Holdings: Computing with Maple

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Bibliographic Details
Main Author:	Wright, Francis J. (Author)
Format:	Book
Language:	English
Published:	Boca Raton, FL [u.a.] Chapman & Hall/CRC 2002
Series:	Chapman & Hall/CRC mathematics
Subjects:	Maple (Computer file) Datenverarbeitung Algebra > Data processing Computeralgebra Maple V
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	xvii, 532 p. graph. Darst.
ISBN:	1584882360

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Record in the Search Index

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adam_text	COMPUTING WITH MAPLE FRANCIS WRIGHT CHAPMAN & HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS PREFACE XIII 1 INTRODUCTION 1 1.1 LEARNING COMPUTING 1 1.2 BACKGROUND REFERENCES 3 1.2.1 COMPUTER PROGRAMMING IN GENERAL 4 1.2.2 MAPLE IN PARTICULAR - 4 1.2.3 ALGORITHMS IN GENERAL 5 1.2.4 COMPUTER ALGEBRA ALGORITHMS 5 1.2.5 NUMERICAL ALGORITHMS 5 1.2.6 ONLINE REFERENCES 6 1.3 FUNDAMENTAL TERMINOLOGY 6 1.4 MAPLE INTERFACES 8 1.5 THE MAPLE WORKSHEET INTERFACE 11 1.5.1 THE ONLINE HELP SYSTEM 11 1.5.2 BALLOON HELP 13 1.5.3 USE OF THE MOUSE 13 1.5.4 USEFUL KEYBOARD SHORTCUTS 15 1.5.5 NEW LINES AND EXECUTION GROUPS 15 1.5.6 OPENING AND EXECUTING WORKSHEETS 17 1.5.7 APPLICATION AND DOCUMENT WINDOWS 17 1.5.8 AVERTING DISASTER 17 1.5.9 MY WORKSHEET SHRANK! 19 1.5.10 DON T WORK IN THE DARK 19 1.5.11 COMPATIBILITY WITH MAPLE V 19 1.6 EXERCISES: THE WORKSHEET INTERFACE 20 2 REVIEW OF BASICS 23 2.1 MAPLE SYNTAX: SPECIAL SYMBOLS 23 2.1.1 VARIABLES, ASSIGNMENTS, EQUATIONS, PROCEDURES, AND MAPPINGS 24 2.1.2 QUOTES 25 2.1.3 BRACKETS 28 VI CONTENTS 2.1 A MATHEMATICAL SYMBOLS 30 2.1.5 PROGRAMMING SYMBOLS 33 2.2 ASSIGNMENT, EVALUATION, SUBSTITUTION, AND SIMPLIFICATION . . . . 41 2.2.1 ASSIGNMENT AND EVALUATION 42 2.2.2 EVALUATION AND SUBSTITUTION 46 2.2.3 MULTIPLE SUBSTITUTIONS 48 2.2.4 SIMPLIFICATION 49 2.3 COMMON ERRORS 51 2.3.1 JUXTAPOSITION 51 2.3.2 UPPER AND LOWER CASE LETTERS 52 2.3.3 THE EXPONENTIAL FUNCTION AND THE LETTER E 53 2.3.4 ASSIGNMENTS AND EQUATIONS 54 2.4 SEQUENCES, LISTS, AND SETS 55 2.4.1 PARALLEL ASSIGNMENT 55 2.4.2 FUNCTIONS AND THEIR ARGUMENT SEQUENCES 57 2.4.3 AUTOMATIC SIMPLIFICATION; INERT FUNCTIONS 57 2.4.4 FUNCTIONS AND OPERATORS 58 2.4.5 OPERATIONS ON SEQUENCES, LISTS, AND SETS: OP 59 2.4.6 OPERATIONS ON ELEMENTS OF SEQUENCES, LISTS, AND SETS: OP, [ ] 60 2.4.7 THE EMPTY SEQUENCE: NULL 63 2.4.8 CONSTRUCTING SEQUENCES, LISTS, AND SETS 64 2.4.9 RELATIVES OF SEQUENCES: SUMS AND PRODUCTS 66 2.5 CHARACTERS AND STRINGS 68 2.6 EXERCISES 70 3 TWO-DIMENSIONAL PLOTTING 73 3.1 SIMPLE PLOTTING 73 3.1.1 PLOTTING GRAPHS OF FUNCTIONS 73 3.1.2 PLOTTING GRAPHS OF STRICTLY NUMERICAL FUNCTIONS . . . . 