Solving polynomial equation systems: 4 Buchberger theory and beyond
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Cambridge University Press
2016
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
158 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 820 S. |
| ISBN: | 9781107109636 |
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MARC
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| 100 | 1 | |a Mora, Teo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Solving polynomial equation systems |n 4 |p Buchberger theory and beyond |c Teo Mora |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York |b Cambridge University Press |c 2016 | |
| 300 | |a XI, 820 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Adieu page ix
PART SEVEN: Beyond 1
46 Zacharias 3
46.1 Buchberger-Zacharias Theory 5
46.2 Kandri-Rody-Kapur: Strong Gröbner Bases over
a Euclidean Domain 27
46.3 Pan: Strong Gröbner Bases over a Principal Ideal Domain 31
46.4 Zacharias Rings 37
46.5 Möller : Gröbner Bases over Zacharias Rings 42
46.6 Möller: Gröbner Bases over a Principal Ideal Ring 48
46.7 Useless S-pairs and Gebauer-Möller Set in Principal
Ideal Rings 50
46.8 Möller: Structural Theorem for Gröbner Bases over
a Principal Ideal Ring 54
46.9 Lazard’s Structural Theorem over a Principal Ideal Ring 56
46.10 Ore Conditions 63
46.11 Ore Theory 68
46.12 Lazard’s Structural Theorem for Ore Extensions
over a Principal Ideal Domain 83
46.13 Multivariate Ore Extensions 85
46.14 Ideal of Vanishing Polynomial 96
47 Bergman 100
47.1 Möller Left Lifting Theorem for Free Associative Algebras 102
47.2 Left Gröbner Bases for Free Associative Algebras 107
47.3 Möller’s Right Lifting Theorem and Right Gröbner Bases
for Free Associative Algebras 115
47.4 Bilateral Gröbner Bases: The Lifting Theorem 117
47.5 Bilateral Gröbner Bases: Pritchard’s Module 121
47.6 Bilateral Gröbner Bases of an Ideal in a Free Monoid
Rings over a Field 124
47.7 Pritchard’s Procedure
47.8 La Scala-Levandovskyy: Letterplace Ideals
47.9 Grobner Basis for Weaker Algebras
47.10 Green: Path Algebras
47.11 Reinert: Buchberger Theory on Function Rings
47.12 de Graaf-Wisliceny-Gerritzen: Grobner Bases
on Magma Algebras
48 Ufnarovski
48.1 Ufnarovski Graph
48.2 Ufnarovski: Finite-State Automata and Infinite Grobner
Basis Computation
48.3 2-Variable Graph
48.4 Shirayanagi: Word Tree
48.5 Anick’s Resolution
48.6 Borges: Elimination Orderings and Symmetric Groups
48.7 Taxonomy of Term Orderings
48.8 Ideal Theoretical Operation
49 Weispfenning
49.1 Apel-Lassner: Lie Algebras and Buchberger Theory
49.2 Bergman: Diamond Lemma
49.3 Skew and Solvable Polynomial Rings
49.4 Kredel Conditions
49.5 Kandri-Rody-Weispfenning: Solvable Polynomial Rings
49.6 Twisted Polynomial Rings
49.7 Structural Theorem for Bilateral Ideals of a Twisted
Polynomial Ring
49.8 Gateva’s Monoid
49.9 Gateva: Noetherianity of Finitely Presented Algebras
49.10 Gateva: Binomial Skew Polynomial Rings
49.11 Weispfenning Rings
49.12 La Scala-Levandovskyy: Ore Extension of Multivariate
Polynomial Rings
49.13 La Scala: Buchberger Theory for Partial Difference Ideals
50 Spear 2
50.1 Zacharias’ Canonical Representation
50.2 Term Ordering
50.3 Pseudovaluations
50.4 Grobner Bases and Buchberger Theory
50.5 Moller’s Lifting Theorem
50.6 Spear’s Theorem
50.7 Pseudovaluations (2)
50.8 Toward Buchberger’s Algorithm
50.9 Buchberger’s Algorithms
50.10 The Arithmetic of the Associated Graded Ring
144
148
157
164
172
184
191
192
198
206
207
212
217
221
246
256
258
261
264
268
271
278
284
288
291
298
314
324
332
335
336
349
351
359
363
371
377
381
383
386
394
397
399
423
425
429
436
441
444
446
449
454
457
459
465
468
471
492
510
514
519
528
531
536
542
552
565
567
572
576
581
587
589
592
593
597
597
601
604
611
50.11 Noetherianity
50.12 Canonical Forms
50.13 Case Studies
Weispfenning II
51.1 Comprehensive Grobner Bases
51.2 Montes’ Algorithm
51.3 Canonical Comprehensive Grobner Bases
51.4 Wibmer: Regular Functions
51.5 Kapur et al.: Branching via Solving Techniques
