Computational commutative algebra: 2
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | X, 586 S. graph. Darst. |
| ISBN: | 3540255273 9783540255277 |
Internformat
MARC
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| 245 | 1 | 0 | |a Computational commutative algebra |n 2 |c Martin Kreuzer ; Lorenzo Robbiano |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a X, 586 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Algèbre commutative |2 rasuqam | |
| 650 | 7 | |a Anéis e álgebras comutativos |2 larpcal | |
| 650 | 7 | |a Base de Groebner |2 rasuqam | |
| 650 | 7 | |a Calcul formel |2 rasuqam | |
| 650 | 7 | |a Fonction caractéristique |2 rasuqam | |
| 650 | 7 | |a Polynôme |2 rasuqam | |
| 650 | 7 | |a Traitement des données |2 rasuqam | |
| 650 | 7 | |a Álgebra computacional |2 larpcal | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Commutative algebra |x Data processing | |
| 650 | 4 | |a Gröbner bases | |
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Datensatz im Suchindex
| _version_ | 1804133548959989760 |
|---|---|
| adam_text | Kreuzer • Robbiano
Computational Commutative
Computational Commutative Algebra
uation of Computational Commutative Algebra
twists, starting with the differently coloured cover graphics.
The first volume had
some amusing quotes. Since bigger is better, this book contains
3
as big as a whole chapter), and
section). The number of jokes and quotes has increased exponen¬
tially due to the little-known fact that a good mathematical joke
is better than a dozen mediocre papers.
The main part of this book is a breathtaking
through the computational domains of graded rings and mod¬
ules and their Hubert functions. Besides
encounter
SuperG bases. The tutorials traverse areas ranging from algebra¬
ic geometry and combinatorics to photogrammetry, magic
squares, coding theory, statistics, and automatic theorem prov¬
ing. Whereas in the first volume gardening and chess playing
were not treated, in this volume they are.
This is a book for learning, teaching, reading, and most of
all, enjoying the topic at hand. The theories it describes can be
applied to anything from children s toys to oil production. If you
buy it, probably one spot on your desk will be lost forever!
Contents
Foreword
Introduction
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
4.
4.1
4.1.A Gradings by Matrices
4.1.B Graded Modules
4.1.C Gradings of Positive Type
Tutorial
Tutorial
4.2
4.2.A Positive Gradings
4.2.B Macaulay Bases
Tutorial
Tutorial
4.3
4.3.A Homogenization of Polynomials and Ideals
4.3.B Macaulay Bases and Homogenization
Tutorial
Tutorial
Tutorial
Tutorial
4.4
Tutorial
VIII
Tutorial 54- Regulär
Tutorial 55.
4.5
4.5.A The Homogeneous Buchberger Algorithm
4.5.B Truncated
Tutorial
Tutorial
4.6
Tutorial
Tutorial
4.7
4.7.A Existence and Uniqueness of Minimal Presentations
4.7.B Idealization of Graded Modules and Presentations
4.7.C Computation of Minimal Homogeneous Presentations
Tutorial
Tutorial
4.8
4.8.A Existence and Uniqueness of Minimal Free Resolutions
4.8.B Computation of Minimal Graded Eree Resolutions
Tutorial
Tutorial
5.
5.1
5.1.A Integer Functions of Polynomial Type
5.1.B Hubert Functions in the Standard Graded Case
Tutorial
5.2
5.2.Á
5.2.B Hubert Series in the Standard Graded Case
Tutorial
Tutorial
Tutorial
5.3
Tutorial
Tutorial
5.4
5.4.A Dimension and Multiplicity of Standard Algebras
5.4.B Hilbert Polynomials in the Standard Graded Case
Tutorial
Tutorial
Tutorial
5.5
5.5.A Binomial Representations
5.5.B Lex-Segment Spaces and Ideals
Contents
5.5.C
Tutorial
Tutorial
Tutorial
5.6 Affine
5.6.Á
5.6.B Primary Decomposition in Noetherian Rings
5.6.C The Krull Dimension of an
Tutorial
Tutorial
5.7
5.7.À
5.7.B Transcendence Degrees
Tutorial
Tutorial
5.8
5.8.A Rings of Multivariate Laurent Series
5.8.B Hilbert Functions in the General Case
5.8.C Change of Gradings
Tutorial
Tutorial
Tutorial
Tutorial
6.