76 3.1.3 PLOT RANGES 77 3.1.4 MULTIPLE PLOTS 78 3.1.5 PARAMETRIC PLOTTING 79 3.1.6 PLOTTING POINTS 81 3.1.7 PLOT OPTIONS 82 3.1.8 PLOTTING DISCONTINUOUS FUNCTIONS 84 3.1.9 DISPLAYING AND MANIPULATING PLOTS 85 3.2 THE PLOTS PACKAGE AND ANIMATION 88 3.2.1 ASIDE: PACKAGES AND THE WITH COMMAND 88 3.2.2 SIMPLE ANIMATION: ANIMATE 89 3.2.3 COMBINING AND ANIMATING PLOTS: DISPLAY 90 3.2.4 CHANGING DEFAULT PLOTTING OPTIONS: SETOPTIONS 93 3.2.5 ANNOTATING PLOTS: TEXTPLOT 93 3.2.6 A SIMPLE GEOMETRICAL EXAMPLE 94 3.3 A GRAPHICAL INVESTIGATION OF THE CARDIOID 94 CONTENTS VII 3.3.1 THE BASIC GEOMETRY 95 3.3.2 THE GEOMETRY IN MORE DETAIL 97 3.3.3 ANIMATING THE GEOMETRY 98 3.4 EXPORTING PLOTS (AND WORKSHEETS) 100 3.5 EXERCISES: THE CYCLOID 101 3.6 APPENDIX: CODE TO PLOT THE FIGURES 103 4 THREE-DIMENSIONAL PLOTTING 105 4.1 THE PLOT3D FUNCTION 106 4.1.1 GRAPHS OF REAL-VALUED FUNCTIONS OF TWO REAL VARIABLES . . 106 4.1.2 PARAMETRIC PLOTTING OF SURFACES 107 4.1.3 MULTIPLE THREE-DIMENSIONAL PLOTS 110 4.2 THREE-DIMENSIONAL PLOTTING OPTIONS 110 4.3 INTERACTING WITH THREE-DIMENSIONAL PLOTS 112 4.4 USING THE PLOTS PACKAGE 112 4.4.1 SETTING DEFAULT OPTIONS AND PLOTTING TEXT: SETOPTIONS3D, TEXTPLOT3D 112 4.4.2 COMBINING AND ANIMATING THREE-DIMENSIONAL PLOTS: ANIMATE3D, DISPLAY3D 112 4.4.3 PLOTTING CURVES IN SPACE: SPACECURVE 113 4.4.4 PLOTTING CONTOURS: CONTOURPLOT3D, CONTOURPLOT .... 114 4.4.5 PLOTTING GRADIENT FIELDS: GRADPLOT 117 4.4.6 IMPLICIT PLOTTING: IMPLICITPLOT 118 4.5 THREE-DIMENSIONAL BOUNCING BALL ANIMATION 119 4.6 EXPORTING THREE-DIMENSIONAL PLOTS 121 4.7 EXERCISES 123 4.8 APPENDIX: CODE TO PLOT THE FIGURES 125 5 NUMERICAL AND SEMI-NUMERICAL COMPUTATION 127 5.1 NUMBER SYSTEMS 128 5.1.1 NUMBER SYSTEMS IN MATHEMATICS 128 5.1.2 NUMBER SYSTEMS IN MAPLE 131 5.1.3 NUMBER SYSTEMS IN OTHER LANGUAGES 139 5.2 FLOATING-POINT COMPUTATION IN MAPLE 139 5.2.1 FLOATING-POINT EVALUATION: EVALF, EVALHF 140 5.2.2 SOLUTION OF ALGEBRAIC EQUATIONS: SOLVE, F SOLVE 142 5.2.3 NUMERICAL INTEGRATION (QUADRATURE): EVALF/INT 146 5.2.4 SOLUTION OF DIFFERENTIAL EQUATIONS: DSOLVE 148 5.3 MULTIPLE ROOTS 150 5.4 ALIASES AND ALGEBRAIC NUMBERS 151 5.4.1 ALIAS 151 5.4.2 ALGEBRAIC NUMBERS 152 5.4.3 IMPLICIT DEPENDENCE 153 5.5 COMPUTING WITH MODULAR INTEGERS 154 5.6 EXERCISES 156 VIII CONTENTS 5.7 APPENDIX: CODE TO PLOT THE FIGURES 158 6 NUMERICAL LINEAR ALGEBRA 159 6.1 LINEAR ALGEBRA IN MAPLE 159 6.2 NUMERICAL LINEAR ALGEBRA 160 6.3 INTERACTIVE LINEAR ALGEBRA 161 6.4 VIEWING LARGE MATRICES AND VECTORS 164 6.5 USING THE LINEARALGEBRA PACKAGE 166 6.6 SOLVING SYSTEMS OF LINEAR EQUATIONS 167 6.7 SPECIAL MATRICES 169 6.8 EIGENVALUE PROBLEMS 172 6.9 ILL-CONDITIONED PROBLEMS 176 6.10 UNDER- AND OVER-DETERMINED PROBLEMS 180 6.10.1 UNDER-DETERMINED PROBLEMS 180 6.10.2 OVER-DETERMINED PROBLEMS 181 6.10.3 