Computational methods in commutative algebra and algebraic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Edition: | 3. print. |
| Series: | Algorithms and computation in mathematics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 408 S. Ill., graph. Darst. |
| ISBN: | 3540213112 |
Staff View
MARC
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| 100 | 1 | |a Vasconcelos, Wolmer V. |d 1937- |e Verfasser |0 (DE-588)115627421 |4 aut | |
| 245 | 1 | 0 | |a Computational methods in commutative algebra and algebraic geometry |c Wolmer V. Vasconcelos ; with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman |
| 250 | |a 3. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XIII, 408 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v 2 | |
| 650 | 4 | |a Algebraische Geometrie - Computeralgebra | |
| 650 | 4 | |a Kommutative Algebra - Computeralgebra | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Commutative algebra |x Data processing | |
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Record in the Search Index
| _version_ | 1804132996151771136 |
|---|---|
| adam_text | Contents
Introduction
..................................................... 1
1 Fundamental
Algorithms
...................................... 7
1.1 Gröbner Basics ............................................ 8
1.2 Division
Algorithms
........................................ 12
1.3
Computation of Syzygies
.................................... 18
1.4
Hubert Functions
........................................... 21
1.5
Computer Algebra Systems
.................................. 26
2
Toolkit
..................................................... 29
2.1
Elimination Techniques
..................................... 30
2.2
Rings of Endomorphisms
.................................... 35
2.3
Noether Normalization
...................................... 37
2.4
Fitting Ideals
.............................................. 41
2.5
Finite and Quasi-Finite Morphisms
........................... 46
2.6
Flat Morphisms
............................................ 49
2.7
Cohen—Macaulay Algebras
.................................. 58
3
Principles of Primary Decomposition
............................ 65
3.1
Associated Primes and Irreducible Decomposition
............... 67
3.2
Equidimensional Decomposition of an Ideal
.................... 77
3.3
Equidimensional Decomposition Without Exts
.................. 83
3.4
Mixed Primary Decomposition
............................... 85
3.5
Elements of Factorizers
..................................... 90
4
Computing in
Artin
Algebras
..................................103
4.1
Structure of
Artin
Algebras
.................................. 104
4.2
Zero-Dimensional Ideals
.................................... 109
4.3
Idempotents versus Primary Decomposition
.................... 113
4.4
Decomposition via Sampling
................................. 115
4.5
Root Finders
.............................................. 120
XII Contents
5 Nullstellensätze..............................................127
5.1
Radicals via Elimination
..................................... 128
5.2
Modules of Differentials and Jacobian Ideals
.................... 130
5.3
Generic Socles
............................................. 134
5.4
Explicit
Nullstellensätze..................................... 136
5.5
Finding Regular Sequences
.................................. 141
5.6
Top Radical and Upper Jacobians
............................. 146
6
Integral Closure
.............................................149
6.1
Integrally Closed Rings
..................................... 151
6.2
Multiplication Rings
........................................ 154
6.3
S^-ification of an
Affine
Ring
................................ 159
6.4
Desingularization in Codimension One
........................ 167
6.5
Discriminants and Multipliers
................................ 173
6.6
Integral Closure of an Ideal
.................................. 176
6.7
Integral Closure of a Morphism
............................... 184
7
Ideal Transforms and Rings of Invariants
........................189
7.1
Divisorial Properties of Ideal Transforms
....................... 190
7.2
Equations of Blowup Algebras
............................... 193
7.3
Subrings
.................................................. 202
7.4
Rings
ofinvariants
......................................... 209
8
Computation of Cohomology
...................................219
8.1
Eyeballing
................................................ 220
8.2
Local Duality
.............................................. 222
8.3
Approximation
............................................. 224
9
Degrees of Complexity of a Graded Module
......................227
9.1
Degrees of Modules
........................................ 230
9.2
Index of Nilpotency
......................................... 244
9.3
Qualitative Aspects of Noether Normalization
................... 249
9.4
Homological Degrees of a Module
............................ 263
9.5
Complexity Bounds in Local Rings
............................ 273
A A Primer on Commutative Algebra
.............................281
A.I NoetherianRings
........................................... 281
A.2 Krull Dimension
........................................... 288
A.3 Graded Algebras
........................................... 295
A.4 Integral Extensions
......................................... 298
A.5 Finitely Generated Algebras over Fields
........................ 305
A.6 The Method of Syzygies
..................................... 309
A.7 Cohen-Macaulay Rings and Modules
.......................... 321
A.8 Local Cohomology
......................................... 329
A.9 Linkage Theory
............................................ 338
Contents XIII
В
Hubert
Functions
............................................343
B.I G-Graded Rings and G-Filtrations
............................. 343
B.2 The Study of
R mgrF(R)
................................... 347
B.3 The Hilbert-Samuel Function
................................ 352
B.4 Hubert Functions, Resolutions and Local Cohomology
........... 356
B.5 Lexsegment Ideals and Macaulay Theorem
..................... 359
B.6 The Theorems of Green and Gotzmann
........................ 362
С
Using Macaulay
2.............................................367
C.I Elementary Uses of Macaulay
2.............................. 368
C.2 Local Cohomology of Graded Modules
........................ 382
C.3 Cohomology of a Coherent Sheaf
............................. 387
References
......................................................393
Index
...........................................................405
|
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| author | Vasconcelos, Wolmer V. 1937- |
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| ctrlnum | (OCoLC)249883900 (DE-599)BVBBV019628744 |
| dewey-full | 512.44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.44 |
| dewey-search | 512.44 |
| dewey-sort | 3512.44 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 3. print. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:41Z |
| institution | BVB |
| isbn | 3540213112 |
| language | English |
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| physical | XIII, 408 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spelling | Vasconcelos, Wolmer V. 1937- Verfasser (DE-588)115627421 aut Computational methods in commutative algebra and algebraic geometry Wolmer V. Vasconcelos ; with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman 3. print. Berlin [u.a.] Springer 2004 XIII, 408 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 2 Algebraische Geometrie - Computeralgebra Kommutative Algebra - Computeralgebra Datenverarbeitung Commutative algebra Data processing Geometry, Algebraic Data processing Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Computeralgebra (DE-588)4010449-7 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Algorithms and computation in mathematics 2 (DE-604)BV011131286 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012957928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vasconcelos, Wolmer V. 1937- Computational methods in commutative algebra and algebraic geometry Algorithms and computation in mathematics Algebraische Geometrie - Computeralgebra Kommutative Algebra - Computeralgebra Datenverarbeitung Commutative algebra Data processing Geometry, Algebraic Data processing Algebraische Geometrie (DE-588)4001161-6 gnd Computeralgebra (DE-588)4010449-7 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4010449-7 (DE-588)4164821-3 |
| title | Computational methods in commutative algebra and algebraic geometry |
| title_auth | Computational methods in commutative algebra and algebraic geometry |
| title_exact_search | Computational methods in commutative algebra and algebraic geometry |
| title_full | Computational methods in commutative algebra and algebraic geometry Wolmer V. Vasconcelos ; with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman |
| title_fullStr | Computational methods in commutative algebra and algebraic geometry Wolmer V. Vasconcelos ; with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman |
| title_full_unstemmed | Computational methods in commutative algebra and algebraic geometry Wolmer V. Vasconcelos ; with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman |
| title_short | Computational methods in commutative algebra and algebraic geometry |
| title_sort | computational methods in commutative algebra and algebraic geometry |
| topic | Algebraische Geometrie - Computeralgebra Kommutative Algebra - Computeralgebra Datenverarbeitung Commutative algebra Data processing Geometry, Algebraic Data processing Algebraische Geometrie (DE-588)4001161-6 gnd Computeralgebra (DE-588)4010449-7 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Algebraische Geometrie - Computeralgebra Kommutative Algebra - Computeralgebra Datenverarbeitung Commutative algebra Data processing Geometry, Algebraic Data processing Algebraische Geometrie Computeralgebra Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012957928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
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