Polynomial algorithms in computer algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wien [u.a.]
Springer
1996
|
| Series: | Texts and monographs in symbolic computation
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 270 S. graph. Darst. |
| ISBN: | 3211827595 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 What is computer algebra? 1
1.2 Program systems in computer algebra 8
1.3 Algebraic preliminaries 13
1.4 Representation of algebraic structures 18
1.5 Measuring the complexity of algorithms 22
1.6 Bibliographic notes 24
2 Arithmetic in basic domains 26
2.1 Integers 26
2.2 Polynomials 37
2.3 Quotient fields 43
2.4 Algebraic extension fields 45
2.5 Finite fields 47
2.6 Bibliographic notes 50
3 Computing by homomorphic images 51
3.1 The Chinese remainder problem and the modular method 51
3.2 /7 adic approximation 61
3.3 The fast Fourier transform 67
3.4 Bibliographic notes 81
4 Greatest common divisors of polynomials 82
4.1 Polynomial remainder sequences 82
4.2 A modular gcd algorithm 91
4.3 Computation of resultants 96
4.4 Squarefree factorization 101
4.5 Squarefree partial fraction decomposition 104
4.6 Integration of rational functions 105
4.7 Bibliographic notes 111
5 Factorization of polynomials 112
5.1 Factorization over finite fields 112
5.2 Factorization over the integers 115
5.3 A polynomial time factorization algorithm over the integers 125
5.4 Factorization over algebraic extension fields 140
viii
5.5 Factorization over an algebraically closed field 146
5.6 Bibliographic notes 150
6 Decomposition of polynomials 151
6.1 A polynomial time algorithm for decomposition 151
6.2 Bibliographic notes 156
7 Linear algebra solving linear systems 157
7.1 Bareiss s algorithm 157
7.2 Hankel matrices 163
7.3 Application of Hankel matrices to polynomial problems 166
7.4 Bibliographic notes 171
8 The method of Grobner bases 172
8.1 Reduction relations 172
8.2 Polynomial reduction and Grobner bases 179
8.3 Computation of Grobner bases 183
8.4 Applications of Grobner bases 189
8.5 Speed ups and complexity considerations 201
8.6 Bibliographic notes 202
9 Quantifier elimination in real closed fields 204
9.1 The problem of quantifier elimination 204
9.2 Cylindrical algebraic decomposition 206
9.3 Bibliographic notes 214
10 Indefinite summation 215
10.1 Gosper s algorithm 215
10.2 Bibliographic notes 223
11 Parametrization of algebraic curves 224
11.1 Plane algebraic curves 224
11.2 A parametrization algorithm 230
11.3 Bibliographic notes 236
Solutions of selected exercises 237
References 249
Subject index 265
|
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| dewey-tens | 510 - Mathematics |
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| spelling | Winkler, Franz Verfasser aut Polynomial algorithms in computer algebra F. Winkler Wien [u.a.] Springer 1996 VIII, 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in symbolic computation Algorithmes Algoritmen gtt Algèbre - Données, traitement des ram Algèbre - Informatique algorithme décomposition inriac algèbre linéaire inriac base Gröbner inriac factorisation polynôme inriac homomorphisme inriac mathématique symbolique inriac Datenverarbeitung Algebra -- Data processing Computer 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085240&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Winkler, Franz Polynomial algorithms in computer algebra Algorithmes Algoritmen gtt Algèbre - Données, traitement des ram Algèbre - Informatique algorithme décomposition inriac algèbre linéaire inriac base Gröbner inriac factorisation polynôme inriac homomorphisme inriac mathématique symbolique inriac Datenverarbeitung Algebra -- Data processing Computer algorithms Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4010449-7 |
| title | Polynomial algorithms in computer algebra |
| title_auth | Polynomial algorithms in computer algebra |
| title_exact_search | Polynomial algorithms in computer algebra |
| title_full | Polynomial algorithms in computer algebra F. Winkler |
| title_fullStr | Polynomial algorithms in computer algebra F. Winkler |
| title_full_unstemmed | Polynomial algorithms in computer algebra F. Winkler |
| title_short | Polynomial algorithms in computer algebra |
| title_sort | polynomial algorithms in computer algebra |
| topic | Algorithmes Algoritmen gtt Algèbre - Données, traitement des ram Algèbre - Informatique algorithme décomposition inriac algèbre linéaire inriac base Gröbner inriac factorisation polynôme inriac homomorphisme inriac mathématique symbolique inriac Datenverarbeitung Algebra -- Data processing Computer algorithms Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Algorithmes Algoritmen Algèbre - Données, traitement des Algèbre - Informatique algorithme décomposition algèbre linéaire base Gröbner factorisation polynôme homomorphisme mathématique symbolique Datenverarbeitung Algebra -- Data processing Computer algorithms Algorithmus Computeralgebra |
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