Algorithms in real algebraic geometry:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin
Springer
[2006]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Algorithms and computation in mathematics
volume 10 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2791379&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014902457&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | IX, 662 Seiten Illustrationen 24 cm |
| ISBN: | 9783540330981 3540330984 |
Internformat
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| 264 | 1 | |a Berlin |b Springer |c [2006] | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 MAT 140f 2008 A 6269(2) |
|---|---|
| DE-BY-TUM_katkey | 1638039 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020777746 |
| _version_ | 1821933256069611520 |
| adam_text | SAUGATA BASU RICHARD POLLACK MARIE-FRANCOISE ROY ALGORITHMS IN REAL
ALGEBRAIC GEOMETRY SECOND EDITION WITH 37 FIGURES 4Y SPRINGER TABLE OF
CONTENTS INTRODUCTION 1 1 ALGEBRAICALLY CLOSED FIELDS 11 1.1 DEFINITIONS
AND FIRST PROPERTIES 11 1.2 EUCLIDEAN DIVISION AND GREATEST COMMON
DIVISOR 14 1.3 PROJECTION THEOREM FOR CONSTRUCTIBLE SETS 20 1.4
QUANTIFIER ELIMINATION AND THE TRANSFER PRINCIPLE 25 1.5 BIBLIOGRAPHICAL
NOTES 27 2 REAL CLOSED FIELDS 29 2.1 ORDERED, REAL AND REAL CLOSED
FIELDS 29 2.2 REAL ROOT COUNTING 44 2.2.1 DESCARTES S LAW OF SIGNS AND
THE BUDAN-FOURIER THE- OREM 44 2.2.2 STURM S THEOREM AND THE CAUCHY
INDEX 52 2.3 PROJECTION THEOREM FOR ALGEBRAIC SETS 57 2.4 PROJECTION
THEOREM FOR SEMI-ALGEBRAIC SETS 63 2.5 APPLICATIONS 69 2.5.1 QUANTIFIER
ELIMINATION AND THE TRANSFER PRINCIPLE . . 69 2.5.2 SEMI-ALGEBRAIC
FUNCTIONS 71 2.5.3 EXTENSION OF SEMI-ALGEBRAIC SETS AND FUNCTIONS ... 72
2.6 PUISEUX SERIES 74 2.7 BIBLIOGRAPHICAL NOTES 81 3 SEMI-ALGEBRAIC SETS
83 3.1 TOPOLOGY 83 3.2 SEMI-ALGEBRAICALLY CONNECTED SETS 86 3.3
SEMI-ALGEBRAIC GERMS 87 VI TABLE OF CONTENTS 3.4 CLOSED AND BOUNDED
SEMI-ALGEBRAIC SETS 93 3.5 IMPLICIT FUNCTION THEOREM 94 3.6
BIBLIOGRAPHICAL NOTES 99 4 ALGEBRA 101 4.1 DISCRIMINANT AND
SUBDISCRIMINANT 101 4.2 RESULTANT AND SUBRESULTANT COEFFICIENTS 105
4.2.1 RESULTANT 105 4.2.2 SUBRESULTANT COEFFICIENTS 110 4.2.3
SUBRESULTANT COEFFICIENTS AND CAUCHY INDEX 113 4.3 QUADRATIC FORMS AND
ROOT COUNTING 119 4.3.1 QUADRATIC FORMS 119 4.3.2 HERMITE S QUADRATIC
FORM 127 4.4 POLYNOMIAL IDEALS 132 4.4.1 HILBERT S BASIS THEOREM 132
4.4.2 HILBERT S NULLSTELLENSATZ 136 4.5 ZERO-DIMENSIONAL SYSTEMS 143 4.6
MULTIVARIATE HERMITE S QUADRATIC FORM 149 4.7 PROJECTIVE SPACE AND A
WEAK BEZOUT S THEOREM 153 4.8 BIBLIOGRAPHICAL NOTES 157 5 DECOMPOSITION
