Maple V Library Reference Manual

The design and implementation of the Maple system is an on-going project of the Symbolic Com­ putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked from within a Maple session to view documentation on specific topics. In particular, the command ?updates points the user to documentation updates for each new version of Maple. The Maple project was first conceived in the autumn of 1980, growing out of discussions on the state of symbolic computation at the University of Waterloo. The authors wish to acknowledge many fruitful discussions with colleagues at the University of Waterloo, particularly Morven Gen­ tleman, Michael Malcolm, and Frank Tompa. It was recognized in these discussions that none ofthe locaIly-available systems for symbolic computation provided the facilities that should be expected for symbolic computation in modern computing environments. We concluded that since the basic design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and MACSYMA were based on 1960's computing technology, it would be wise to design a new system "from scratch". Thus we could take advantage of the software engineering technology which had become available in recent years, as well as drawing from the lessons of experience. Maple's basic features (elementary data structures, Input/output, arithmetic with numbers, and elementary simplification) are coded in a systems programming language for efficiency The design and implementation of the Maple system is an on-going project of the Symbolic ComƯ putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked from within a Maple session to view documentation on specific topics. In particular, the command?updates points the user to documentation updates for each new version of Maple. The Maple project was first conceived in the autumn of 1980, growing out of discussions on the state of symbolic computation at the University of Waterloo. The authors wish to acknowledge many fruitful discussions with colleagues at the University of Waterloo, particularly Morven GenƯ tleman, Michael Malcolm, and Frank Tompa. It was recognized in these discussions that none ofthe locaIly-available systems for symbolic computation provided the facilities that should be expected for symbolic computation in modern computing environments. We concluded that since the basic design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and MACSYMA were based on 1960's computing technology, it would be wise to design a new system "from scratch". Thus we could take advantage of the software engineering technology which had become available in recent years, as well as drawing from the lessons of experience. Maple's basic features (elementary data structures, Input/output, arithmetic with numbers, and elementary simplification) are coded in a systems programming language for efficiency The design and implementation of the Maple system is an on-going project of the Symbolic Com­ putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked from within a Maple session to view documentation on specific topics. In particular, the command?updates points the user to documentation updates for each new version of Maple. The Maple project was first conceived in the autumn of 1980 growing out of discussions on the state of symbolic computation at the University of Waterloo. The authors wish to acknowledge many fruitful discussions with colleagues at the University of Waterloo, particularly Morven Gen­ tleman, Michael Malcolm, and Frank Tompa. It was recognized in these discussions that none of the locally-available systems for symbolic computation provided the facilities that should be expected for symbolic computation in modern computing environments. We concluded that since the basic design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and to design a new system MACSYMA were based on 1960's computing technology, it would be wise from scratch taking advantage of the software engineering technology which had become available since then, as well as drawing from the lessons of experience. Maple's basic features (e. g. elementary data structures, input/output, arithmetic with numbers, and elementary simplification) are coded in a systems programming language for efficiency. In symbolic computation on computers, also known as computer algebra, keyboard and display replace the traditional pencil and paper in doing mathematical computations. Interactive computer programs, which are called computer algebra systems, allow their users to compute not only with numbers, but also with symbols, formulae, equations, and so on. Many mathematical computations such as differentiation, integration, and series expansion of functions, and inversion of matrices with symbolic entries, can be carried out quickly, with emphasis on exactness of results, and without much human effort. Computer algebra systems are powerful tools for mathematicians, physicists, chemists, engineers, technicians, psychologists, sociologists,..., in short, for anybody who needs to do mathematical computations. Com­ puter algebra systems are indispensable in modern pure and applied scien­ tific research and education. This book is a gentle introduction to one of the modern computer algebra systems, viz., Maple. Primary emphasis is on learning what can be done with Maple and how it can be used to solve (applied) mathematical problems. To this end, the book contains many examples and exercises, both elementary and more sophisticated. They stimulate you to use Maple and encourage you to find your way through the system. An advice: read this book in conjunction with the Maple system, try the examples, make variations of them, and try to solve the exercises. This book describes the Maple Symbolic Computation System and the Maple V language. It describes the numeric and symbolic expressions that can be used in Maple V. All the basic data types, such as names, polynomials, and functions, as well as structured data types, are covered. The book also gives a complete description of the programming language statements that are provided in the Maple V system and shows how a user can extend the functionality of the Maple V system by adding user-defined routines. The manual also provides a complete description of the Maple V system, including its 2D and 3D graphics. Maple V features a newly designed user interface on many systems. Separate appendices describe how to use Maple V on systems using the X Window System, DOS, and the Macintosh. This tutorial shows how to use Maple both as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding tasks. It covers topics such as the basic data types and statements in the Maple language. It explains the differences between numeric computation and symbolic computation and illustrates how both are used in Maple. Extensive'how-to'examples are used throughout the tutorial to show how common types of calculations can be expressed easily in Maple. The manual also uses many graphics examples to illustrate the way in which 2D and 3D graphics can aid in understanding the behavior of functions. Front Matter....Pages i-xxv The Maple Library....Pages 1-4 Main Routines....Pages 5-328 Packages....Pages 329-478 Packages for Discrete Mathematics....Pages 479-529 Packages for Applied Mathematics....Pages 531-563 Packages for Geometry....Pages 565-640 Miscellaneous Packages....Pages 641-662 Back Matter....Pages 663-699 Shows how to use Maple V both as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding and specialized tasks. Topics covered include the basic data types and statements in the Maple language. Annotation copyright Book News, Inc. Por An introduction to the computer algebra system, Maple, which focuses on its ability to solve applied mathematical problems. The text contains many examples and exercises, both elementary and advanced, which encourage the undergraduate student to use Maple at every given opportunity. A powerful, interactive algebra system for mathematical computation which is symbolic, numeric and graphical. It can be used as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding and specialized tasks An introduction to the Maple Symbolic Computation System and the Maple V language, which describes all basic data types, such as names, polynomials and functions. The book also explains the programming language statements that are provided in the Maple V system. A modern computer algebra system that automates the symbolic, numeric, and graphical computation involved in mathematical problem solving. It provides a gentle presentation of this computer algebra system A system for symbolic, numeric, and graphical computation containing hundreds of built-in mathematical commands, a library of mathematical procedures, and a programming language Bruce W. Char ... [et Al.]. Includes Bibliographical References (p. 237-238) And Index.