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理想、簇与算法 第3版 英文PDF|Epub|txt|kindle电子书版本网盘下载

理想、簇与算法 第3版 英文
  • （美）考克斯（Cox.D.）著影本 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7510058400
  • 出版时间：2013
  • 标注页数：553页
  • 文件大小：87MB
  • 文件页数：569页
  • 主题词：

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图书目录

1．Geometry,Algebra,and Algorithms1

1．Polynomials and Affine Space1

2．Affine Varieties5

3．Parametrizations of Affine Varieties14

4．Ideals29

5．Polynomials of One Variable38

2．Groebner Bases49

1．Introduction49

2．Orderings on the Monomials in k[x1,...,xn]54

3．A Division Algorithm in k[x1...,xn]61

4．Monomial Ideals and Dickson's Lemma69

5．The Hilbert Basis Theorem and Groebner Bases75

6．Properties of Groebner Bases82

7．Buchberger's Algorithm88

8．First Applications of Groebner Bases95

9．(Optional)Improvements on Buchberger's Algorithm102

3．Elimination Theory115

1．The Elimination and Extension Theorems115

2．The Geometry of Elimination123

3．Implicifization128

4．Singular Points and Envelopes137

5．Unique Factorization and Resultants150

6．Resultants and the Extension Theorem162

4．The Algebra-Geometry Dictionary169

1．Hilbert's Nullstellensatz169

2．Radical Ideals and the Ideal-Variety Correspondence175

3．Sums,Products,and Intersections of Ideals183

4．Zariski Closure and Quotients of Ideals193

5．Irreducible Varieties and Prime Ideals198

6．Decomposition of a Variety into Irreducibles204

7．(Optional)Primary Decomposition of Ideals210

8．Summary214

5．Polynomial and Rational Functions on a Variety215

1．Polynomial Mappings215

2．Quotients of Polynomial Rings221

3．Algorithmic Computations in k[x1...,xn]/I230

4．The Coordinate Ring of an Affine Variety239

5．Rational Functions on a Variety248

6．(Optional)Proof of the Closure Theorem258

6．Robotics and Automatic Geometric Theorem Proving265

1．Geometric Description of Robots265

2．The Forward Kinematic Problem271

3．The Inverse Kinematic Problem and Motion Planning279

4．Automatic Geometric Theorem Proving291

5．Wu's Method307

7．Invariant Theory of Finite Groups317

1．Symmetric Polynomials317

2．Finite Matrix Groups and Rings of Invariants327

3．Generators for the Ring of Invariants336

4．Relations Among Generators and the Geometry of Orbits345

8．Projective Algebraic Geometry357

1．The Projective Plane357

2．Projective Space and Projective Varieties368

3．The Projective Algebra-Geometry Dictionary379

4．The Projective Closure of an Affine Variety386

5．Projective Elimination Theory393

6．The Geometry of Quadric Hypersurfaces408

7．Bezout's Theorem422

9．The Dimension of a Variety439

1．The Variety of a Monomial Ideal439

2．The Complement of a Monomial Ideal443

3．The Hilbert Function and the Dimension of a Variety456

4．Elementary Properties of Dimension468

5．Dimension and Algebraic Independence477

6．Dimension and Nonsingularity484

7．The Tangent Cone495

Appendix A．Some Concepts from Algebra509

1．Fields and Rings509

2．Groups510

3．Determinants511

Appendix B．Pseudocode513

1．Inputs,Outputs,Variables,and Constants513

2．Assignment Statements514

3．Looping Structures514

4．Branching Structures515

Appendix C．Computer Algebra Systems517

1．AXIOM517

2．Maple520

3．Mathematica522

4．REDUCE524

5．Other Systems528

Appendix D．Independent Projects530

1．General Comments530

2．Suggested Projects530

References535

Index541

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