Algorithms for computer algebra:
Mathematics of Computing -- Numerical Analysis.
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer
1992
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Mathematics of Computing -- Numerical Analysis. |
| Physical Description: | XVIII, 585 S. |
| ISBN: | 0792392590 |
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Record in the Search Index
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| adam_text | ALGORITHMS FOR COMPUTER ALGEBRA K.O. GEDDES UNIVERSITY OF WATERLOO S.R.
CZAPOR LAURENTIAN UNIVERSITY G. LABAHN UNIVERSITY OF WATERLOO 14 W
KLUWER ACADEMIC PUBLISHERS BOSTON/DORDRECHT/LONDON CONTENTS PREFACE XV
CHAPTER 1 INTRODUCTION TO COMPUTER ALGEBRA 1.1 INTRODUCTION 1 1.2
SYMBOLIC VERSUS NUMERIC COMPUTATION 2 1.3 A BRIEF HISTORICAL SKETCH 4
1.4 AN EXAMPLE OF A COMPUTER ALGEBRA SYSTEM: MAPLE 11 EXERCISES 20
CHAPTER 2 ALGEBRA OF POLYNOMIALS, RATIONAL FUNCTIONS, AND POWER SERIES
2.1 INTRODUCTION 23 2.2 RINGS AND FIELDS 23 2.3 DIVISIBILITY AND
FACTORIZATION IN INTEGRAL DOMAINS 26 2.4 THE EUCLIDEAN ALGORITHM 32 2.5
UNIVARIATE POLYNOMIAL DOMAINS 38 2.6 MULTIVARIATE POLYNOMIAL DOMAINS 46
2.7 THE PRIMITIVE EUCLIDEAN ALGORITHM 52 2.8 QUOTIENT FIELDS AND
RATIONAL FUNCTIONS 60 2.9 POWER SERIES AND EXTENDED POWER SERIES 63 2.10
RELATIONSHIPS AMONG DOMAINS 70 EXERCISES 73 CHAPTER 3 NORMAL FORMS AND
ALGEBRAIC REPRESENTATIONS 3.1 INTRODUCTION 79 3.2 LEVELS OF ABSTRACTION
79 3.3 NORMAL FORM AND CANONICAL FORM 80 3.4 NORMAL FORMS FOR
POLYNOMIALS 84 3.5 NORMAL FORMS FOR RATIONAL FUNCTIONS AND POWER SERIES
88 3.6 DATA STRUCTURES FOR MULTIPRECISION INTEGERS AND RATIONAL NUMBERS
93 3.7 DATA STRUCTURES FOR POLYNOMIALS, RATIONAL FUNCTIONS, AND POWER
SERIES 96 EXERCISES 105 VIII ALGORITHMS FOR COMPUTER ALGEBRA CHAPTER 4
ARITHMETIC OF POLYNOMIALS, RATIONAL FUNCTIONS, AND POWER SERIES 4.1
INTRODUCTION 111 4.2 BASIC ARITHMETIC ALGORITHMS 112 4.3 FAST ARITHMETIC
ALGORITHMS: KARATSUBA S ALGORITHM 118 4.4 MODULAR REPRESENTATIONS 120
4.5 THE FAST FOURIER TRANSFORM 123 4.6 THE INVERSE FOURIER TRANSFORM 128
4.7 FAST POLYNOMIAL MULTIPLICATION 132 4.8 COMPUTING PRIMITIVE N-THROOTS
OF UNITY 133 4.9 NEWTON S ITERATION FOR POWER SERIES DIVISION 136
EXERCISES 145 CHAPTER 5 HOMOMORPHISMS AND CHINESE REMAINDER ALGORITHMS
5.1 INTRODUCTION 151 5.2 INTERMEDIATE EXPRESSION SWELL: AN EXAMPLE 151
5.3 RING MORPHISMS 153 5.4 CHARACTERIZATION OF MORPHISMS 160 5.5
HOMOMORPHIC IMAGES 167 5.6 THE INTEGER CHINESE REMAINDER ALGORITHM 174
5.7 THE POLYNOMIAL INTERPOLATION ALGORITHM 183 5.8 FURTHER DISCUSSION OF
THE TWO ALGORITHMS 189 EXERCISES 196 CHAPTER 6 NEWTON S ITERATION AND
THE HENSEL CONSTRUCTION 6.1 INTRODUCTION 205 6.2 P-ADIC AND IDEAL-ADIC
REPRESENTATIONS 205 6.3 NEWTON S ITERATION FOR F(U)=0 214 6.4 HENSEL S
LEMMA 226 6.5 THE UNIVARIATE HENSEL LIFTING ALGORITHM 232 6.6 SPECIAL
TECHNIQUES FOR THE NON-MONIC CASE 240 6.7 THE MULTIVARIATE
GENERALIZATIOEN OF HENSEL S LEMMA 250 6.8 THE MULTIVARIATE HENSEL LIFTING
ALGORITHM 260 EXERCISES 274 CHAPTER 7 POLYNOMIAL GCD COMPUTATION 7.1
INTRODUCTION 279 7.2 POLYNOMIAL REMAINDER SEQUENCES 280 7.3 THE
SYLVESTER MATRIX AND SUBRESULTANTS 285 7.4 THE MODULAR GCD ALGORITHM 300
7.5 THE SPARSE MODULAR GCD ALGORITHM 311 7.6 GCD SUSING HENSEL LIFTING:
THE EZ-GCD ALGORITHM 314 7.7 A HEURISTIC POLYNOMIAL GCD ALGORITHM 320
EXERCISES 331 CONTENTS IX CHAPTER 8 POLYNOMIAL FACTORIZATION 8.1
INTRODUCTION 337 8.2 SQUARE-FREE FACTORIZATION 337 8.3 SQUARE-FREE
FACTORIZATION OVERFINITE FIELDS 343 8.4 BERLEKAMP S FACTORIZATION
ALGORITHM 347 8.5 THE BIG PRIME BERLEKAMP ALGORITHM 359 8.6 DISTINCT