51.6 Montes-Wibmer: Canonical Grobner Cover
51.7 Von Neumann Regular Rings
51.8 Grobner Bases over Von Neumann Regular Rings
51.9 Comprehensiveness of Grobner Bases over Von Neumann
Regular Rings (1)
51.10 Suzuki-Sato: Alternative Comprehensive Grobner Bases
51.11 Comprehensiveness of Grobner Bases over Von Neumann
Regular Rings (2)
Sweedler
52.1 Valuation Rings
52.2 Mosteing—Sweedler: Valuations and Filtrations
52.3 Mosteing-Sweedler: Characterizing Term Order Filtration
52.4 Subalgebra Bases
52.5 SAGBI Bases for Polynomial Invariants of
Alternating Groups
52.6 Finiteness of SAGBI Bases
52.7 Gobel’s Basis for Invariant Rings
52.8 Buchberger’s Algorithm for Symideals
52.9 Aschenbrenner-Hillar: Buchberger Theory
for Symmetric Ideals
52.10 Variations on SAGBI
Hironaka
53.1 A Theory of Normal Forms
53.2 Normal Forms and Standard Bases
53.3 The Zariskification of the Polynomial Ring
53.4 The Tangent Cone Algorithm
53.5 Standard Basis Algorithms
53.6 The Normal Form Algorithm
53.7 L-adic Valuation, Localization, Zariskification
53.8 Standard Bases in Local Rings
Hironaka II
54.1 Alonso—Luengo-Raimondo Model for Algebraic Power Series
54.2 Canonical Forms in the Ring of Algebraic Power Series
54.3 Standard Bases in the Ring of Algebraic Power Series
54.4 An Effective Version of the Weierstrass Preparation Theorem
54.5 Alonso-Castro-Hauser: An Effective Version of Hironaka’s
Henselian Weierstrass Theorem 620
54.6 Branches of a Curve at a Singular Point 622
54.7 Toward Mac Millan’s Algorithm 626
54.8 Mac Millan’s Algorithm 630
55 Janet 633
55.1 Janet Decomposition 635
55.2 Riquier-Janet Completion 651
55.3 Degree-compatible Term Ordering and Convergency 658
55.4 Janet and Hilbert 661
55.5 Janet: Involutiveness 664
55.6 Term Orderings and the Borel Property in Riquier
and His Followers 682
56 Macaulay V 691
56.1 Macaulay’s Formula 692
56.2 Hilbert Function 700
56.3 Sperner’s Proof of Macaulay’s Formula 702
56.4 Gunther: Borel Relation and Borel Invariancy of
Generic Forms 708
56.5 Gunther: Macaulay-like Formula for the Borel Set 716
56.6 Gunther’s Proof of Macaulay’s Formula 720
56.7 Gunther: Hilbert Function Computation 729
56.8 Gunther: Riquier—Janet Procedure 734
56.9 Bigatti-Hulett: Betti Numbers and Lex Segments 740
56.10 Marinari-Ramella: Revlex Segments 744
56.11 Cioffi-Roggero: J-marked Families 750
57 Gerdt and Faugere 757
57.1 Gerdt 758
57.2 Faugere 778
57.3 Mayr: Space-efficient Grobner Basis Computation 796
57.4 Congedo: Buchberger-Wiesinger-Widi Groebnerian-
Gaussian Bound 800
Bibliography 803
Index 813
|
| any_adam_object | 1 |
| author | Mora, Teo |
| author_facet | Mora, Teo |
| author_role | aut |
| author_sort | Mora, Teo |
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| bvnumber | BV044031028 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| institution | BVB |
| isbn | 9781107109636 |
| language | English |
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| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press |
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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 4 Buchberger theory and beyond Teo Mora 1. publ. New York Cambridge University Press 2016 XI, 820 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 158 Encyclopedia of mathematics and its applications ... (DE-604)BV016980289 4 Encyclopedia of mathematics and its applications 158 (DE-604)BV000903719 158 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=029438301&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 4 Buchberger theory and beyond Teo Mora |
| title_fullStr | Solving polynomial equation systems 4 Buchberger theory and beyond Teo Mora |
| title_full_unstemmed | Solving polynomial equation systems 4 Buchberger theory and beyond Teo Mora |
| title_short | Solving polynomial equation systems |
| title_sort | solving polynomial equation systems buchberger theory and beyond |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029438301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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