Maple V Programming Guide

Maple V Mathematics Programming Guide is the fully updated language and programming reference for Maple V Release 5. It presents a detailed description of Maple V Release 5 - the latest release of the powerful, interactive computer algebra system used worldwide as a tool for problem-solving in mathematics, the sciences, engineering, and education. This manual describes the use of both numeric and symbolic expressions, the data types available, and the programming language statements in Maple. It shows how the system can be extended or customized through user defined routines and gives complete descriptions of the system's user interface and 2D and 3D graphics capabilities.

1. Introduction.- 1.1 Getting Started.- Locals and Globals.- Inputs, Parameters, Arguments.- 1.2 Basic Programming Constructs.- The Assignment Statement.- The for Loop.- The Conditional Statement.- The while Loop.- Modularization.- Recursive Procedures.- Exercise.- 1.3 Basic Data Structures.- Exercise.- Exercise.- A MEMBER Procedure.- Exercise.- Binary Search.- Exercises.- Plotting the Roots of a Polynomial.- 1.4 Computing with Formulae.- The Height of a Polynomial.- Exercise.- The Chebyshev Polynomials, Tn(x).- Exercise.- Integration by Parts.- Exercise.- Computing with Symbolic Parameters.- Exercise.- 2. Fundamentals.- 2.1 Evaluation Rules.- Parameters.- Local Variables.- Global Variables.- Exceptions.- 2.2 Nested Procedures.- Local or Global?.- The Quick-Sort Algorithm.- Creating a Uniform Random Number Generator.- 2.3 Types.- Types that Modify Evaluation Rules.- Structured Types.- Type Matching.- 2.4 Choosing a Data Structure: Connected Graphs.- Exercises.- 2.5 Remember Tables.- The remember Option.- Adding Entries Explicitly.- Removing Entries from a Remember Table.- 2.6 Conclusion.- 3. Advanced Programming.- 3.1 Procedures Which Return Procedures.- Creating a Newton Iteration.- A Shift Operator.- 3.2 When Local Variables Leave Home.- Creating the Cartesian Product of a Sequence of Sets.- Exercises.- 3.3 Interactive Input.- Reading Strings from the Terminal.- Reading Expressions from the Terminal.- Converting Strings to Expressions.- 3.4 Extending Maple.- Defining New Types.- Exercises.- Neutral Operators.- Exercise.- Extending Certain Commands.- 3.5 Writing Your Own Packages.- Package Initialization.- Making Your Own Library.- 3.6 Conclusion.- 4. The Maple Language.- 4.1 Language Elements.- The Character Set.- Tokens.- Token Separators.- 4.2 Escape Characters.- 4.3 Statements.- The Assignment Statement.- Unassignment: Clearing a Name.- The Selection Statement.- The Repetition Statement.- The read and save Statements.- 4.4 Expressions.- Expression Trees: Internal Representation.- The Types and Operands of Integers, Strings, Indexed Names, and Concatenations.- Fractions and Rational Numbers.- Floating-Point (Decimal) Numbers.- Complex Numerical Constants.- Labels.- Sequences.- Sets and Lists.- Functions.- The Arithmetic Operators.- Non-Commutative Multiplication.- The Composition Operators.- The Ditto Operators.- The Factorial Operator.- The mod Operator.- The Neutral Operators.- Relations and Logical Operators.- Arrays and Tables.- Series.- Ranges.- Unevaluated Expressions.- Constants.- Structured Types.- 4.5 Useful Looping Constructs.- The map, select, and remove Commands.- The zip Command.- The seq, add, and mul Commands.- 4.6 Substitution.- 4.7 Conclusion.- 5. Procedures.- 5.1 Procedure Definitions.- Mapping Notation.- Unnamed Procedures and Their Combinations.- Procedure Simplification.- 5.2 Parameter Passing.- Declared Parameters.- The Sequence of Arguments.- 5.3 Local and Global Variables.- Evaluation of Local Variables.- 5.4 Procedure Options and the Description Field.- Options.- The Description Field.- 5.5 The Value Returned by a Procedure.- Assigning Values to Parameters.- Explicit Returns.- Error Returns.- Trapping Errors.- Returning Unevaluated.- Exercise.- 5.6 The Procedure Object.- Last Name Evaluation.- The Type and Operands of a Procedure.- Saving and Retrieving Procedures.- 5.7 Explorations.- Exercises.- 5.8 Conclusion.- 6. Debugging Maple Programs.- 6.1 A Tutorial Example.- 6.2 Invoking the Debugger.- Displaying the Statements of a Procedure.- Breakpoints.- Watchpoints.- Error Watchpoints.- 6.3 Examining and Changing the State of the System.- 6.4 Controlling Execution.- 6.5 Restrictions.- 7. Numerical Programming in Maple.- 7.1 The Basics of evalf.- 7.2 Hardware Floating-Point Numbers.- Newton Iterations.- Computing with Arrays of Numbers.- 7.3 Floating-Point Models in Maple.- Software Floats.- Hardware Floats.- Roundoff Error.- 7.4 Extending the evalf Command.- Defining Your Own Constants.- Defining Your Own Functions.- 7.5 Using the Matlab Package.- 7.6 Conclusion.- 8. Programming with Maple Graphics.- 8.1 Basic Plot Functions.- 8.2 Programming with Plotting Library Functions.- Plotting a Loop.- A Ribbon Plot Procedure.- 8.3 Maple’s Plotting Data Structures.- The PLOT Data Structure.- A Sum Plot.- The PLOT3D Data Structure.- 8.4 Programming with Plot Data Structures.- Writing Graphic Primitives.- Plotting Gears.- Polygon Meshes.- 8.5 Programming with the plottools Package.- A Pie Chart.- A Dropshadow Procedure.- Creating a Tiling.- A Smith Chart.- Modifying Polygon Meshes.- 8.6 Example: Vector Field Plots.- 8.7 Generating Grids of Points.- 8.8 Animation.- 8.9 Programming with Color.- Generating Color Tables.- Adding Color Information to Plots.- Creating A Chess Board Plot.- 8.10 Conclusion.- 9. Input and Output.- 9.1 A Tutorial Example.- 9.2 File Types and Modes.- Buffered Files versus Unbuffered Files.- Text Files versus Binary Files.- Read Mode versus Write Mode.- The default and terminal Files.- 9.3 File Descriptors versus File Names.- 9.4 File Manipulation Commands.- Opening and Closing Files.- Position Determination and Adjustment.- Detecting the End of a File.- Determining File Status.- Removing Files.- 9.5 Input Commands.- Reading Text Lines from a File.- Reading Arbitrary Bytes from a File.- Formatted Input.- Reading Maple Statements.- Reading Tabular Data.- 9.6 Output Commands.- Configuring Output Parameters using the interface Command.- One-Dimensional Expression Output.- Two-Dimensional Expression Output.- Writing Maple Strings to a File.- Writing Arbitrary Bytes to a File.- Formatted Output.- Writing Tabular Data.- Flushing a Buffered File.- Redirecting the default Output Stream.- 9.7 Conversion Commands.- C or FORTRAN Generation.- LATEX or eqn Generation.- Conversion between Strings and Lists of Integers.- Parsing Maple Expressions and Statements.- Formatted Conversion to and from Strings.- 9.8 A Detailed Example.- 9.9 Notes to C Programmers.- 9.10 Conclusion.