Computational Methods In Commutative Algebra And Algebraic Geometry (Google eBook)

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Springer, May 18, 2004 - Computers - 408 pages
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This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
  

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Contents

66 Integral Closure of an Ideal
176
67 Integral Closure of a Morphism
184
Ideal Transforms and Rings of Invariants
189
71 Divisorial Properties of Ideal Transforms
190
72 Equations of Blowup Algebras
193
73 Subrings
202
74 Rings of Invariants
209
Computation of Cohomology
219

22 Rings of Endomorphisms
35
23 Noether Normalization
37
24 Fitting Ideals
41
25 Finite and QuasiFinite Morphisms
46
26 Flat Morphisms
49
27 CohenMacaulay Algebras
58
Principles of Primary Decomposition
65
31 Associated Primes and Irreducible Decomposition
67
32 Equidimensional Decomposition of an Ideal
77
33 Equidimensional Decomposition Without Exts
83
34 Mixed Primary Decomposition
85
35 Elements of Factorizers
90
Computing in Artin Algebras
103
41 Structure of Artin Algebras
104
42 ZeroDimensional Ideals
109
43 Idempotents versus Primary Decomposition
113
44 Decomposition via Sampling
115
45 Root Finders
120
Nullstellensatze
127
51 Radicals via Elimination
128
52 Modules of Differentials and Jacobian Ideals
130
53 Generic Socles
134
54 Explicit Nullstellensatze
136
55 Finding Regular Sequences
141
56 Top Radical and Upper Jacobians
146
Integral Closure
149
61 Integrally Closed Rings
151
62 Multiplication Rings
154
63 S2ification of an Affine Ring
159
64 Desingularization in Codimension One
167
65 Discriminants and Multipliers
173
81 Eyeballing
220
82 Local Duality
222
83 Approximation
224
Degrees of Complexity of a Graded Module
227
91 Degrees of Modules
230
92 Index of Nilpotency
244
93 Qualitative Aspects of Noether Normalization
249
94 Homological Degrees of a Module
263
95 Complexity Bounds in Local Rings
273
Primer on Commutative Algebra
281
A2 Krull Dimension
288
A3 Graded Algebras
295
A4 Integral Extensions
298
A5 Finitely Generated Algebras over Fields
305
A6 The Method of Syzygies
309
A7 CohenMacaulay Rings and Modules
321
A8 Local Cohomology
329
A9 Linkage Theory
338
Hilbert Functions
343
B2 The Study of R via grFR
347
B3 The HilbertSamuel Function
352
B4 Hilbert Functions Resolutions and Local Cohomology
356
B5 Lexsegment Ideals and Macaulay Theorem
359
B6 The Theorems of Green and Gotzmann
362
Using Macaulay 2
367
C1 Elementary Uses of Macaulay 2
368
C2 Local Cohomology of Graded Modules
382
C3 Cohomology of a Coherent Sheaf Mathematical Background
387
References
393
Index
405
Copyright

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JSTOR: Computational Methods in Commutative Algebra and Algebraic ...
7[13-01, 13P99, 14-01, 14Q99]-Computational methods in commutative algebra and algebraic geometry, by Wolmer V. Vasconcelos, Algorithms and Computation in ...
links.jstor.org/ sici?sici=0025-5718(200007)69%3A231%3C1312%3ACMICAA%3E2.0.CO%3B2-K

Computational Methods in Commutative Algebra and Algebraic Geometry
Wolmer V. Vasconcelos. Corrections and Complements to. Computational Methods in. Commutative Algebra and. Algebraic Geometry ...
www.math.rutgers.edu/ ~vasconce/ compur.pdf

Vasconcelos, wv, Computational Methods in Commutative Algebra and ...
Vasconcelos, wv, Computational Methods in Commutative Algebra and Algebraic Geometry. Band 2 der Reihe Algorithms and Computations in Mathematics, ...
www.fachgruppe-computeralgebra.de/ CAR/ CAR22/ node16.html

Michael Stillman: Computer Algebra systems Michael Stillman: Books ...
Michael Stillman: Computer Algebra systems. [1] Macaulay, A system for computing in algebraic geometry and commutative algebra. Available via ...
www.math.cornell.edu/ ~mike/ pubs2007.pdf

Computational methods in commutative algebra and algebraic geometry
Computational methods in commutative algebra and algebraic geometry. Purchase this Book · Purchase this Book. Source, Springer Algorithms And Computation In ...
portal.acm.org/ citation.cfm?id=269988

【楽天市場】Computational Methods in Commutative Algebra and ...
Computational Methods in Commutative Algebra and Algebraic Geometry(Computational ... Computational Methods in Commutative Algebra and Algebraic Geometry ...
item.rakuten.co.jp/ book/ 4945740/

GSCI Digest Friday, June 04, 2004 Volume 2004: Issue 06 For ...
Computational Methods in Commutative Algebra and Algebraic Geometry ----------------------------------------------------------------------
www.scicomp.uni-erlangen.de/ archives/ letter/ v04n06/ v04n06

NSTL国际科学引文数据库-检索细览
W. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Algorithms Comput. Math. vol . 2, Springer-Verlag, Berlin (1998). M ...
citation.nstl.gov.cn/ detail.jsp?internal_id=921983

Biblioteca ISI-CNR
Titolo, Computational Methods in Commutative Algebra and Algebraic Geometry. form_resp. Edizione. Luogo di pubblicazione, Berlin. Editore, Springer ...
biblio.cs.icar.cnr.it/ biblio/ mostraLibro.asp?ID=555

2007-02-02 - Franの日記
休みの間にこれでも読んでみようかな。 Computational Methods in Commutative Algebra and Algebraic Geometry (Algorithms and Computation in Mathematics, V ...
d.hatena.ne.jp/ Fran/ 20070202

About the author (2004)

Author's homepage: http: //www.math.rutgers.edu/~vasconce/

Vasconcelos is a well-known top expert in commutative algebra. Author of Algorithms and Computation in Mathematics 2. ISBN: 3-540-21311-2.

Via the existence of the ACM series he was won as a Springer author in 1995, being a CUP author before.

This new book is a result of the good collaboration with him on ACM 2.

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