@Markiyan Hirnyk Yes, I know that.  My question still remains:  Why don't the commands that I have shown work as advertised?  Let us note that the following produces the correct result:

plot(cos(3*t), t=0..Pi, coords=polar);

@JohnPo It is not clear from your questions whether you are looking for A^(-1) or the solutoin of Ax=b.  The two are equivalent in principle, but very different computationally.  If you have a problem with solving Ax=b, then post a minimal worksheet that exhibits the problem.

When I do M^(-1) for a matrix M, I don't get the error message that you get, so I assume that the problem is in your matrix M.  Post a minimal worksheet that shows the problem.

Hi @Carl Love, your dedication to Maple Primes, and the wealth of your contributions to this forum is undeniable, and I have personally much benefited from your help.  However, I see some harm in your supplying a complete answer to a question which is obviously a homework problem.  The student will submit your solution to the teacher and get a good grade, but is deprived of the intellectual exercise which the homework was intended to provide.

Perhaps a better approach to responding to such questions is to provide hints to point the student in the right direction, but not do a wholesale giveaway of the solution.

@kxiaocai The Maple expression Matrix(3,3, (i,j)->f(i,j)) produces a 3×3 matrix whose (i,j) entry is f(i,j).  In your case, we want the (i,j) entry to be ∂Ri/∂pj. so that's what I wrote.

@nm What is the utility/software shown in your screen capture, and it is in what operating system?

@Axel Vogt The ultimate goal to to insert the saved graphics in LaTeX articles which the students write.  Saving in raster formats, such as gif or jpeg produces poor results.  EPS or PDF are the right choices there.  We chose PDF for various secondary reasons.

@Markiyan Hirnyk Yes, I know about the problem that you have shown in plot1.pdf.  I get a similar result when I attempt to export a graphic interactively.  I think this is a bug in Mathematica 10.0.2.0 implementation on Linux.

The Export[] command, however, works just fine, as in Export["plot2.pdf", %].   See: plot2.pdf

@Alejandro Jakubi thanks for your input.  I suspect that Maple is not capable of doing this.  This is unfortunate, since I see that as a factor that drives my student away from Maple and toward that other competing CAS which does handle PDF exports properly.

This is not a big problem for myself personally—I work exclusively in Linux where I export Maple's graphics as EPS, then from the command-line I apply epstopdf to convert to PDF.  However, my undergraduate students who work on platforms other than Linux don't like command-line tools, so they are turned off by Maple for this reason.

This is a serious issue for Maple's marketability, and I hope that it will be addressed soon.

@pmdearing 

The choice of alpha < Pi/2 versus alpha <=Pi/2 is not at issue here. The range 0 <= alpha < Pi/2 corresponds to the entire sheet of the hyperboloid which has infinite extent, and therefore it won't fit in your computer screen.  You will have to cut alpha off at a finite distance away from Pi/2 to produce a finite sheet.  I chose to cut it off at Pi/3.

As to:

> limiting alpha to the positive domain gives one of two sheets

Extending alpha to the negative region will not produce the other sheet.  Your formula is that of a single sheet of a hyperboloid.  To get the other sheet replace the vector v by -v.

As to:

> Assuming v to be an elementary unit vector is too limited.

The choice v = <1,0,0> was only for illustration.  You may take v to be any unit vector that you wish.  If it is not a unit vector, e.g., v = <1,2,3>, then divide it by its own length, that is change it to v = <1,2,3>/sqrt(14).  That normalizes it to a unit vector.

@spm71 In your original question you wrote that you want to type the commands into a file and then execute the file.  But now you write "when I type ... in the command prompt...".  So, do you want to write commands to a file, or type them at the command prompt?

Anyway, when you type at the command prompt, pressing "Enter" tells Maple to go ahead and execute what you have typed.  However, "for i from 1 to 5 do" is not a complete command, so understandably Maple refuses to execute it.  To break a line rather than execute it, hold down then Shift key and then press Enter.

As to your question regarding executing a file, I have already written that you do it in Maple with the command:

    read "thefilename";

@Carl Love That's interesting.  Following your line of investigation, I produced the following minimal example which demonstrates the problem:

> eq := Pi*x = piecewise(t<1, 2 , 3);

> solve(eq, x);

> plot(%, t=0..4);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

As you have pointed out, the problem is that the pieces of the solution are expressed as lists rathen than simple expressions.  I will report this to Maple Support for a possible fix.

@H-R I know nothing about Word so I cannot be of help here.  I think writing mathematics in Word is quite uncommon.  Most mathematics is written in LaTeX, and the EPS format integrates quite nicely with LaTeX.

@Carl Love Thank you very much for your very thorough explanation of the issue.  I should have looked at the case x$0 more closely.

@sazroberson I have had no problems with exporting images in the EPS format and including them in books and journal articles.  Perhaps erik10's needs go beyond the basic usage which I have dealt with.

That said, I do realize that a major shortcoming of the EPS format is its inability to handle transparency, but that is not a fault of Maple; it is a limitation of EPS.  In a few cases where I have had to deal with transparency, I have exported the image as PNG and then wrapped the result in EPS.