Maple V Language 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 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.

1 Introduction.- 1.1 Some General Examples.- 1.2 Numbers.- 1.3 Examples from Calculus.- 1.4 Data Structures.- 1.5 Examples from Linear Algebra.- 1.6 Equation Solving.- 1.7 Output and Programming.- 2 Language Elements.- 2.1 Character Set.- 2.2 Tokens.- 2.3 Escape Characters.- 2.4 Blanks, Lines, Comments, and Continuation.- 2.5 Files.- 3 Statements and Expressions.- 3.1 Types of Statements.- 3.2 Expressions.- 3.3 Formal Syntax.- 4 Data Types.- 4.1 Basic Data Types.- 4.2 Map, Subs, and Subsop.- 5 Type Testing.- 5.1 Definition of a Type in Maple.- 5.2 Simple Types.- 5.3 Structured Types.- 5.4 Surface and Nested Types.- 5.5 Simplification of Types.- 5.6 Parameter Type Testing.- 5.7 Undesirable Simplifications and Evaluations of Types.- 5.8 Type Testing Versus Pattern Matching.- 6 Arrays and Tables.- 6.1 Overview.- 6.2 Creating Tables.- 6.3 Evaluation Rules for Tables and Table Components.- 6.4 Tables as Objects.- 6.5 Indexing Functions.- 7 Procedures.- 7.1 Procedure Definitions.- 7.2 Parameter Passing.- 7.3 Local Variables.- 7.4 Options.- 7.5 Remember Tables.- 7.6 Assigning Values to Parameters.- 7.7 Error Returns and Explicit Returns.- 7.8 Simplification and Returning Unevaluated.- 7.9 Boolean Procedures.- 7.10 Reading and Saving Procedures.- 8 Operators.- 8.1 Operator Definition.- 8.2 Syntactic Definition.- 8.3 Semantic Definition.- 8.3.1 Application Versus Composition.- 8.4 Partial Definition of Operators.- 8.5 Example: The Differentiation Operator D.- 9 Internal Representation and Manipulation.- 9.1 Internal Organization.- 9.2 Internal Representation of Data Types.- 9.3 The Use of Hashing in Maple.- 9.4 Portability of the Maple System.- 10 Plotting.- 10.1 Introduction.- 10.2 Plots in 2D.- 10.3 Plots in 3D.- 10.4 Saving Plots.- 10.5 Plots Package.- 10.6 Examples.- 11 Miscellaneous Facilities.- 11.1 Debugging Facilities: Detecting Syntax Errors.- 11.2 Debugging Facilities: Monitoring Run-Time Execution.- 11.3 Alias and Macro.- 11.4 Monitoring Space and Time.- 11.5 Global Variables.- 11.6 User Interface Variables.- 11.7 Maple Command Line Options.- 11.8 Other Facilities.- 12 Overview of the Maple Library.- 12.1 Introduction.- 12.2 Description of the Maple Library.- 12.3 Format of Library Function Descriptions.- 12.4 Printing Maple Help Files.- 12.5 Library Index.- A Maple under UNIX.- A.1 Introduction.- A.2 Maple Initialization Files.- A.3 Quit and Interrupt Characters.- A.4 Temporarily Escaping from Maple.- A.5 Redirection of Input and Output.- A.6 Maple Command Line Options for UNIX.- A.6.1 Overview of Maple command line options.- A.6.2 Library Specification Option: -b.- A.6.3 Suppress Initialization Option: -s.- A.6.4 Quiet Option: -q.- A.7 Mint.- A.8 Summary of Site- and UNIX- Dependent Aspects of Maple.- B Using Maple with X.- B.1 Introduction.- B.2 Getting Started.- B.3 Entering Commands in Maple.- B.4 Editing.- B.5 Maple Input and Output Cells.- B.6 Including and Saving Text.- B.7 Searching.- B.8 Resource Usage.- B.9 Interrupt, Pause and Quit Buttons.- B.10 Resizing Windows.- B.11 Help Windows.- B.12 2D Plot Windows.- B.13 3D Plot Windows.- B.14 Customizing Maple Under X.- B.15 Tips.- B.16 Troubleshooting.- B.17 Information for Xperts.- C Maple under DOS.- C.1 Introduction.- C.2 Using Maple V.- C.2.1 Exiting Maple.- C.2.2 The Status Line.- C.2.3 The Command Line Editor.- C.2.4 Expression Editing.- C.2.5 File Editing.- C.2.6 Accessing Maple Help.- C.2.7 Session Review Mode.- C.2.8 Using the Menu.- C.2.9 Input/Output Capture Mode.- C.3 Manipulating Graphical Output.- C.3.1 Three Dimensional Graphics Display Driver.- C.3.2 Two Dimensional Graphics Display Driver.- C.3.3 Printing and Saving Graphic Output.- C.3.4 Using Maple Plots in Other Programs.