Char, Bruce W.; Geddes, Keith O.; Gonnet, Gaston H.; Leong, Benton L.; Monagan, Michael B.; Watt, Stephen M. Maple V Library reference manual. (English) Zbl 0763.68046 New York etc.: Springer-Verlag. xxv, 698 p. (1991). During the past ten years various computer algebra systems – that is software packages designed primarily for non-numerical computations – have become widely available on several different types of computers. Examples of such systems are Derive, Macsyma, Maple, Mathematica, and Reduce. A comparison of the performance of some such systems occurs in the survey of B. Simon [Notices of AMS, Vol. 37 No 7, pp. 861-868 (1990)].Maple V is the name of the current version of the symbolic computation system designed at the University of Waterloo. The design and implementation of Maple is an on-going project – the first version was published about ten years ago. The earlier versions of Maple have been well received by users – a part of the Maple system is included in the MathCAD software and the number of books about Maple and its applications is steadily growing. The present version is available for several different kinds of computers starting with IBM PC computers with 2M of main memory and including several UNIX machines. The Maple systems provides hundreds of functions for use at all mathematical levels. In addition to extensive symbolic computation features there are functions for numerical computation, graphical representation of curves, surfaces, and data as well as for many other computational tasks. For efficiency some parts of the Maple system reside in libraries or ”packages” and they must be loaded before use. Packages cover a wide range of topics – some examples are calculus, linear algebra, statistics, simplex linear optimization, Gröbner bases, discrete mathematics, number theory, applied mathematics, and geometry. The Maple gallery of higher transcendental functions contains all the standard functions and also e.g. the highly useful generalized hypergeometric function \({}_ pF_ q\) as well as the Meier \(G-\)function. The user can also write own programs or extend the system using the Maple programming language. The Maple V documentation comprises several volumes covering various features of its use and its features on a particular computer. The Maple V Library Reference Manual covers all of the functions that are available in the Maple library. The action of each function is carefully explained with an example of its use. Several examples are provided for more complicated functions to illuminate various fine points. A remarkable feature is that the user has access to the Maple language source code of most functions. The Library Reference Manual is exemplary in its clarity and in its pleasant format to read. Reviewer: M.Vuorinen (Helsinki) Cited in 3 ReviewsCited in 49 Documents MSC: 68W30 Symbolic computation and algebraic computation 65-04 Software, source code, etc. for problems pertaining to numerical analysis 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science Keywords:mathematical software; computer algebra; symbolic computation Software:Maple; Mathcad PDFBibTeX XMLCite \textit{B. W. Char} et al., Maple V Library reference manual. New York etc.: Springer-Verlag (1991; Zbl 0763.68046)