Verfügbarkeit: C++ for mathematicians

C++ for mathematicians: an introduction for students and professionals

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Bibliographische Detailangaben
1. Verfasser:	Scheinerman, Edward R. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton [u.a.] Chapman & Hall [u.a.] 2006
Schlagworte:	C++ Mathematik C > Programmiersprache
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXIII, 496 S. 1 CD-ROM (12 cm)
ISBN:	158488584X

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Datensatz im Suchindex

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adam_text	CONTENTS LIST OF PROGRAMS XIII LIST OF FIGURES XVII PREFACE XIX I PROCEDURES 1 1 THE BASICS 3 1.1 WHAT IS C++? ............................ 3 1.2 HELLO C++ .............................. 4 1.3 EXERCISES .............................. 8 2 NUMBERS 11 2.1 THE INTEGER TYPES .......................... 1 1 2.2 THE REAL NUMBER TYPES ....................... 14 2.3 THEBOO1.ANDCHARTYPES ..................... 14 2.4 CHECKING THE SIZE AND CAPACITY OF THE DIFFERENT TYPES ....... 15 2.5 STANDARD OPERATIONS ......................... 18 2.6 COMPARISONS AND BOOLEAN OPERATIONS ............... 22 2.7 COMPLEX NUMBERS .......................... 23 2.8 NAMING VARIABLES .......................... 2 7 2.9 EXERCISES .............................. 28 3 GREATEST COMMON DIVISOR 31 3.1 THEPROBLEM ............................. 31 3.2 A FIRST APPROACH ........................... 31 3.3 EUCLID S METHOD ........................... 37 3.4 LOOPING WITH FOR. WHILE. AND DO ................ 41 3.5 AN EXHAUSTIVE APPROACH TO THE GCD PROBLEM ........... 43 3.6 EXTENDED GCD. CALL BY REFERENCE. AND OVERLOADING ......... 45 3.7 EXERCISES .............................. 49 4 RANDOM NUMBERS 53 4.1 PSEUDO RANDOM NUMBER GENERATION ................. 53 4.2 UNIFORM RANDOM VALUES ....................... 54 4.3 MORE ON PSEUDO RANDOM NUMBER GENERATION ............ 57 4.4 A MONTE CARLO PROGRAM FOR THE GCD PROBLEM ........... 6 0 VI C++ FOR MATHEMATICIANS 4.5 NORMAL RANDOM VALUES ...................... . 4.6 EXERCISES ............................. . 5 ARRAYS 5.1 EULER S TOTIENT ........................... . 5.2 ARRAY FUNDAMENTALS ........................ . 5.3 A PROCEDURE TO FACTOR INTEGERS .................. . 5.4 A PROCEDURE TO CALCULATE EULER S TOTIENT .............. . 5.5 THE SIEVE OF ERATOSTHENES: NEW AND DELETE [ ] ........ . 5.6 A FASTER TOTIENT .......................... . 5.7 COMP~TINGP~FORLARGEN ..................... . 5.8 THEANSWER ............................ . 5.9 EXERCISES ............................. . 11 OBJECTS 6 POINTS IN THE PLANE 6.1 DATA AND METHODS ......................... . 6.2 DECLARING THE POINT CLASS .................... . 6.3 DATA HIDING ............................ . 6.4 CONSTRUCTORS ............................ . 6.5 ASSIGNMENT AND CONVERSION .................... . 6.6 METHODS .............................. . 6.7 PROCEDURES USING ARGUMENTS OF TYPE POINT ........... . 6.8 OPERATORS ............................. . 6.9 EXERCISES ............................. . 7 PYTHAGOREAN TRIPLES 7.1 GENERATING F YTHAGOREAN TRIPLES .................. . 7.2 DESIGNING A PRIMITIVE PYTHAGOREAN TRIPLE CLASS .......... . 7.3 IMPLEMENTATION OF THE P ~R IPLE CLASS .............. . 7.4 FINDING AND SORTING THE TRIPLES .................. . 7.5 EXERCISES ............................. . 8 CONTAINERS 8.1 SETS ................................ . 8.2 SET ITERATORS ............................ . 8.3 MULTISETS ............................. . 8.4 ADJUSTABLE ARRAYS VIA THE VECTOR CLASS ............. . 8.5 ORDERED PAIRS ........................... . 8.6 MAPS ............................... . 8.7 LISTS. STACKS. AND ASSORTED QUEUES ................. . 8.7.1 LISTS ............................ . 8.7.2 STACKS ........................... . 8.7.3 QUEUES ........................... . TABLE OF CONTENRS VII 8.7.4 DEQUES ............................ 149 8.7.5 PRIORITY QUEUES ....................... 150 8.8 EXERCISES .............................. 151 9 MODULAR ARITHMETIC 157 9.1 TYPE ...................... . DESIGNING THE ~ O D 157 9.2 THECODE ............................... 158 9.3 THE DEFAULT MODULUS: STATIC CLASS VARIABLES AND METHODS ..... 163 9.4 AND GET/SET METHODS ................. . CO~S~NC~OE 167 9.5 COMPARISON OPERATORS ........................ 167 9.6 ARITHMETIC OPERATORS ........................ 169 9.7 WRITING MOD OBJECTS TO OUTPUT STREAMS ............... 172 9.8 A MAIN TO DEMONSTRATE THE MOD CLASS ............... 172 9.9 EXERCISES .............................. 174 10 THE PROJECTIVE PLANE 177 10.1 INTRODUCTION TO THE PROJECTIVE PLANE. &!!P2 .............. 177 10.2 DESIGNINGTHECLASSESPPOINTANDPLINE ............ 178 10.3 INHERITANCE ............................. 181 10.4 PROTECTED CLASS MEMBERS ...................... 184 10.5 CLASS AND FILE ORGANIZATION FOR PPOINT AND PLINE ........ 186 10.6 THE PARENT CLASS POB JECT ..................... 187 10.7 THE CLASSES PPOINT AND PLINE .................. 195 10.8 DISCOVERING AND REPAIRING A BUG .................. 200 10.9 PAPPUS REVISITED ........................... 207 10.10 EXERCISES .............................. 211 11 PERMUTATIONS 215 1 1.1 ULAM S PROBLEM ........................... 215 11.2 DESIGNINGTHEPERMUTATIONCLASS ................ 217 11.2.1 DATA ............................. 218 11.2.2 CONSTMCTORS AND DESTRUCTORS ................ 218 1 1.2.3 COPY AND ASSIGN ....................... 220 11.2.4 BASIC INSPECTION AND MODIFICATION METHODS ......... 223 1 1.2.5 PERMUTATION OPERATIONS ................... 224 1 1.2.6 COMPARISON OPERATORS .................... 225 1 1.2.7 OUTPUT ............................ 225 11.2.8 THECODEFI1EERMUTATION.C .............. 225 1 1.3 FINDING MONOTONE SUBSEQUENCES .................. 229 11.4 EXERCISES .............................. 232 V111 ... C++ FOR MATHEMATICIANS 12 POLYNOMIALS 12.1 PROCEDURE TEMPLATES ........................ . 12.2 CLASS TEMPLATES .......................... . 12.2.1 USING CLASS TEMPLATES ................... . 12.2.2 CREATING CLASS TEMPLATES .................. . 12.3 THE POLYNOMIAL CLASS TEMPLATE ................ . 12.3.1 DATA ............................ . 12.3.2 CONS~CTORS ........................ . 12.3.3 GET AND SET METHODS .................... . 12.3.4 FUNCTION METHODS ..................... . 12.3.5 EQUALITY .......................... . 12.3.6 ARITHMETIC ......................... . 12.3.7 OUTPUT TO THE SCREEN .................... . 12.3.8 GCD ............................ . 12.3.9 THECODE .......................... . 12.4 THE GCD PROBLEM REVISITED .................... . 12.5 WORKING IN BINARY ......................... . 12.5.1 SIGNED VERSUS UNSIGNED INTEGERS ............. . 12.5.2 BIT OPERATIONS ....................... . 12.5.3 THE BITSET CLASS TEMPLATE ............... . 12.5.4 CLASS TEMPLATES WITH NON-TYPE ARGUMENTS ......... . 12.6 EXERCISES ............................. . 