SOLUTION BY SINGULAR VALUE DECOMPOSITION 182 6.10.4 LEAST SQUARES SOLUTION 184 6.11 EXERCISES 185 7 LOGIC AND CONTROL STRUCTURES 187 7.1 RELATIONAL OPERATORS: , =, , =,=, 187 7.2 BOOLEAN ALGEBRA 191 7.3 BOOLEAN OPERATORS IN MAPLE: AND, OR, NOT 191 7.3.1 TRUTH TABLES IN MAPLE 192 7.3.2 BOOLEAN EXPRESSIONS 193 7.4 CONDITIONAL EXECUTION: IF 194 7.4.1 SIMPLE CONDITIONAL EXECUTION: IF 194 7.4.2 ALTERNATIVE EXECUTION: ELSE 195 7.4.3 MULTIPLE ALTERNATIVE EXECUTION: ELIF 196 7.5 PIECEWISE-DEFINED FUNCTIONS 198 7.5.1 PIECEWISE-DEFINED FUNCTIONS USING IF 198 7.5.2 PIECEWISE-DEFINED FUNCTIONS USING PIECEWISE 201 7.5.3 CONTINUITY CLASS 202 7.5.4 CONDITIONAL EVALUATION: THE IF FUNCTION 204 7.6 LOOPS: DO, WHILE, FOR 204 7.6.1 THE GENERAL CONTROLLED LOOP: WHILE 205 7.6.2 NESTED CONTROL STRUCTURES 206 7.6.3 ITERATING OVER AN INTEGER RANGE: FOR ... TO 207 7.6.4 ITERATING OVER A STRUCTURE: FOR ... IN 210 7.6.5 OTHER WAYS TO CONTROL LOOPS: BREAK, NEXT 211 7.6.6 THE FOR ... TO-LOOP IMPLEMENTED AS A WHILE-LOOP . . . 212 7.6.7 DOUBLE LOOPS 212 7.7 EXERCISES 216 CONTENTS IX 8 PROCEDURES AND RECURSION 219 8.1 DEFINING AND USING PROCEDURES 220 8.1.1 RETURNING VERSUS PRINTING VALUES 220 8.2 GENERAL PROCEDURE DEFINITION SYNTAX 221 8.3 VARIABLE SCOPE 222 8.4 PROCEDURE ARGUMENTS 225 8.5 SPECIAL IDENTIFIERS IN PROCEDURES 227 8.5.1 VARIABLE NUMBERS OF ARGUMENTS: NARGS, ARGS 227 8.5.2 RETURNING UNEVALUATED: PROCNAME 229 8.6 TERMINATING PROCEDURE EXECUTION 231 8.7 EXAMPLES: INTEGER FACTORIZATION 232 8.7.1 ASIDE: IFACTOR 236 8.8 DISPLAYING MAPLE PROCEDURES 237 8.9 PROCEDURE OPTIONS AND REMEMBER TABLES 238 8.9.1 REMEMBER TABLES 239 8.10 MORE ABOUT VARIABLE SCOPE 241 8.10.1 LEXICAL SCOPING 241 8.10.2 RETURNING LOCAL VARIABLES 242 8.11 RECURSION 244 8.11.1 THE FACTORIAL FUNCTION 244 8.11.2 RECURSION AND STACKS 245 8.11.3 AVOIDING INFINITE RECURSION 246 8.11.4 RECURSIVE SUMMATION 247 8.11.5 RECURSIVE POWER COMPUTATION 248 8.12 PROCEDURES THAT OUTPUT PLOTS 250 8.13 RECURSIVE PLOTTING 253 8.14 ANIMATING THE KOCH SNOWFLAKE FRACTAL 255 8.14.1 THE SNOWFLAKE CONSTRUCTION 256 8.14.2 BASIC GEOMETRY 256 8.14.3 CONSTRUCTING A SINGLE SIDE 257 8.14.4 ANIMATING THE GROWTH OF A SNOWFLAKE 258 8.14.5 CODE TO PLOT THE SNOWFLAKE CONSTRUCTION 259 8.15 PROGRAM DESIGN 259 8.15.1 UNDERSTAND THE PROBLEM 260 8.15.2 DESIGN THE ALGORITHM 261 8.15.3 WRITE THE PROGRAM 261 8.15.4 TEST THE PROGRAM 262 8.16 EXERCISES 263 9 OPERATORS AND FUNCTIONS 267 9.1 OPERATORS 267 9.1.1 SYNTAX 267 9.1.2 INERT OPERATORS 268 9.1.3 ACTIVE OPERATORS 270 9.2 CONVERTING BETWEEN EXPRESSIONS AND MAPPINGS 273, X CONTENTS 9.3 COMPOSITION OF MAPPINGS AND FUNCTIONS 274 9.4 THE DERIVATIVE OPERATOR D 275 9.4.1 PARTIAL DERIVATIVES 278 9.4.2 SPECIFYING CONDITIONS ON DIFFERENTIAL EQUATIONS 279 9.5 SET OPERATIONS 279 9.5.1 UNION 279 9.5.2 INTERSECTION 280 9.5.3 DIFFERENCE 281 9.5.4 SYMMETRIC DIFFERENCE 281 9.5.5 MEMBERSHIP 282 9.5.6 SET ALGEBRA 284 9.5.7 POWER SETS 284 9.6 EXAMPLES OF RECURSIVE INTEGER AND POLYNOMIAL FUNCTIONS . . . . 