DEGREE FACTORIZATION 368 8.7 FACTORING POLYNOMIALS OVER THE RATIONAIS
374 8.8 FACTORING POLYNOMIALS OVER ALGEBRAIC NUMBER FIELDS 378 EXERCISES
384 CHAPTER 9 SOLVING SYSTEMS OF EQUATIONS 9.1 INTRODUCTION 389 9.2
LINEAR EQUATIONS AND GAUSSIAN ELIMINATION 390 9.3 FRACTION-FREE GAUSSIAN
ELIMINATION 393 9.4 ALTERNATIVE METHODS FOR SOLVING LINEAR EQUATIONS 399
9.5 NONLINEAR EQUATIONS AND RESULTANTS 405 EXERCISES 422 CHAPTER 10
GROEBNER BASES FOR POLYNOMIAL IDEALS 10.1 INTRODUCTION 429 10.2 TERM
ORDERINGS AND REDUCTION 431 10.3 GROEBNER BASES AND BUCHBERGER S
ALGORITHM 439 10.4 IMPROVING BUCHBERGER S ALGORITHM 447 10.5
APPLICATIONS OF GROEBNER BASES 451 10.6 ADDITIONAL APPLICATIONS 462
EXERCISES 466 CHAPTER 11 INTEGRATION OF RATIONAL FUNCTIONS 11.1
INTRODUCTION 473 11.2 BASIC CONCEPTS OF DIFFERENTIAL ALGEBRA 474 11.3
RATIONAL PART OF THE INTEGRAL: HERMITE S METHOD 482 11.4 RATIONAL PART
OF THE INTEGRAL: HOROWITZ METHOD 488 11.5 LOGARITHMIC PART OF THE
INTEGRAL 492 EXERCISES 508 X ALGORITHMS FOR COMPUTER ALGEBRA CHAPTER 12
THE RISCH INTEGRATION ALGORITHM 12.1 INTRODUCTION 511 12.2 ELEMENTARY
FUNCTIONS 512 12.3 DIFFERENTIATION OF ELEMENTARY FUNCTIONS 519 12.4
LIOUVILLE S PRINCIPLE 523 12.5 THE RISCH ALGORITHM FOR TRANSCENDENTAL
ELEMENTARY FUNCTIONS .529 12.6 THE RISCH ALGORITHM FOR LOGARITHMIC
EXTENSIONS 530 12.7 THE RISCH ALGORITHM FOR EXPONENTIAL EXTENSIONS 547
12.8 INTEGRATION OF ALGEBRAIC FUNCTIONS 561 EXERCISES 569 / NOTATION 575
INDEX 577
|
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| author | Geddes, Keith O. 1947- Czapor, Stephen R. 1957- Labahn, George 1951- |
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| author_sort | Geddes, Keith O. 1947- |
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| discipline | Informatik Mathematik |
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| physical | XVIII, 585 S. |
| publishDate | 1992 |
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| spelling | Geddes, Keith O. 1947- Verfasser (DE-588)172524857 aut Algorithms for computer algebra K. O. Geddes ; S. R. Czapor ; G. Labahn Boston [u.a.] Kluwer 1992 XVIII, 585 S. txt rdacontent n rdamedia nc rdacarrier Mathematics of Computing -- Numerical Analysis. Datenverarbeitung Algebra Data processing Algorithms Algorithmus (DE-588)4001183-5 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Computeralgebra (DE-588)4010449-7 s Algorithmus (DE-588)4001183-5 s DE-604 Czapor, Stephen R. 1957- Verfasser (DE-588)172524865 aut Labahn, George 1951- Verfasser (DE-588)136812279 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004234140&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Geddes, Keith O. 1947- Czapor, Stephen R. 1957- Labahn, George 1951- Algorithms for computer algebra Datenverarbeitung Algebra Data processing Algorithms Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4010449-7 |
| title | Algorithms for computer algebra |
| title_auth | Algorithms for computer algebra |
| title_exact_search | Algorithms for computer algebra |
| title_full | Algorithms for computer algebra K. O. Geddes ; S. R. Czapor ; G. Labahn |
| title_fullStr | Algorithms for computer algebra K. O. Geddes ; S. R. Czapor ; G. Labahn |
| title_full_unstemmed | Algorithms for computer algebra K. O. Geddes ; S. R. Czapor ; G. Labahn |
| title_short | Algorithms for computer algebra |
| title_sort | algorithms for computer algebra |
| topic | Datenverarbeitung Algebra Data processing Algorithms Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Datenverarbeitung Algebra Data processing Algorithms Algorithmus Computeralgebra |
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