111 TOPICS 13 USING OTHER PACKAGES 13.1 ARBITRARY PRECISION ARITHMETIC: THE GMP PACKAGE ........ . 13.2 LINEAR ALGEBRA ........................... . 13.2.1 TWO-DIMENSIONAL ARRAYS IN C++ .............. . 13.2.2 THE TNT AND JAMA PACKAGES .............. . 13.2.3 THE NEWMAT PACKAGE ................... . 13.3 OTHER PACKAGES .......................... . 13.4 EXERCISES ............................. . 14 STRINGS. INPUT/OUTPUT. AND VISUALIZATION 14.1 CHARACTER ARRAYS .......................... . 14.2 THESTRINGCLASS ........................ . 14.2.1 INITIALIZATION ........................ . 14.2.2 FUNDAMENTAL OPERATIONS .................. . 14.2.3 SEARCHING ......................... . 14.2.4 CONVERTING BETWEEN STRING AND CHAR* TYPES ...... 14.3 COMMAND LINE ARGUMENTS ..................... . 14.4 READING AND WRITING DATA IN FILES ................. . 14.4.1 OPENING FILES FOR INPUTFOUTPUT ............... . 14.4.2 READING AND WRITING .................... . TABLE OF CONTENTS IX 14.4.3 DETECTING THE END OF AN INPUT FILE .............. 304 14.4.4 OTHER METHODS FOR INPUT ................... 305 14.5 STRING STREAMS ............................ 307 14.6 FORMATTING .............................. 308 14.6.1 SETTING PRECISION ...................... 309 14.6.2 SHOWING ALL DIGITS ...................... 309 14.6.3 SETTING THE WIDTH ...................... 310 14.6.4 OTHER MANIPULATORS ..................... 311 14.7 ACLASSTOPARSEFILES ........................ 311 14.8 VISUALIZATION ............................ 315 14.8.1 INTRODUCING AND INSTALLING THE PLOTUT ILS PACKAGE .... 316 14.8.2 DRAWING WITH PLOTUT ILS-A FIRST EXAMPLE ....... 317 14.8.3 PASCAL S TRIANGLE MODULO TWO ................ 322 14.8.4 TRACING THE MOTION OF A POINT MOVING RANDOMLY IN A TRIANGLE 324 14.8.5 DRAWING PALEY GRAPHS .................... 326 14.9 EXERCISES .............................. 330 15 ODDS AND ENDS 333 15.1 THE SWITCH STATEMENT ....................... 333 15.2 LABELS AND THE GOTO STATEMENT ................... 336 15.3 EXCEPTION HANDLING ......................... 338 15.3.1 THE BASICS OF TRY. THROW. AND CATCH .......... 338 15.3.2 OTHER FEATURES OF THE EXCEPTION-HANDLING SYSTEM ...... 342 15.4 FRIENDS ............................... 344 15.5 OTHER WAYS TO CREATE TYPES ..................... 347 15.5.1 STRUCTURES .......................... 347 15.5.2 ENUMERATIONS ........................ 348 15.5.3 UNIONS ............................ 348 15.5.4 USING TYPEDEF ...................... 349 15.6 POINTERS ............................... 350 15.6.1 POINTER BASICS ........................ 350 15.6.2 DEREFERENCING ........................ 351 15.6.3 ARRAYS AND POINTER ARITHMETIC ................ 353 15.6.4 NEW AND DELETE REVISITED ................. 355 15.6.5 WHY USE POINTERS? ...................... 356 15.7 EXERCISES .............................. 358 IV APPENDICES 361 A YOUR C++ COMPUTING ENVIRONMENT 363 A.1 PROGRAMMING WITH A COMMAND WINDOW AND A TEXT EDITOR ..... 363 A . 1.1 WHAT YOU NEED AND HOW TO GET IT (FOR FREE) ......... 364 A . 1.2 EDITING PROGRAM FILES .................... 365 A . 1.3 COMPILING AND RUNNING YOUR PROGRAM ........... 366 A . 1.4 COMPILER OPTIONS ...................... 368 C++ FOR MATHEMATICIANS A.1.5 INTRODUCTION TO MAKE .................... 370 A.2 PROGRAMMING WITH AN INTEGRATED DEVELOPMENT ENVIRONMENT .... 372 A.2.1 VISUAL C++ FOR WINDOWS .................. 373 A.2.2 XCODE FOR MACINTOSH OS X ................. 376 A.3 GENERAL ADVICE ON DEBUGGING .................... 