Solving polynomial equation systems: 3 Algebraic solving
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Cambridge University Press
2015
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
157 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 275 S. |
| ISBN: | 9780521811552 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
39
40
41
Preface page xi
Setting Xlll
PART SIX: Algebraic Solving 1
Trinks 3
39.1 Recalling Gröbner 3
39.2 Trinks’ Algorithm 6
39.3 Gianni-Kalkbrener Algorithm 9
39.4 An Ecumenical Notion of Solving 12
39.5 Delassus-Gunther Solver 13
Stetter 19
40.1 Endomorphisms of an Algebra 20
40.2 Toward the Auzinger-Stetter Theorem 23
40.3 Auzinger-Stetter: The Radical Case 26
40.4 Möller: Endomorphisms and Dual Space 30
40.5 Möller-Stetter: The General Case 36
40.6 The Univariate Case 39
40.7 Derogatoriness 42
40.8 Stetter Algorithm via Grobnerian Technology 44
40.9 Stetter Algorithm 46
40.10 Lundqvist: Analysis and Improvements of Möller’s Algorithm 46
40.11 Lex Game: Analysis and Improvements on Cerlienco-
Mureddu Correspondence 54
40.12 Lundqvist: A Gröbner-free Solver 58
40.13 Derogatoriness and Allgemeine Coordinates 59
Macaulay IV 66
41.1 The Resultant of r Forms in r Variables 68
41.2 Bezout’s Generating Set 70
41.3 Macaulay’s Matrix 72
41.4 The Extraneous Factor 78
41.5 Macaulay’s Resultant 84
41.6 Macaulay: The ¿/-Resultant 89
41.7 Kronecker’s Resolvent 92
41.8 Kronecker: The «-Resolvent 94
41.9 Kronecker Parametrization 95
41.10 Historical Intermezzo: From Bezout to Cayley 97
41.11 Dixon’s Resultant 112
41.12 Toward Cardinal’s Conjecture 117
41.13 Cardinal-Mourrain Algorithm 123
41.14 Mourrain: Proving Cardinal’s Conjecture 131
41.15 Mourrain: A Grobner-free Solver 135
42 Lazard II 138
42.1 Ritt: Characteristic Sets for Differential Polynomial Ideals 139
42.2 Ritt: Characteristic Sets for Polynomial Ideals 147
42.3 Ritt’s and Wu’s Solvers 152
42.4 Lazard: Triangular Sets 157
42.5 Admissible Lazard Sequence 159
42.6 Lazard’s Solver 165
42.7 Ritt Bases and Grobner Bases 172
42.8 Moller’s Zero-dimensional Solver 175
42.9 Rouillier: Rational Univariate Representation 180
43 Lagrange II 192
43.1 Representation of Groups as Permutation Groups 192
43.2 Representation as Permutation Group of Roots 199
43.3 Universal Lagrange Resolvent 200
43.4 Cauchy Modules 203
43.5 Resolvents and Polynomial Roots 210
43.6 Lagrange Resolvent and Galois Group 214
43.7 Computing Galois Groups of a Polynomial 219
44 Kronecker IV 222
44.1 Kronecker Parametrization 223
44.2 Lifting Points 226
44.3 Newton-Hensel Lifting 228
44.4 Kronecker Package: Description 231
44.5 Kronecker Package: Lifting Step 233
44.6 Kronecker Package: Intersection Step 234
44.7 Kronecker Package: Cleaning Step 240
44.8 Genericity Conditions 240
44.9 Complexity Considerations 243
45 Duval II 247
45.1 Kronecker-Duval Model 248
45.2 Allgemeine Representation 248
45.3 Kronecker Parametrization and Rational Univariate
Represen tation 25 3
45.4 Gröbner Representation 257
45.5 Linear Representation 266
Bibliography 267
Index 273
|
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| indexdate | 2024-07-10T07:09:33Z |
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| isbn | 9780521811552 |
| language | English |
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| physical | XVIII, 275 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Mora, Teo Verfasser aut Solving polynomial equation systems 3 Algebraic solving Teo Mora 1. publ. New York Cambridge University Press 2015 XVIII, 275 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 157 Encyclopedia of mathematics and its applications ... (DE-604)BV016980289 3 Encyclopedia of mathematics and its applications 157 (DE-604)BV000903719 157 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028213937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mora, Teo Solving polynomial equation systems Encyclopedia of mathematics and its applications |
| title | Solving polynomial equation systems |
| title_auth | Solving polynomial equation systems |
| title_exact_search | Solving polynomial equation systems |
| title_full | Solving polynomial equation systems 3 Algebraic solving Teo Mora |
| title_fullStr | Solving polynomial equation systems 3 Algebraic solving Teo Mora |
| title_full_unstemmed | Solving polynomial equation systems 3 Algebraic solving Teo Mora |
| title_short | Solving polynomial equation systems |
| title_sort | solving polynomial equation systems algebraic solving |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028213937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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