Benton Leong

Iris: design of an user interface program for symbolic algebra

We present the design of a user interface program that can be used with Maple and other symbolic algebra packages. Through the use of a standard communications protocol to such a program, symbolic algebra packages can shed the bulk of code not directly related to algebraic manipulations but can still use the facilities of a powerful user interface. This interface program is designed to be used on a variety of workstations in a consistent fashion.

The Maple Library

This manual describes all the functions available in the Maple library. The library is where the code for over 95% of Maple’s mathematical knowledge and expertise resides. The library routines are available for your inspection, study, and when appropriate, modification and extension. Each of these routines is written in the Maple programming language. Through the library, the Maple system and the algorithms that it uses can be dynamically extended and customized.

Global access to Maple information

Where can you turn when on-line help (?), this tutorial, or the Maple V Language Reference Manual do not help you overcome difficulties in using Maple? Who can you talk to about solving your special kinds of problems with Maple? In this section, we discuss additional sources of information available in person, in print, and through electronic media.

Less Simple Maple

We have seen how to use Maple as a calculator for algebraic and numerical computations, and for graphics. In this section, we explore how to use Maple in more sophisticated ways.

The Maple Programming Language

We have already seen many examples of two key elements of Maple’s programming language, the expression statement (a command or expression) and the assignment statement.

Interactive Use of Maple

Maple runs on many types of computer systems. Macintosh, DOS (with or without MS Windows), Unix (with or without the X Window System), SunView, NeXT, IBM CMS, and DEC VMS are some that Maple runs on. Nevertheless, all versions of Maple use essentially the same internal programming to perform the mathematical calculations. This part of Maple is known as the computational engine or algebra engine.

Measuring and improving performance

As any Maple user can easily observe, a complicated Maple computation can take seconds, minutes, or more. Symbolic computation can often require a lot of computer memory as well. Computer memory requirements are dictated not only by the length of the answer (the number of terms, number of symbols, or the number of digits in numbers), but also the size of the expressions generated in intermediate steps before the final result. If you are concerned about a Maple computation taking ”too long” or ”too much memory”, the first step to trying to remedy the situation is to find out how much time or memory the computation takes. In this section we discuss ways you can monitor how these resources are being consumed.

Statements and Expressions

There are eight types of statements in Maple. They will be described informally here. The formal syntax is given in Section 3.3.

Overview of the Maple Library

The Maple V Library Reference Manual describes all the functions available in the Maple library. The library is where the code for over 95% of Maple’s mathematical knowledge and expertise resides. The library routines are available for your inspection, study, and when appropriate, modification and extension. Each of these routines is written in the Maple programming language. Through the library, the Maple system and the algorithms that it uses can be dynamically extended and customized.

Arrays and Tables

One of the data types in Maple is the table structure. The array structure in Maple is a specialization of the table data structure in which the indices must be integer expression sequences lying within user-specified bounds. Arrays are used similarly to those in other programming languages, while tables correspond roughly to the ones provided in Snobol or Icon.