That convert in essence replaces D with diff, and we do know that diff works.  That doesn't say why D doesn't work.

@Carl Love I posted my That Clarifies reply to Preben before seeing your mesage.  It agrees with what you have written above.

@Preben Alsholm Ah, that clarifies things even more.  When plotting a vertical segment, if the x coordinate's data is fuzzy even a little bit, the horizontal range is set according to the data.  But if the data is absolutely constant, then the horizontal range is set out of other considerations.  For instance, the following command  sets the x range from -1 to 1 although no view is specified:

plot([0,t, t=0..1]);

@Preben Alsholm Of course! Your observations is right on the mark.  Asking Maple to draw a vertical line segment is not enough.  What is it to take for the horizontal range?

I had assumed implicitly that a polar plot will inclulde the origin.  But there is no basis for that assumption.  If we want to inlcude the origin, then we do:

plot([0, 1/cos(t)], t=0..Pi/3, coords=polar);

and get the correct plot.

In view of this, I am now somewhat puzzled with Kitonum's comment whereby the Classic worksheet produces the correct plot.  Perhaps the Classic worksheet includes the origin in a polar plot by default.

Note added a minute later: To counter my own argument, how do we explain this then?

plot([1,t, t=0..1]);

I don't use the Classic interface.  In the regular interface the bug goes back to at least MapleV-R4.   I was reminded of this while cleaning up my old mailbox today.  I had brought this up in the MUG (Maple Users Group -- remember that?) in 1999 (!).   I should have filed a formal bug report then, but I didn't, assuming that Maple developers were reading the MUG messages.

I suspect that Maple developers do read Maple Primes now.  If no one from Maple responds, I will file a formal bug report.

@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.