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First leaves: a tutorial introduction to Maple V. (English) Zbl 0758.68037

New York, NY etc.: Springer-Verlag. XVIII, 253 p. (1992).
Computer algebra systems allow, instead of working with numerical data, the manipulation of formulas and mathematical expressions. The impact of computer algebra for future teaching and research in mathematics, as well as in science and engineering in general, will be considerable.
Among the many computer algebra systems on the market Maple is one of the best. It is fast, easy to use, highly dependable and has a collection of excellent algorithms in its library. The design of Maple and its kernel has set a standard which will be difficult to follow.
The only weak point of the system were the user interface and the documentation. At present the user interface is undergoing considerable changes and a new set of documentation has been published by the Springer Verlag. The documentation is enlarged and consists of three books published as separate volumes. These are: the tutorial, the Maple library reference manual and the Maple language description.
Although documentation for computer algebra packages are never really perfect, the documentation of Maple at present is rather satisfactory, and it provides the user with information suitable for all levels of experience.
The tutorial starts with a potpourri of commands and capabilities of the system. This section is meant to arise the curiosity of the reader. In the first chapter the user is introduced into all aspects of the interactive session, tables show him the available commands and their functionality. The sections are complemented by special paragraphs calling to his attention possible errors, furthermore particularities are pointed out to the user while he is making his first steps through the system.
The second chapter deals with simplification and evaluation. This usually in computer algebra systems is a difficult part to explain. The essential parts of the system are explained on a nontechnical level; this section is easy understandable but not too detailed. Quotations in Maple and the effect of different quotation marks (to the reviewer one of the weak points with respect to user friendliness of the system) are only explained briefly.
Then after these basic remarks on simplification and quotation different datatypes are introduced and the functionality of more advanced commands and packages is explained.
Chapter 3 explains the Maple programming language. After some introductory explanation of programming the reader will find in this section a lot of information he does not expect under this heading, like functional operators, the use of the Maple initialization file and how helpfiles are created for user defined functions. Then debugging of programs written in the Maple language is introduced. Debugging is either done by using functions like trace and printlevel or by mint.
In chapter 4 an introduction to the improved graphics capabilities of the Maple system is given. Then one of the shortest chapters is chapter 5 where measuring and improvement of performance is discussed. Since experienced Maple programmers know an abundance of tips and tricks for improving Maple programs by making use of some insight of the internal functioning of the system, it is a mystery to the reviewer why this section has not been enlarged considerably.
The most important section of the tutorial is that one with advanced examples. Here eight detailed examples illustrate the use of computer algebra. The examples range from balancing chemical reactions, then go over to stock market computations by use of the linear algebra package, and finally a discussion of some questions of numerical approximation of functions is given.
In general a well written tutorial which can be used as a text in introductory courses and which provides interesting information even for non-Maple users.

MSC:

68W30 Symbolic computation and algebraic computation
12Y05 Computational aspects of field theory and polynomials (MSC2010)
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
13P99 Computational aspects and applications of commutative rings

Software:

Maple
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