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

7 | |

8 | |

12 | |

18 | |

21 | |

26 | |

Toolkit | 29 |

21 Elimination Techniques | 30 |

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 |

393 | |

405 | |

### Common terms and phrases

### References from web pages

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