MuPAD

MuPAD comes with a very full-featured programming language. So much so, that I would say that this is one of MuPAD's greatest strengths. In contradistinction to other CASs, MuPAD allows:

It would take far more than an introductory exposition such as this to even scratch the surface of MuPAD's programming power, so we shall just look at a few simple examples. For more involved examples, try the expose command, or look at some of the files in your $MuPAD/share/examples directory.

For procedural programming, MuPAD offers all the standard programming requirements: loops of various sorts, branching, and recursion. Here, for example, is a simple procedure designed to implement Hofstadter's chaotic function, with line numbers as shown:

1   q:=proc(n) option remember;
2   begin
3   if n<=2 then
4       1
5   else
6       q(n-q(n-1))+q(n-q(n-2))
7   end_if;
8   end_proc;

Suppose we create a small file called Hofstadter.mu containing these lines, and we read it into MuPAD with

>> read("Hofstadter.mu");

>> q(i)$i=1..20;
      1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, 11, 12

>> plot2d([Mode = List,[point(u,q(u)) $ u=1..10000]]);

We can define simple functions very readily by using an “arrow” definition:

>> f:=x->x^2+1;

Curiously, I can't find any reference to this in the manual.

For a slightly more involved example, suppose we try to write a program to generate truth tables. That is, so that something like

>> tt(p and q);

will produce

                                  p, q, p and q
                                  T, T, T
                                  T, F, F
                                  F, T, F
                                  F, F, F

 1  tt:=proc()
 2  local i,j,n,l,ft,f,r,rf;
 3  begin
 4      if args(0) <= 1 then error("Must include all variables");
 5      end_if;
 6
 7      ft:=[FALSE,TRUE];
 8      n:=args(0)-1;
 9      print(Unquoted,args(j)$j=2..args(0),expr2text(args(1)));
10
11      for j from 2^n-1 downto 0 do
12         f:=args(1);
13
14         for i from 1 to n do
15            l[i]:=floor(j/(2^(n-i))) mod 2;
16         end_for;
17
18         for i from 1 to n do
19            f:=subs(f,args(i+1)=ft[l[i]+1]);
20         end_for;
21
22         for i from 1 to n do
23            r[i]:=_if(l[i]=0,"F","T");
24         end_for;
25
26         rf:=_if(simplify(f,logic),"T","F");
27
28         print(Unquoted,r[i]$hold(i)=1..n,rf);
29      end_for;
30  end_proc:

This program may be considered as skeletal only; for example, it does no type checking.

There are several ways of obtaining information about MuPAD: through the extensive on-line help facility, or from published articles.

A few MuPAD books are currently available, but I haven't seen one. The on-line documentation is excellent. It exists in two forms: plain ASCII (for use with MuPAD in terminal mode); and dvi with hyperlinks, when using MuPAD under X.

For ASCII, the help commands are obtained with a question mark:

>> ?<command>

will provide a few screens of information about <command>. Notice that this is the only MuPAD command which doesn't require a terminating colon or semicolon. The amount of documentation varies; but usually includes a basic description, some examples, and a list of related commands. Some help files are very large indeed; others very small. For example

>> ?stats::median

>> ?Dom::Matrix

Information about a MuPAD library can be obtained with the info command; for example

>> info(numlib);

provides a list of all commands in the numlib library. You can also use

>> ?numlib

You can see the MuPAD programs which define a function with the use of expose. Again, programs vary greatly in length. For example

>> expose(length);

returns a short function defined by a six-line program, but

>> expose(D)

>> op(Dom::Matrix);

The documentation for xmupad is provided in the form of a dvi file of the manual, with lots of hyperlinks. The manual can actually be read independently of MuPAD with the hypage command. As with the commands for starting MuPAD, this is a call to a shell script. However, hypage is started automatically with xmupad.

All the relevant documentation is provided in the form of hyTeX dvi files; that is, dvi files with embedded hyperlinks. If you are used to TeX and dvi viewers, this approach will seem very sensible: the mathematics is superbly typeset, as you'd expect, and there are plenty of included graphics. It may seem a bit odd at first to use a book (with all the trimmings: table of contents, chapters, an index) as the paradigm for on-line documentation, but in fact it works very well. And after all, everybody is familiar with the structure of a book, so there is no need to learn the particular exigencies and peculiarities of some new and strange help system.

The amount of information is superb. As well as discussions on all commands and functions, there are extensive chapters on graphics, programming, and debugging, as well as two excellent demos. Moreover, as well as the manual, there are hytex dvi files covering all the MuPAD libraries, as well a handy quick reference.

Once xmupad and hypage are up and running, the help command

>> ?<command>

will open up the manual at the relevant page. Once inside the manual, you can use the hyperlinks to travel through other similar commands. I find hypage very easy to use. If you have installed MuPAD, you should find this entire article redundant, as everything in it is covered in far greater depth in the manual.

A screen shot of hypage is shown in Figure 4.

Figure 4. Hypage—MuPAD's Graphics Hypertext Manual

However, I have a few niggles with hypage. The main one is that there is no way of changing the font size or page layout. If you reduce the size of the hypage window, for example, the text is not reformatted to fit the available window size, and so you have to use inconvenient scroll bars to view the text. This makes hypage nearly unworkable on a 640x480 VGA screen (such as on my laptop). Moreover, all the text is in the same colour (hyperlinks are given by underlines), which I find a bit dull. There also doesn't seem to be much in the way of keystroke movements. I found three (they aren't listed in the manual): p for previous page; f for forward, and r for return (to the linking page).

On the other hand, with a higher resolution screen, hypage is a delight to use.