@MrYouMath I have nothing against Tom Leslie's answer; it's totally correct. But I can't see how it's what you're looking for and mine isn't. Didn't you say that you want to use alpha (implicit function) rather than alpha(t) (explicit function)?

@sand15 Statistics:-Sample is a fine way to solve the problem. It's quite efficient for the "known" distributions. It simply hadn't occurred to me to mention it. The job can also be done by LinearAlgebra:-RandomVector.

@codell In order to answer your Question "why this happens", I need an example of "this", the phenomenon in question. I don't know how to make up such an example myself. If you can make a smaller example of "a particular type of system", great; if not, I can work with the quadratics in 16 variables. And please point out with a comment:

1. "a particular variable free"
2. "where this variable is the root of a polynomial"

I'm also curious whether using eliminate instead of solve will correct this problem. Simply replace solve with eliminate; the argument syntax is the same:

eliminate({equations}, {variables that you don't want to be free});

Please post an example in Maple code, the need for which should've been obvious.

Please don't change a Question after it has been Answered, ever. Instead, post a new Question. Changing the Question makes the already-posted Answer look like nonsense, which is extremely disrespectful to the person who wrote the Answer.

@jacksonmeg To avoid the RootOfs, you need to use option explicit, as shown by Kitonum.

@brownr Yes, that's essentially correct. Vote up. The only quibble that I have is with the word "kernel". It should be replaced with "default" or "non-package" or "global". The default int isn't a kernel command because it's written in Maple.

There are a great many Posts and Questions that have disappeared, and even more Answers and Replies are missing although their Questions and Posts remain. It has been reported here many times. I doubt that it has anything to do with spam filtering.

I wonder if there's a record of when things were deleted.

@jcrook Please carefully reread my first reponse titled "Problem with theta range." It explains precisely why your answers are double the correct answers.

Note that the "kernel connection" message, while correct in a very narrow sense, is also very misleading, because the vast majority of times that you get that message are due to the kernel crashing due to its own internal bugs. If you get this message during an active Maple session (as opposed to a session that has just started), I'd guess that the chance that the problem has anything to do with firewalls is less than 1 in 10,000.

@Joe Riel Is your proposed orseq any better than ormap?

@BOverdorp Erasing all variables is an unusual thing to do, although if you insist, I could give you a command for it. Almost certainly you should try a different approach. The .mpl file should contain a procedure with parameter H. You read that file once, before entering the loop. The statement in the loop should be an invocation of the procedure. The local variables of the procedure are automatically re-initialized each time the procedure is run.

@tomleslie Command-line Maple won't run worksheets, but it will run .mpl files. The .mpl file to be run can be put on the command line that invokes cmaple in the manner that the OP was trying (see ?maple). Like I told the OP, this is not the solution to his problem, but it is occasionally useful. Indeed, I use something like this to update archives (libraries).

@one man The new surface plots look excellent, and I think that you can how see much superior they are compared to those produced with implicitplot3d. Did you use plot3d? You don't show any Maple code, so I don't know exactly what you mean by "array" and "matrix". If you haven't done so already, I should be able to take your procedure and turn it into something that can be used with plot3d in the form

plot3d([X, Y, Z], a..b, c..d);

@one man A parametrization of a surface is a function from R^2 to R^3 (with some smoothness requirements). We can safely ignore the smoothness requirements, but we need the function. If you could provide a purely numeric procedure of two real arguments that returns a list of three reals, that would be a great achievement and a facilitator of 3D plotting. Perhaps you could take what you have done with curves and do some interpolating. See ?CurveFitting,ArrayInterpolation.