Solving polynomial equation systems: 2 Macaulay's paradigm and Gröbner technology
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| Format: | Book |
| Language: | English |
| Published: |
New York
Cambridge University Press
2005
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
99 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXII, 759 S. |
| ISBN: | 9780521811569 0521811562 |
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| _version_ | 1804132997817958400 |
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| adam_text | IMAGE 1
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
SOLVING POLYNOMIAL EQUATION SYSTEMS II
MACAULAY S PARADIGM AND GROBNER TECHNOLOGY
TEO MORA UNIVERSITY OF GENOA
CAMBRIDGE UNIVERSITY PRESS
IMAGE 2
CONTENTS
PREFACE PAGE XI
SETTING XIV
PART THREE: GAUSS, EUCLID, BUCHBERGER: ELEMENTARY GROBNER BASES 1
20 HILBERT 3
20.1 AFFINE ALGEBRAIC VARIETIES AND IDEALS 3
20.2 LINEAR CHANGE OF COORDINATES 8
20.3 HILBERT S NULLSTELLENSATZ 10
20.4 *KRONECKER SOLVER 15
20.5 PROJECTIVE VARIETIES AND HOMOGENEOUS IDEALS 22
20.6 *SYZYGIES AND HILBERT FUNCTION 28
20.7 *MORE ON THE HILBERT FUNCTION 34
20.8 HILBERT S AND GORDAN S BASISSATZE * 36
21 GAUSS II 46
21.1 SOME HERETICAL NOTATION 47
21.2 GAUSSIAN REDUCTION 51
21.3 GAUSSIAN REDUCTION AND EUCLIDEAN ALGORITHM REVISITED 63 22
BUCHBERGER 72
22.1 FROM GAUSS TO GROBNER 75
22.2 GROBNER BASIS , 78
22.3 TOWARD BUCHBERGER S ALGORITHM 83
22.4 BUCHBERGER S ALGORITHM (1) 96
22.5 BUCHBERGER S CRITERIA 98
22.6 BUCHBERGER S ALGORITHM (2) 104
23 MACAULAYL 109
23.1 HOMOGENIZATION AND AFFINIZATION 110
23.2 H-BASES 114
VI
IMAGE 3
CONTENTS VII
23.3 MACAULAY S LEMMA 119
23.4 RESOLUTION AND HILBERT FUNCTION FOR MONOMIAL IDEALS 122
23.5 HILBERT FUNCTION COMPUTATION: THE DIVIDE-AND-CONQUER ALGORITHMS
136
23.6 H-BASES AND GROBNER BASES FOR MODULES 138
23.7 LIFTING THEOREM 142
23.8 COMPUTING RESOLUTIONS 146
23.9 MACAULAY S NULLSTELLENSATZ BOUND 152
23.10 *BOUNDS FOR THE DEGREE IN THE NULLSTELLENSATZ 156 24 GROBNERI 170
24.1 REWRITING RULES 173
24.2 GROBNER BASES AND REWRITING RULES 183
24.3 GROBNER BASES FOR MODULES 188
24.4 GROBNER BASES IN GRADED RINGS 195
24.5 STANDARD BASES AND THE LIFTING THEOREM 198
24.6 HIRONAKA S STANDARD BASES AND VALUATIONS 203
24.7 *STANDARD BASES AND QUOTIENTS RINGS 21 8
24.8 *CHARACTERIZATION OF STANDARD BASES IN VALUATION RINGS 223
24.9 TERM ORDERING: CLASSIFICATION AND REPRESENTATION 234
24.10 *GR6BNER BASES AND THE STATE POLYTOPE 247
25 GEBAUER AND TRAVERSO 255
25.1 GEBAUER-MOLLER AND USELESS PAIRS 255
25.2 BUCHBERGER S ALGORITHM (3) . 264
25.3 TRAVERSO S CHOICE 271
25.4 GEBAUER-MOLLER S STAGGERED LINEAR BASES AND FAUGERE S F$ . 21A
26 SPEAR 289
26.1 ZACHARIAS RINGS 291
26.2 LEXICOGRAPHICAL TERM ORDERING AND ELIMINATION IDEALS 300 26.3 IDEAL
THEORETICAL OPERATION 304
26.4 *MULTIVARIATE CHINESE REMAINDER ALGORITHM 313 26.5 TAG-VARIABLE
TECHNIQUE AND ITS APPLICATION TO SUBALGEBRAS 316
26.6 CABOARA-TRAVERSO MODULE REPRESENTATION 321
26.7 *CABOARA ALGORITHM FOR HOMOGENEOUS MINIMAL RESOLUTIONS 329
IMAGE 4
VIII CONTENTS
PART FOUR: DUALITY 333
27 NOETHER 335
27.1 NOETHERIAN RINGS 337
340 345 350 356
364 368 371 374
378 380 384 390
28 MOLLER I 393
393 401
29 LAZARD 414
415 418 426 432
440 444
30 MACAULAYLL - 451
452 456
461 466 478 492 494
31 GROBNER II 500
501 502 504 508
509 512
27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9
27.10 27.11 27.12 27.13 MOLLER
28.1 28.2 LAZARD 29.1 29.2 29.3 29.4 29.5 29.6
PRIME, PRIMARY, RADICAL, MAXIMAL IDEALS LASKER-NOETHER DECOMPOSITION:
EXISTENCE LASKER-NOETHER DECOMPOSITION: UNIQUENESS CONTRACTION AND
EXTENSION
DECOMPOSITION OF HOMOGENEOUS IDEALS *THE CLOSURE OF AN IDEAL AT THE
ORIGIN GENERIC SYSTEM OF COORDINATES IDEALS IN NOETHER POSITION
*CHAINS OF PRIME IDEALS DIMENSION ZERO-DIMENSIONAL IDEALS AND
MULTIPLICITY UNMIXED IDEALS I
DUALITY MOLLER ALGORITHM [ THE FGLM PROBLEM
THE FGLM ALGORITHM BORDER BASES AND GROBNER REPRESENTATION IMPROVING
MOLLER S ALGORITHM HILBERT DRIVEN AND GROBNER WALK
*THE STRUCTURE OF THE CANONICAL MODULE MACAULAY II 30.1 30.2
30.3
30.4 30.5 30.6 30.7
THE LINEAR STRUCTURE OF AN IDEAL INVERSE SYSTEM REPRESENTING AND
COMPUTING THE LINEAR STRUCTURE OF AN IDEAL
NOETHERIAN EQUATIONS DIALYTIC ARRAYS OF M^ AND PERFECT IDEALS
MULTIPLICITY OF PRIMARY IDEALS THE STRUCTURE OF PRIMARY IDEALS AT THE
ORIGIN GROBNER II 31.1 31.2
31.3 31.4 31.5
31.6
NOETHERIAN EQUATIONS STABILITY GROBNER DUALITY
LEIBNIZ FORMULA DIFFERENTIAL INVERSE FUNCTIONS AT THE ORIGIN TAYLOR
FORMULA AND GROBNER DUALITY
IMAGE 5
CONTENTS IX
32 GROBNER III 517
32.1 MACAULAY BASES 518
32.2 MACAULAY BASIS AND GROBNER REPRESENTATION 521
32.3 MACAULAY BASIS AND DECOMPOSITION OF PRIMARY IDEALS 522 32.4 HORNER
REPRESENTATION OF MACAULAY BASES 527
32.5 POLYNOMIAL EVALUATION AT MACAULAY BASES 531
32.6 CONTINUATIONS 533
32.7 COMPUTING A MACAULAY BASIS 542
33 MOLLER II 549
33.1 MACAULAY S TRICK 550
33.2 THE CERLIENCO-MUREDDU CORRESPONDENCE 554
33.3 LAZARD STRUCTURAL THEOREM 560
33.4 SOME FACTORIZATION RESULTS 562
33.5 SOME EXAMPLES 569
33.6 AN ALGORITHMIC PROOF 574
PART FIVE: BEYOND DIMENSION ZERO 583
34 GROBNER IV 585
34.1 NULLDIMENSIONALEN BASISSATZE 586
34.2 PRIMITIVE ELEMENTS AND ALLGEMEINE BASISSATZ 593 34.3
HIGHER-DIMENSIONAL PRIMBASISSATZ 598
34.4 IDEALS IN ALLGEMEINE POSITIONS 601
34.5 SOLVING 605
34.6 GIANNI-KALKBRENER THEOREM 608
35 GIANNI-TRAGER-ZACHARIAS 614
35.1 DECOMPOSITION ALGORITHMS . 615
35.2 ZERO-DIMENSIONAL DECOMPOSITION ALGORITHMS 616 35.3 THE GTZ SCHEME .
622
35.4 HIGHER-DIMENSIONAL DECOMPOSITION ALGORITHMS 631 35.5 DECOMPOSITION
ALGORITHMS FOR ALLGEMEINE IDEALS 634 35.5.1 ZERO-DIMENSIONAL ALLGEMEINE
IDEALS 634 35.5.2 HIGHER-DIMENSIONAL ALLGEMEINE IDEALS 637
35.6 SPARSE CHANGE OF COORDINATES 640
35.6.1 GIANNI S LOCAL CHANGE OF COORDINATES 641 35.6.2 GIUSTI-HEINTZ
COORDINATES 645
35.7 LINEAR ALGEBRA AND CHANGE OF COORDINATES 650
35.8 DIRECT METHODS FOR RADICAL COMPUTATION 654