6.1
6.1.A Toric Ideals
6.1.B Hilbert Bases
Tutorial
Tutorial
Tutorial
6.2
Tutorial
6.3
6.3.A
6.3.B Projective Point Sets
6.3.C Hilbert Functions of Points
Tutorial
Tutorial
Tutorial
6.4
6.4.A Existence and Uniqueness of Border Bases
6.4.B Characterizations of Border Bases
Tutorial
Tutorial
X
6.5 Filtrations.............................................453
6.5.1 General Filtrations...............................454
6.5.B Adic Filtrations
Tutorial 93.
Tutorial 94. Hubert
Tutorial
6.6
6.6.A Definition and Basic Properties of SAGBI Bases
6.6.B Characterization of SAGBI Bases
6.6.C Computation of SAGBI Bases
Tutorial
Tutorial
Tutorial
6.7
6.7.A The Tribulations of Automation
6.7.B
6.7.C Optimal Hypothesis Ideals and Minimal Conditions
Tutorial
A. The ABC of
B. One Graphical Interface for Everybody
C. More on CbCaA. Programming
D. Suggestions for Further Reading
E. Hints for Selected Exercises
Notation
Bibliography
Index
|
| any_adam_object | 1 |
| author | Kreuzer, Martin Robbiano, Lorenzo 1944- |
| author_GND | (DE-588)122293304 |
| author_facet | Kreuzer, Martin Robbiano, Lorenzo 1944- |
| author_role | aut aut |
| author_sort | Kreuzer, Martin |
| author_variant | m k mk l r lr |
| building | Verbundindex |
| bvnumber | BV019998962 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251.3 |
| callnumber-search | QA251.3 |
| callnumber-sort | QA 3251.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)61658966 (DE-599)BVBBV019998962 |
| dewey-full | 512.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.24 |
| dewey-search | 512.24 |
| dewey-sort | 3512.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019998962 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:28Z |
| institution | BVB |
| isbn | 3540255273 9783540255277 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013320727 |
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| physical | X, 586 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Springer |
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| spelling | Kreuzer, Martin Verfasser aut Computational commutative algebra 2 Martin Kreuzer ; Lorenzo Robbiano Berlin [u.a.] Springer 2005 X, 586 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre commutative rasuqam Anéis e álgebras comutativos larpcal Base de Groebner rasuqam Calcul formel rasuqam Fonction caractéristique rasuqam Polynôme rasuqam Traitement des données rasuqam Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd rswk-swf Computeralgebra (DE-588)4010449-7 s DE-604 Robbiano, Lorenzo 1944- Verfasser (DE-588)122293304 aut (DE-604)BV013382620 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013320727&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013320727&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kreuzer, Martin Robbiano, Lorenzo 1944- Computational commutative algebra Algèbre commutative rasuqam Anéis e álgebras comutativos larpcal Base de Groebner rasuqam Calcul formel rasuqam Fonction caractéristique rasuqam Polynôme rasuqam Traitement des données rasuqam Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4010449-7 |
| title | Computational commutative algebra |
| title_auth | Computational commutative algebra |
| title_exact_search | Computational commutative algebra |
| title_full | Computational commutative algebra 2 Martin Kreuzer ; Lorenzo Robbiano |
| title_fullStr | Computational commutative algebra 2 Martin Kreuzer ; Lorenzo Robbiano |
| title_full_unstemmed | Computational commutative algebra 2 Martin Kreuzer ; Lorenzo Robbiano |
| title_short | Computational commutative algebra |
| title_sort | computational commutative algebra |
| topic | Algèbre commutative rasuqam Anéis e álgebras comutativos larpcal Base de Groebner rasuqam Calcul formel rasuqam Fonction caractéristique rasuqam Polynôme rasuqam Traitement des données rasuqam Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Algèbre commutative Anéis e álgebras comutativos Base de Groebner Calcul formel Fonction caractéristique Polynôme Traitement des données Álgebra computacional Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013320727&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013320727&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013382620 |
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