286 9.6.1 EUCLIDEAN DIVISION 286 9.6.2 GREATEST COMMON DIVISORS 287 9.6.3 DIGITS AND COEFFICIENTS 288 9.7 EXERCISES 291 10 DATA TYPES 295 10.1 PRIMITIVE TYPES: WHATTYPE 296 10.2 USE OF TYPE INFORMATION: ERROR CHECKING, POLYMORPHISM . . . . 298 10.3 ALTERNATIVE TYPES: {TYPEL, TYPE2, ...} 298 10.4 THE MAIN MAPLE DATA TYPES 299 10.4.1 NUMERICAL TYPES 299 10.4.2 ALGEBRAIC TYPES 300 10.4.3 BOOLEAN TYPES 300 10.4.4 STRUCTURAL TYPES 300 10.4.5 PROGRAMMING TYPES 301 10.5 TYPE TESTING: TYPE AND :: 301 10.5.1 ERROR-CHECKING OF PROCEDURE ARGUMENTS USING :: . . . . 301 10.5.2 GENERAL TYPE TESTING: TYPE OR :: 302 10.5.3 QUOTING TYPE SPECIFICATIONS 303 10.6 BOOLEAN COMBINATIONS OF TYPES: AND, OR, NOT 304 10.7 STRUCTURED OR NESTED DATA TYPES 305 10.7.1 GENERIC STRUCTURED TYPES 306 10.7.2 SPECIFIC STRUCTURED TYPES 307 10.7.3 TYPE-TESTING COMMUTING OPERATORS 308 10.7.4 TYPE-TESTING SEQUENCES 310 10.8 SPECIAL PROCEDURE-ARGUMENT TYPES 311 10.9 EXAMPLES OF POLYMORPHIC PROCEDURES 313 10.9.1 ACTIVE RELATIONAL OPERATORS 314 10.9.2 A MORE GENERAL MAXIMUM FUNCTION 315 10.9.3 A MORE GENERAL (RATIONAL) FACTORIAL FUNCTION 318 10.9.4 A MORE GENERAL DIGIT-SEQUENCE FUNCTION 320 10.10 DEFINING NEW TYPES 321 CONTENTS XI 10.11 EXERCISES 323 11 CONVENTIONAL PROGRAMMING 329 11.1 OPERATIONS ON STRUCTURES 330 11.1.1 MAPPING OVER STRUCTURES: MAP 330 11.1.2 MAPPING ON OTHER ARGUMENTS: MAP2 331 11.1.3 HOW IS MAP DEFINED? 332 11.1.4 MAPPING OVER ARRAYS AND TABLES 334 11.1.5 SELECTING FROM STRUCTURES: SELECT, REMOVE 335 11.2 IMPLEMENTING VECTOR AND MATRIX ALGEBRA 337 11.2.1 VECTOR ADDITION 338 11.2.2 SCALAR PRODUCT 339 11.2.3 MATRIX MULTIPLICATION 341 11.3 DATA PROCESSING IN MAPLE 342 11.3.1 OUTPUTTING TO A FILE 342 11.3.2 INPUTTING FROM A FILE 343 11.3.3 ELEMENTARY STATISTICS 344 11.3.4 OTHER METHODS OF INPUT AND OUTPUT 346 11.3.5 ASIDE: OFFLINE PROCESSING 346 11.4 INTERACTIVE PROGRAMS IN MAPLE 347 11.5 ERROR HANDLING: TRY, CATCH 351 11.6 DEBUGGING 354 11.6.1 INFOLEVEL 356 11.6.2 PRINTLEVEL 357 11.6.3 DEBUG AND TRACE 359 11.6.4 INTERACTIVE DEBUGGING 360 11.7 EXERCISES 364 12 ALGEBRAIC PROGRAMMING 369 12.1 UNIVARIATE POLYNOMIAL ALGORITHMS 369 12.1.1 SQUAREFREE FACTORIZATION 369 12.1.2 STURM SEQUENCES 373 12.1.3 FINDING ZEROS BY INTERVAL HALVING 377 12.2 MULTIVARIATE POLYNOMIAL ALGORITHMS 381 12.2.1 GENERALIZED POLYNOMIAL DIVISION 381 12.2.2 GROBNER BASES 388 12.3 EXERCISES 397 13 SPREADSHEETS 399 13.1 INTRODUCTION 400 13.2 COPYING AND MOVING CELLS 402 13.3 WORKING WITH SEQUENCES 405 13.4 TABULATING DATA 406 13.5 PROGRAMMING SPREADSHEETS 410 13.6 CASE