I was only looking withing a specific range on purpose. I had hoped that the student would at least investigate a little.

The question only asks for a (one) maximum and a (one) saddle-point, as I understand it.

@Scot Gould StringTools:-StringBuffer constructs a module, and is implemented in an OO manner. But it is not an Object (in the sense that its return value is not of type object, or in the technical Object sense which I believe was part of the OP's original queries.) It has no static exports and each instance carries its own copy of its exports.

That is in contrast to the Today constructor of the Calendar package.

[edit] Just to make this more confusing, there is also an example StringBuffer on the objects,methods Help page, and that is implemented with an Object constructor.

@Joe Riel Thanks, Joe. I wasn't paying attention and completely misunderstood the purpose of the example. My Answer clearly doesn't satisfy the quoted request.

Perhaps I should simply delete the answer.

[edit] I will let it stand, and instead quote from the object,methods Help page:

    Object Must Be Passed into Methods
    If you declare a method that needs to access the contents of
    an object, that object must be passed into the method as an
    argument.  This is in contrast to some object oriented languages
    which allow access to the contents of an object associated with
    the current invocation, either through direct access to the
    object's members or through a self variable.  The method will
    have access to the local variables of any object of the same
    class that the method was declared in.

@janhardo The idea of an interval of convergence was mentioned before. And this allows your last example to succeed.

value(Sum(x^(n - 1), n = 1 .. infinity)) assuming x>-1, x<1;

                                1
                            - -----
                              x - 1

You could also use active sum(...) instead of value(Sum(...)). And you could use abs(x)<1 instead of the pair x>-1, x<1.

What have you managed to do so far, with this?

@janhardo 

restart;
R := convert(ln(1+x),FPS):
value(R) assuming x>-1, x<1;
                             ln(1 + x)

sum(op(R), formal);
                             ln(1 + x)

[edit] The series does not converge for all x. The `sum` command is being careful about what it returns here. (It doesn't even converge for all real x. And judging by the context of this and earlier textbook questions this is not about complex numbers.)

You should show us what you've done so far, or describe with which details you got stuck, etc.