3 Programming in Maple (p.186-187)

[Lady Fiorinda was] in the theoric of these matters liberally grounded    through daily sage expositions and informations by Doctor Vandermast, who had these four years past been to her for instructor and tutor. To try her paces and put in practice the doctor’s principles and her own most will-o’-the-wisp and unexperimental embroiderings upon them, ready means lay to hand. . .
- E. R. Eddison, The Mezentian Gate, Book VI.


Maple is useful as a collection of "black boxes," but it is more useful still as a very high-level programming language. Since most of the tasks undertaken by Maple are "one-off" calculations (as opposed to "batch" calculations, which require many executions of the same program), it makes sense that Maple is an interpreted, rather than compiled, language. This is true even for the Maple library, because for large problems the cost will be dominated by the manipulation of large objects. Some crucial operations, though, are performed by kernel routines, which are compiled for efficiency.

With the external calling features, new to Maple 6 and improved for Maple 7, it is now possible to "tune" these efficiency tradeoffs more closely for any particular application. With the external calling features, new to Maple 6 and improved for Maple 7, it is now possible to "tune" these efficiency tradeoffs more closely for any particular application.

Maple procedures can be divided loosely into two types: operators, and more general procedures. Procedures and related structures may be bundled together into a module. An operator is meant to imitate a mathematical operator, both in notation (insofar as this is possible in ASCII) and in action. The .rst section of this chapter deals with general procedures and their uses. These can do essentially anything computable. Since Maple is a high-level language, you can express these actions in many ways. The section following that looks at operators.

For more in-depth information on how to program in Maple, see [44] and the detailed examples in the directory samples/ch06, which can be found on Windows systems in the directory Program Files/Maple 7. For an extended example of revising a program for efficiency, see [50]. For examples of useful programs, see [21].

3.1 Procedures

A Maple procedure always returns a value. It is the value of the last statement executed in the procedure before returning, or else the value of an explicit return statement. See ?return. This value may be NULL, which does not print anything on output. The distinction between NULL and "no value" is academic. One important consequence of a procedure returning NULL is that the environment variables %, %%, and %%% are not changed. The procedures print and lprint use this deliberately. [We will discuss environment variables in more detail later.] The procedures solve, fsolve, and dsolve, for example, will return NULL if they .nd no solution, and sometimes this takes special handling in programs. One simple way to deal with this with solve is to enclose the results from solve in set braces ( { } ), converting a possible NULL value to the empty set (and incidentally removing multiplicity; use list brackets if you wish to preserve multiplicity).