OF SEMI-ALGEBRAIC SETS 159 5.1 CYLINDRICAL DECOMPOSITION 159 5.2
SEMI-ALGEBRAICALLY CONNECTED COMPONENTS 168 5.3 DIMENSION 170 5.4
SEMI-ALGEBRAIC DESCRIPTION OF CELLS 172 5.5 STRATIFICATION 174 5.6
SIMPLICIAL COMPLEXES 181 5.7 TRIANGULATION 183 5.8 HARDT S TRIVIALITY
THEOREM AND CONSEQUENCES 186 5.9 SEMI-ALGEBRAIC SARD S THEOREM 191 5.10
BIBLIOGRAPHICAL NOTES 194 6 ELEMENTS OF TOPOLOGY 195 6.1 SIMPLICIAL
HOMOLOGY THEORY 195 6.1.1 THE HOMOLOGY GROUPS OF A SIMPLICIAL COMPLEX
.... 195 6.1.2 SIMPLICIAL COHOMOLOGY THEORY 199 6.1.3 A CHARACTERIZATION
OF H 1 IN A SPECIAL CASE 201 6.1.4 THE MAYER-VIETORIS THEOREM 206 TABLE
OF CONTENTS VII 6.1.5 CHAIN HOMOTOPY 209 6.1.6 THE SIMPLICIAL HOMOLOGY
GROUPS ARE INVARIANT UNDER HOMEOMORPHISM 213 6.2 SIMPLICIAL HOMOLOGY OF
CLOSED AND BOUNDED SEMI-ALGEBRAIC SETS 221 6.2.1 DEFINITIONS AND FIRST
PROPERTIES 221 6.2.2 HOMOTOPY 223 6.3 HOMOLOGY OF CERTAIN LOCALLY CLOSED
SEMI-ALGEBRAIC SETS . . 226 6.3.1 HOMOLOGY OF CLOSED SEMI-ALGEBRAIC SETS
AND OF SIGN CON- DITIONS 226 6.3.2 HOMOLOGY OF A PAIR 228 6.3.3
BOREL-MOORE HOMOLOGY 231 6.3.4 EULER-POINCARE CHARACTERISTIC 234 6.4
BIBLIOGRAPHICAL NOTES 236 QUANTITATIVE SEMI-ALGEBRAIC GEOMETRY 237 7.1
MORSE THEORY 237 7.2 SUM OF THE BETTI NUMBERS OF REAL ALGEBRAIC SETS 256
7.3 BOUNDING THE BETTI NUMBERS OF REALIZATIONS OF SIGN CONDITIONS 262
7.4 SUM OF THE BETTI NUMBERS OF CLOSED SEMI-ALGEBRAIC SETS . . 268 7.5
SUM OF THE BETTI NUMBERS OF SEMI-ALGEBRAIC SETS 273 7.6 BIBLIOGRAPHICAL
NOTES 280 COMPLEXITY OF BASIC ALGORITHMS 281 8.1 DEFINITION OF
COMPLEXITY 281 8.2 LINEAR ALGEBRA 292 8.2.1 SIZE OF DETERMINANTS 292
8.2.2 EVALUATION OF DETERMINANTS 294 8.2.3 CHARACTERISTIC POLYNOMIAL 299
8.2.4 SIGNATURE OF QUADRATIC FORMS 300 8.3 REMAINDER SEQUENCES AND
SUBRESULTANTS 301 8.3.1 REMAINDER SEQUENCES 301 8.3.2 SIGNED
SUBRESULTANT POLYNOMIALS 303 8.3.3 STRUCTURE THEOREM FOR SIGNED
SUBRESULTANTS 307 8.3.4 SIZE OF REMAINDERS AND SUBRESULTANTS 314 8.3.5
SPECIALIZATION PROPERTIES OF SUBRESULTANTS 316 8.3.6 SUBRESULTANT
COMPUTATION 317 8.4 BIBLIOGRAPHICAL NOTES 322 VIII TABLE OF CONTENTS 9
CAUCHY INDEX AND APPLICATIONS 323 9.1 CAUCHY INDEX 323 9.1.1 COMPUTING
THE CAUCHY INDEX 323 9.1.2 BEZOUTIAN AND CAUCHY INDEX 326 9.1.3 SIGNED
SUBRESULTANT SEQUENCE AND CAUCHY INDEX ON AN INTERVAL 330 9.2 HANKEL
MATRICES 333 9.2.1 HANKEL MATRICES AND RATIONAL FUNCTIONS 334 9.2.2
SIGNATURE OF HANKEL QUADRATIC FORMS 337 9.3 NUMBER OF COMPLEX ROOTS WITH
NEGATIVE REAL PART 344 9.4 BIBLIOGRAPHICAL NOTES 350 10 REAL ROOTS 351
10.1 BOUNDS ON ROOTS 351 10.2 ISOLATING REAL ROOTS 360 10.3 SIGN
