@sunflower 

1. Don't remove a Reply after it has already been replied to. That makes my previous Reply seem out of context. You had asked for an explanation of the lines where I defined rectangle.

2. If you want another house, you'll need to tell me what to put on it. I don't have much artistic imagination. And why do you want another house? How about just asking a question directly?

3. I have no idea what you mean by "form".

4. Your English doesn't make me unhappy.

@sunflower I don't know if this'll be much help to you, but those two lines mean the same thing as

rectangle:= proc(Point, height, width)
     plots:-polygonplot(
          [Point, Point+[width,0], Point+[width,height], Point+[0,height], Point],
          args[4..]
     )
end proc:

You should look up ?parameter in the Maple help. That should keep you occupied for a few days.

The integral I5 clearly converges for any real x0! I'd expect even my good calculus II students to see that (without using Maple). The expression under the radical is strictly positive, so there are no poles to worry about. Do a limit comparison test with Int(1/x^4, x= 1..infinity).

P.S.: I just saw that Preben said essentially the same thing.

Your example doesn't make sense. What does Oy mean? What does "limit by y, x=1, y=5" mean?

To understand what a tubeplot is, you must first understand what a spacecurve is. Look up the help for spacecurve (?spacecurve). Let me know if you understand that. If you don't understand that, we'll need to start there.

@tomleslie Tom's Answer is the true answer (an exposition of The Way), not a fake. If you want to do symbolic computation, don't use floats. His Answer works on irrational bases also, despite what he says, and any float can be converted to a rational.

Kitonum's Answer uses a fake technique. This is not meant as a disparagement of Kitonum's Answer---the fake can be useful sometimes.

@Markiyan Hirnyk I think that four digits accuracy is pretty darn good from a plot which consists of exactly 225 points, that is, only three digits worth of points. It is big win for plot that it found this small turn in the function. Another way of looking at it is that your maximum and my maximum are visually indistinguishable on the scale of the plot. And why should you expect a plot to contain information that can't be visually distinguished? My program is intended to find the extremal points that actually occur on plots, not the extrema of analytic functions. You intentionally poison the well with your intentionally irrelevant comparisons.

@Markiyan Hirnyk I made a small adjustment to my plaintext code. I believe that now when you paste it into 2D input it'll work (although I have no interest in testing this myself). Give it another try. I do always expect/hope for my plaintext code to work in 2D input, although I personally wouldn't touch the 2D input with a ten-foot pole for programming. For static display of mathematical expressions, it's okay, not great.

@Duplax The link that you gave opens the file as an XML tree (in browser Chrome). But how did you download the file?

@rlopez Surely we all know that the actual matrix A that you use doesn't matter. Not being able to regenerate your A, your worksheet can be read as a static document, as if it were in a book. But I like to use Maple to generate "active" content, so that there's an extra dimension to it not present when reading a book. As a reader, I like to read a worksheet starting with its output removed and having the output computed line by line as I read.

My experience is that most (but certainly not all) good-reading worksheets have some randomly generated examples. I don't think that it's widely known that Maple's random results are reproducible by other users as long as you start from a restart point and don't use the command randomize() (with no arguments). Using randomize(n) for constants n is fine.

@taro I have very little experience with monomial orderings. I have more experience with rearranging the side relations to produce a desired outcome. All I can say about the monomial orderings is that the plex works better if you specify more variables.

@Carl Love Well, did that work for you? It disturbs me to not get any response to an Answer.

I also haven't been able to reproduce Dr Lopez's matrix A, rerunning the loop ten times, for a total of 50,000 candidate matrices. It isn't clear whether he used restart. If he had used restart, then he'd be able to say something like "From the matrices with determinant 1, I chose the 34th" and then that would be reproducible for anyone else running the code as long as they also started from restart.

Markiyan's point is that none of his randomly generated matrices are exactly the same matrix A as that used by Dr Lopez.

@Thomas Richard On Unix, you can just use Maple's system command to invoke Unix's mail command. No need for a shell script or command-line Maple.

@vv I appreciate what you're saying, and I was going to suggest using smaller random numbers, but I thought that I'd work with the OP's own function. But what do you mean by "will not work"? My code does produce an answer, and it's an answer that's different than the answer produced when R is constant; indeed, it's very similar to the answer produced by your code.

@taro What I like about my solution is that it uses one command and only the four equations given by the OP. The substitution equations need to be arranged so that the eliminated expressions are on the left and the substitued variable is on the right, but that is the only change that is needed.

Since the purpose of this post is to explain simplify with side relations, the need for this left-to-right reversal should be pointed out explicitly.