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E-Book

Essential Maple 7. An Introduction for Scientific Programmers

AutorRobert M. Corless
VerlagSpringer-Verlag
Erscheinungsjahr2002
Seitenanzahl297 Seiten
ISBN9780387215570
FormatPDF
KopierschutzDRM
GerätePC/MAC/eReader/Tablet
Preis39,95 EUR
The best book on Maple just got better. This lively book is bursting with clear descriptions, revealing examples and top tips. It is gentle enough to act as an introduction and yet sufficiently comprehensive and well organised to serve as a reference manual. Maple Release 7 is significantly different to earlier releases, so this book will appeal even to hardened users who want to catch up fast.
- Des Higham, University of Strathclyde, UK

This book provides an accelerated introduction to Maple for scientific programmers who already have experience in other computer languages (such as C, Pascal, or FORTRAN). It gives an overview of the most commonly used constructs and provides an elementary introduction to Maple programming. This edition of the book has been extensively updated for Maple Release 7 with future releases in mind. This has involved a substantial update of all programs, examples and exercises. Extensive new material has also been added, including an appendix on complex variables in a computer algebra context. 

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Horizontale Tabs

Leseprobe

3 Programming in Maple (p.186-187)

[Lady Fiorinda was] in the theoric of these matters liberally grounded    through daily sage expositions and informations by Doctor Vandermast, who had these four years past been to her for instructor and tutor. To try her paces and put in practice the doctor’s principles and her own most will-o’-the-wisp and unexperimental embroiderings upon them, ready means lay to hand. . .
-
E. R. Eddison, The Mezentian Gate, Book VI.


Maple is useful as a collection of "black boxes," but it is more useful still as a very high-level programming language. Since most of the tasks undertaken by Maple are "one-off" calculations (as opposed to "batch" calculations, which require many executions of the same program), it makes sense that Maple is an interpreted, rather than compiled, language. This is true even for the Maple library, because for large problems the cost will be dominated by the manipulation of large objects. Some crucial operations, though, are performed by kernel routines, which are compiled for efficiency.

With the external calling features, new to Maple 6 and improved for Maple 7, it is now possible to "tune" these efficiency tradeoffs more closely for any particular application. With the external calling features, new to Maple 6 and improved for Maple 7, it is now possible to "tune" these efficiency tradeoffs more closely for any particular application.

Maple procedures can be divided loosely into two types: operators, and more general procedures. Procedures and related structures may be bundled together into a module. An operator is meant to imitate a mathematical operator, both in notation (insofar as this is possible in ASCII) and in action. The .rst section of this chapter deals with general procedures and their uses. These can do essentially anything computable. Since Maple is a high-level language, you can express these actions in many ways. The section following that looks at operators.

For more in-depth information on how to program in Maple, see [44] and the detailed examples in the directory samples/ch06, which can be found on Windows systems in the directory Program Files/Maple 7. For an extended example of revising a program for efficiency, see [50]. For examples of useful programs, see [21].

3.1 Procedures

A Maple procedure always returns a value. It is the value of the last statement executed in the procedure before returning, or else the value of an explicit return statement. See ?return. This value may be NULL, which does not print anything on output. The distinction between NULL and "no value" is academic. One important consequence of a procedure returning NULL is that the environment variables %, %%, and %%% are not changed. The procedures print and lprint use this deliberately. [We will discuss environment variables in more detail later.] The procedures solve, fsolve, and dsolve, for example, will return NULL if they .nd no solution, and sometimes this takes special handling in programs. One simple way to deal with this with solve is to enclose the results from solve in set braces ( { } ), converting a possible NULL value to the empty set (and incidentally removing multiplicity; use list brackets if you wish to preserve multiplicity).