35.9 CABOARA-CONTI-TRAVERSO DECOMPOSITION ALGORITHM 658
35.10 SQUAREFREE DECOMPOSITION OF A ZERO-DIMENSIONAL IDEAL 660
IMAGE 6
X CONTENTS
36 MACAULAY III 665
36.1 HILBERT FUNCTION AND COMPLETE INTERSECTIONS 666
36.2 THE COEFFICIENTS OF THE HILBERT FUNCTION 670
36.3 PERFECTNESS 678
37 GALLIGO 686
37.1 GALLIGO THEOREM (1): EXISTENCE OF GENERIC ESCALIER 686 37.2 BOREL
RELATION 697
37.3 *GALLIGO THEOREM (2): THE GENERIC INITIAL IDEAL IS BOREL INVARIANT
706
37.4 *GALLIGO THEOREM (3): THE STRUCTURE OF THE GENERIC ESCALIER 710
714 725 726 728 733 735
741
749 758
37.5
38 GIUSTI
38.1 38.2 38.3 38.4
38.5
BIBLIOGRAPHY INDEX
EHAHOU-KERVAIRE RESOLUTIO
THE COMPLEXITY OF AN IDEAL TOWARD GIUSTI S BOUND GIUSTI S BOUND MAYR AND
MEYER S EXAMPLE
OPTIMALITY OF REVLEX
|
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| author_facet | Mora, Teo |
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| edition | 1. publ. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:01:43Z |
| institution | BVB |
| isbn | 9780521811569 0521811562 |
| language | English |
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| physical | XXII, 759 S. |
| publishDate | 2005 |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Mora, Teo Verfasser aut Solving polynomial equation systems 2 Macaulay's paradigm and Gröbner technology Teo Mora 1. publ. New York Cambridge University Press 2005 XXII, 759 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 99 Encyclopedia of mathematics and its applications ... Hier auch später erschienene, unveränderte Nachdrucke (DE-604)BV016980289 2 Encyclopedia of mathematics and its applications 99 (DE-604)BV000903719 99 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012959109&sequence=000001&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 2 Macaulay's paradigm and Gröbner technology Teo Mora |
| title_fullStr | Solving polynomial equation systems 2 Macaulay's paradigm and Gröbner technology Teo Mora |
| title_full_unstemmed | Solving polynomial equation systems 2 Macaulay's paradigm and Gröbner technology Teo Mora |
| title_short | Solving polynomial equation systems |
| title_sort | solving polynomial equation systems macaulay s paradigm and grobner technology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012959109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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