DETERMINATION 383 10.4 ROOTS IN A REAL CLOSED FIELD 397 10.5
BIBLIOGRAPHICAL NOTES 401 11 CYLINDRICAL DECOMPOSITION ALGORITHM 403
11.1 COMPUTING THE CYLINDRICAL DECOMPOSITION 404 11.1.1 OUTLINE OF THE
METHOD 404 11.1.2 DETAILS OF THE LIFTING PHASE 408 11.2 DECISION PROBLEM
415 11.3 QUANTIFIER ELIMINATION 423 11.4 LOWER BOUND FOR QUANTIFIER
ELIMINATION 426 11.5 COMPUTATION OF STRATIFYING FAMILIES 428 11.6
TOPOLOGY OF CURVES 430 11.7 RESTRICTED ELIMINATION 440 11.8
BIBLIOGRAPHICAL NOTES 444 12 POLYNOMIAL SYSTEM SOLVING 445 12.1 A FEW
RESULTS ON GROBNER BASES 445 12.2 MULTIPLICATION TABLES 451 12.3 SPECIAL
MULTIPLICATION TABLE 456 12.4 UNIVARIATE REPRESENTATION 462 12.5 LIMITS
OF THE SOLUTIONS OF A POLYNOMIAL SYSTEM 471 12.6 FINDING POINTS IN
CONNECTED COMPONENTS OF ALGEBRAIC SETS . 483 12.7 TRIANGULAR SIGN
DETERMINATION 495 TABLE OF CONTENTS IX 12.8 COMPUTING THE EULER-POINCARE
CHARACTERISTIC OF AN ALGEBRAIC SET 498 12.9 BIBLIOGRAPHICAL NOTES 503 13
EXISTENTIAL THEORY OF THE REALS 505 13.1 FINDING REALIZABLE SIGN
CONDITIONS 506 13.2 A FEW APPLICATIONS 516 13.3 SAMPLE POINTS ON AN
ALGEBRAIC SET 519 13.4 COMPUTING THE EULER-POINCARE CHARACTERISTIC OF
SIGN CONDI- TIONS 528 13.5 BIBLIOGRAPHICAL NOTES 532 14 QUANTIFIER
ELIMINATION 533 14.1 ALGORITHM FOR THE GENERAL DECISION PROBLEM 534 14.2
QUANTIFIER ELIMINATION 547 14.3 LOCAL QUANTIFIER ELIMINATION 551 14.4
GLOBAL OPTIMIZATION 557 14.5 DIMENSION OF SEMI-ALGEBRAIC SETS 558 14.6
BIBLIOGRAPHICAL NOTES 562 15 COMPUTING ROADMAPS AND CONNECTED COMPONENTS
OF ALGE- BRAIC SETS 563 15.1 PSEUDO-CRITICAL VALUES AND CONNECTEDNESS
564 15.2 ROADMAP OF AN ALGEBRAIC SET 568 15.3 COMPUTING CONNECTED
COMPONENTS OF ALGEBRAIC SETS .... 580 15.4 BIBLIOGRAPHICAL NOTES 592 16
COMPUTING ROADMAPS AND CONNECTED COMPONENTS OF SEMI- ALGEBRAIC SETS 593
16.1 SPECIAL VALUES 593 16.2 UNIFORM ROADMAPS 601 16.3 COMPUTING
CONNECTED COMPONENTS OF SIGN CONDITIONS . . . 608 16.4 COMPUTING
CONNECTED COMPONENTS OF A SEMI-ALGEBRAIC SET . 614 16.5 ROADMAP
ALGORITHM 617 16.6 COMPUTING THE FIRST BETTI NUMBER OF SEMI-ALGEBRAIC
SETS . 627 16.7 BIBLIOGRAPHICAL NOTES 633 REFERENCES 635 INDEX OF
NOTATION 645 INDEX 655
|
| any_adam_object | 1 |
| author | Basu, Saugata Pollack, Richard 1935- Roy, Marie-Françoise 1950- |
| author_GND | (DE-588)1167961595 (DE-588)124810403 (DE-588)120268221 |
| author_facet | Basu, Saugata Pollack, Richard 1935- Roy, Marie-Françoise 1950- |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | Second edition |
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| id | DE-604.BV021688363 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:39:26Z |