Blick ins Buch
Inhaltsverzeichnis
What’s in This Book7
Acknowledgements9
Contents11
List of Figures13
1 Basics16
1.1 Getting Started16
1.1.1 Basic Command Syntax18
1.1.2 Use of Context-Sensitive Menus to Execute Maple Commands19
1.1.3 Sample Maple Sessions19
1.1.4 Arithmetic36
1.1.5 Interrupting a Maple Computation39
1.1.6 Saving Work39
1.2 Some Things to Watch Out For41
1.2.1 Good Worksheet Hygiene41
1.2.2 Common Syntax Errors42
1.2.3 Assigning Values to Variables43
1.2.4 Removing Values from Variables44
1.2.5 sign versus signum versus csgn45
1.2.6 Accidental Creation of a Remember Table46
1.2.7 Fences: Parentheses ( ) versus Braces { } versus Brackets [ ] versus Angle Brackets47
1.2.8 Quotation marks: Left versus Right versus String47
1.2.9 Precedence of Operators49
1.2.10 Protected and Reserved Names50
1.2.11 Having Different Assumptions about Domains52
1.3 Documenting YourWork52
1.4 The Three Levels of Maple “Black Boxes”57
1.5 No Nontrivial Software Package is Bug-Free58
1.6 Evaluation Rules59
1.6.1 Working With Complex Numbers and Expressions62
1.6.2 Inert Functions63
1.7 The assume Facility67
2 Useful One-Word Commands71
2.1 Simplification71
2.1.1 normal72
2.1.2 collect73
2.1.3 factor83
2.1.4 expand89
2.1.5 combine90
2.1.6 simplify91
2.2 Solving Equations94
2.2.1 solve94
2.2.2 fsolve97
2.2.3 dsolve101
2.2.4 rsolve113
2.2.5 Linear Equations114
2.2.6 Other Solvers117
2.2.7 Systems of Polynomial Equations117
2.3 Manipulations from Calculus125
2.3.1 diff125
2.3.2 int127
2.3.3 limit135
2.3.4 series135
2.4 Adding Terms versus the Finite-Difference Calculus139
2.5 Floating-Point Evaluation144
2.5.1 Using evalhf146
2.5.2 Signed Zero150
2.6 The Most Helpful Maple Utilities150
2.6.1 I/O Utilities151
2.6.2 alias and macro152
2.6.3 Interacting with the Operating System and External Calls152
2.6.4 Mapping Functions Onto Compound Objects152
2.6.5 Code Generation154
2.7 Plotting in Maple157
2.7.1 Two-Dimensional Plots157
2.7.2 Three-Dimensional Plots170
2.7.3 Contour Plots and Other Plots174
2.7.4 Common Errors183
2.7.5 Getting Hard Copy of your Plots185
2.8 Packages in Maple188
2.8.1 The MATLAB Link189
2.8.2 numapprox193
2.8.3 Units194
2.8.4 MathML199
3 Programming in Maple201
3.1 Procedures202
3.1.1 Structured Types205
3.1.2 Example: Modified Gram–Schmidt206
3.2 Operators and Modules211
3.2.1 A Module for Finite-Difference Operators216
3.2.2 Remarks on Mathematical Operators219
3.3 Data Structures220
3.4 Local versus Global versus Environment Variables226
3.4.1 Exporting Local Variables226
3.4.2 Global Variables227
3.4.3 Environment Variables227
3.4.4 Nested Lexical Scopes230
3.5 Recursion and option remember230
3.6 Variable Number or Type of Arguments239
3.7 Returning More Than One Result241
3.8 Debugging Maple Programs243
3.9 Sample Maple Programs250
3.9.1 Parametric Solution of Algebraic Equations250
3.9.2 Path Following in p(x, y) = 0254
3.9.3 Large Expression Management, Revisited260
3.9.4 Fourier Sine Series, Revisited260
3.9.5 Solution of y (t) = ay(t - 1)266
Appendix A A Primer on Complex Variables273
A.1 Polar Coordinates and the Two-Argument Arctan Function274
A.2 The Exponential Function275
A.3 The Natural Logarithm277
A.4 Trig Functions and Hyperbolic Functions279
A.5 Inverse Trigs and Hyperbolics279
Bibliography286
Index290
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