STUDY: THE SIMPLE PENDULUM 412 XII CONTENTS 13.6.1 EXACT SOLUTIONS FOR SMALL AND LARGE AMPLITUDE 413 13.6.2 APPROXIMATE NUMERICAL SOLUTION 415 13.6.3 NUMERICAL COMPUTATION OF THE PERIOD 418 13.6.4 NUMERICAL COMPUTATION OF THE AMPLITUDE 421 13.7 EXERCISES 423 14 TEXT PROCESSING 425 14.1 TEXT FILES 426 14.2 COUNTING LINES, WORDS, AND CHARACTERS 428 14.2.1 COUNTING WORDS AND CHARACTERS WITHIN A LINE 428 14.2.2 COUNTING LINES, WORDS, AND CHARACTERS IN A FILE 433 14.3 TEXT FORMATTING 436 14.4 A MARKOV CHAIN ALGORITHM 440 14.5 EXERCISES 444 15 OBJECT ORIENTATION AND MODULES 445 15.1 INTRODUCTION TO OBJECT ORIENTATION 446 15.2 BLOCK MATRICES 447 15.3 MODULES AS RECORDS 448 15.4 MODULES IN MORE DETAIL 450 15.5 MODULE CONSTRUCTORS 451 15.6 MODULES AS OBJECTS 455 15.7 DATA ENCAPSULATION 457 15.8 ACCESSING BLOCK MATRIX ELEMENTS 463 15.9 SQUARE AND INVERSE BLOCK MATRICES 464 15.10 MODULES AND TYPES 466 15.11 BLOCK MATRIX MULTIPLICATION 467 15.12 LIMITATIONS OF MODULES AS OBJECTS 469 15.13 OPERATOR OVERLOADING 470 15.14 USING A PRIVATE MAPLE LIBRARY ^ . . 477 15.15 MODULES AS PACKAGES 481 15.16 ADDING ONLINE HELP 485 15.17 EXERCISES 487 BIBLIOGRAPHY 489 INDEX 491
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spelling	Wright, Francis J. Verfasser aut Computing with Maple Francis Wright Boca Raton, FL [u.a.] Chapman & Hall/CRC 2002 xvii, 532 p. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematics Includes bibliographical references and index Maple (Computer file) Datenverarbeitung Algebra Data processing Computeralgebra (DE-588)4010449-7 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Maple V (DE-588)4276266-2 s Computeralgebra (DE-588)4010449-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009838958&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Wright, Francis J. Computing with Maple Maple (Computer file) Datenverarbeitung Algebra Data processing Computeralgebra (DE-588)4010449-7 gnd Maple V (DE-588)4276266-2 gnd
subject_GND	(DE-588)4010449-7 (DE-588)4276266-2
title	Computing with Maple
title_auth	Computing with Maple
title_exact_search	Computing with Maple
title_full	Computing with Maple Francis Wright
title_fullStr	Computing with Maple Francis Wright
title_full_unstemmed	Computing with Maple Francis Wright
title_short	Computing with Maple
title_sort	computing with maple
topic	Maple (Computer file) Datenverarbeitung Algebra Data processing Computeralgebra (DE-588)4010449-7 gnd Maple V (DE-588)4276266-2 gnd
topic_facet	Maple (Computer file) Datenverarbeitung Algebra Data processing Computeralgebra Maple V
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009838958&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT wrightfrancisj computingwithmaple

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