| institution | BVB |
| isbn | 9783540330981 3540330984 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014902457 |
| oclc_num | 70573945 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-706 DE-19 DE-BY-UBM DE-83 DE-739 DE-11 DE-384 DE-188 DE-634 |
| owner_facet | DE-20 DE-703 DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-706 DE-19 DE-BY-UBM DE-83 DE-739 DE-11 DE-384 DE-188 DE-634 |
| physical | IX, 662 Seiten Illustrationen 24 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spellingShingle | Basu, Saugata Pollack, Richard 1935- Roy, Marie-Françoise 1950- Algorithms in real algebraic geometry Algorithms and computation in mathematics Algebraïsche meetkunde gtt Algoritmos larpcal Geometria algébrica real larpcal Datenverarbeitung Algorithms Geometry, Algebraic Data processing Computeralgebra (DE-588)4010449-7 gnd Reelle algebraische Geometrie (DE-588)4192004-1 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4192004-1 |
| title | Algorithms in real algebraic geometry |
| title_auth | Algorithms in real algebraic geometry |
| title_exact_search | Algorithms in real algebraic geometry |
| title_full | Algorithms in real algebraic geometry Saugata Basu, Richard Pollack, Marie-Françoise Roy |
| title_fullStr | Algorithms in real algebraic geometry Saugata Basu, Richard Pollack, Marie-Françoise Roy |
| title_full_unstemmed | Algorithms in real algebraic geometry Saugata Basu, Richard Pollack, Marie-Françoise Roy |
| title_short | Algorithms in real algebraic geometry |
| title_sort | algorithms in real algebraic geometry |
| topic | Algebraïsche meetkunde gtt Algoritmos larpcal Geometria algébrica real larpcal Datenverarbeitung Algorithms Geometry, Algebraic Data processing Computeralgebra (DE-588)4010449-7 gnd Reelle algebraische Geometrie (DE-588)4192004-1 gnd |
| topic_facet | Algebraïsche meetkunde Algoritmos Geometria algébrica real Datenverarbeitung Algorithms Geometry, Algebraic Data processing Computeralgebra Reelle algebraische Geometrie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2791379&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014902457&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
| work_keys_str_mv | AT basusaugata algorithmsinrealalgebraicgeometry AT pollackrichard algorithmsinrealalgebraicgeometry AT roymariefrancoise algorithmsinrealalgebraicgeometry |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Physik
| Signatur: |
0202 MAT 140f 2008 A 6269(2)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |