Hints for using Maple 6

Syntax

As you type in commands, Maple waits for a semicolon ; or a colon : before it evaluates the expression. If a colon is entered, the result is not displayed. This is useful when reading files or defining procedures.

Maple interpretes several characters differently than other programming languages:

The colon-equal := is assignment to variables. Note that Maple does not syntactically distinguish between variables and indeterminates. Hence x := x+1 will cause a bad crash, because now the variable x contains the value of x + 1, which is a self-reference. [In newer Maple versions, such recursion is caught without crashing.]
The equal sign = designates an equation, which yields an expression, not an assignment. A common mistake is to write x = 2 meaning x := 2 instead.
The percent sign % refers to the result of the last eval uation, and two %% to the penultimate result. [In older Maple versions, the double quote " refers to the result of the last evaluation (ditto character) and does not deliminate strings.]
The double quote " deliminates strings, as in "REF.mpl". The backquote ` deliminates variables names with special characters, as in `My Documents`.
The double vertical bar || is string concatenation. [In older Maple versions, the period . is string concatenation. Thus REF.mpl is actually the symbol REFmpl. It is now used as the non-commutative multiplication symbol.]
The single quote ' is used to delay evaluation. Thus 'T' evaluates to the symbol T rather than the value that T may have been assigned.
The circumflex ^ is used as the exponentiation operator.
The pound sign # is used to indicates comments. Everything following the # sign to the end of the line is ignored.

Unexpected behaviour

solve returns nothing if the system is inconsistent.
When a variable is assigned a matrix (from the linalg library), the variable evaluates to itself, rather than the value. To get the assigned matrix, you must call evalm.
Similarly, evalb tests if the matrices are at the same storage location; equal tests them as equal.
When computing the value of a matrix expression by evalm you must use &* for matrix multiplication. This is because Maple assumes that the operator * is commutative and will perform simplifications before calling evalm.

Useful tricks

You may obtain help to almost anything that you read. For example, you can type ?while to obtain the syntax of a while loop. Even the code that I provide has help files built in, so you can do ?ref to obtain the specifications of that function.
The printlevel variable controls how much tracing information you get. In mathematical computations it is often important to know how a certain result was obtained. If you set printlevel:=3 the functions that I write will provide you with the intermediate results that you will find in the book.
Producing multiple plots. A plot in Maple is an object that is assignable to a variable. If assignment is done, it is not displayed. The plots library package contains a function display that then allows to view the plots. For example, to show simultaneously the sin function and 2 points you can type:
```
   plot1 := plot(sin(x), x=0 .. 2 * Pi):
   plot2 := plot([[1,2], [3,4]], style=point):
   plots[display]({plot1, plot2});
```
You can also animate multiple plots by displaying them in sequence. First, set the Plot Display to a separate Window via the Options menu on your Maple window. Then display the plot with the option insequence=true. Finally, Play the plot by clicking the right mouse button on the plot and selecting the Animation submenu.

Packages

In Maple, as in many languages, one may package a collection of procedures for purpose of

avoiding name conflicts of the procedures with the users' variables
dynamically loading of selected procedures in a package
accessing the entire package via short names for the procedures
providing online help, for example, for a package and its procedures

Each purpose is accomplished by Maple by a different command.

the customary protection mechanism of a name is by giving the procedures in a package compound names, such as `pkg_name/proc_name`, where pkg_name is the name of the package and proc_name the name of the procedure. An alternative is to use a subscripted name pkg_name['proc_name'] for the procedures in the package. In any case, pkg_name must be protected.
readlib is used to load a previously saved procedure. The global Maple variable libname contains the paths to all the directories that are searched for the procedure.
with ``points'' a selected procedure or an entire package to their short names. The names of the procedures in the package are retrieved from a Maple table that has to be stored in the variable pkg_name before issuing the with command. Each proc_name has an entry of the form pkg_name[proc_name] := 'readlib(`pkg_name/proc_name`)'; or a direct definition pkg_name[proc_name] := proc...end; in this table.
?proc_name retrieves the help file from a library. The help file is stored in the database maple.hdb by the makehelp command.