378 B DOCUMENTATION WITH DOXYGEN 381 B . 1 DOXYGEN COMMENTS ......................... 381 B.L.L DOCUMENTING FILES ...................... 382 B . 1.2 DOCUMENTING PROCEDURES .................. 382 B.1.3 DOCUMENTING CLASSES. DATA, AND METHODS .......... 383 B.2 USING DOXYGEN ........................... 386 B.2.1 CONFIGURING DOXYGEN .................... 38 6 B.2.2 RUNNING DOXYGEN ...................... 389 B . 2.3 MORE FEATURES ........................ 389 C C++ REFERENCE 391 C.L VARIABLES AND TYPES ......................... 391 C . 1.1 FUNDAMENTAL TYPES ..................... 391 C . 1.2 STANDARD CLASSESLTERNPLATES ................. 391 C . 1.3 DECLARING VARIABLES ..................... 392 C.1.4 STATIC VARIABLES AND SCOPE .................. 392 C.1.5 CONSTANTSANDTHEKEYWORDCONST ............. 393 C.F.6 ARRAYS ............................ 393 C.2 OPERATIONS .............................. 394 C.2.1 ASSIGNMENT ......................... 394 C.2.2 ARITHMETIC .......................... 394 C.2.3 COMPARISON OPERATORS .................... 394 C.2.4 LOGICAL OPERATORS ...................... 394 C.2.5 BIT OPERATORS ......................... 395 C.2.6 POTPOURRI .......................... 395 C.3 CONTROL STATEMENTS ......................... 396 C.3.1 IF-ELSE .......................... 396 C.3.2 LOOPING: FOR.WHILE.ANDDO ............... 396 C.3.3 SWITCH ........................... 397 C.3.4 GOTO ............................ 398 C.3.5 EXCEPTIONS .......................... 398 C.4 PROCEDURES .............................. 398 C.4.1 FILE ORGANIZATION ...................... 399 C.4.2 CALL BY VALUE VERSUS CALL BY REFERENCE ........... 399 C.4.3 ARRAY (AND POINTER) ARGUMENTS ............... 400 C.4.4 DEFAULT VALUES FOR ARGUMENTS ................ 400 C.4.5 TEMPLATES .......................... 400 C.4.6 IN LINE PROCEDURES ..................... 401 C.5 CLASSES ............................... 401 TABLE OF CONTENTS XI C.5.1 OVERVIEW AND FILE ORGANIZATION ............... 401 C.5.2 CONSTRUCTORS AND DESTRUCTORS ................ 402 C.5.3 OPERATORS .......................... 403 C.5.4 COPY AND ASSIGN ....................... 404 C.5.5 STATIC DATA AND METHODS ................. 405 C5.6 THIS ............................ 406 C.5.7 FRIENDS ........................... 406 C.5.8 CLASS TEMPLATES ....................... 407 C.5.9 INHERITANCE .......................... 407 C.6 STANDARD FUNCTIONS ......................... 408 C.6.1 MATHEMATICAL FUNCTIONS ................... 408 C.6.2 MATHEMATICAL CONSTANTS ................... 411 C.6.3 CHARACTER PROCEDURES .................... 41 1 C.6.4 OTHER USEFUL FUNCTIONS .................... 413 D ANSWERS 415 INDEX 487
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title	C++ for mathematicians an introduction for students and professionals
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title_full	C++ for mathematicians an introduction for students and professionals Edward Scheinerman
title_fullStr	C++ for mathematicians an introduction for students and professionals Edward Scheinerman
title_full_unstemmed	C++ for mathematicians an introduction for students and professionals Edward Scheinerman
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title_sort	c for mathematicians an introduction for students and professionals
title_sub	an introduction for students and professionals
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topic_facet	C++ Mathematik C Programmiersprache
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