正版现货 理想、簇与算法 第3版 考克斯 著 英文版 世图科技 Ideals Varieties and Algorithms 计算数学 高校本科生研究生教材
9787510058400
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北京东城
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作者David
出版社世界图书出版公司
ISBN9787510058400
出版时间2015-01
装帧平装
货号552717943095
上书时间2024-12-24
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名称：理想、簇与算法 第3版 考克斯 著 英文版 世图科技 Ideals Varieties and Algorithms 计算数学 高校本科生研究生教材
作者：David
品相：全新
出版时间：2015-01
装订：平装
ISBN：9787510058400
出版社：世界图书出版公司
商品描述：
定价：89.00元 《理想、簇与算法(第3版)(英文版)》是Springer出版的《大学生数学教材》丛书之一，1992年首次出版，1997年第2版，这是第三版，将原来的版本作了若干修订，是一本交换代数与计算代数几何的教科书，各章均附有相当数量的练习题。阅读《理想、簇与算法(第3版)(英文版)》需要的预备知识为抽象代数基础。 目录 Preface to the First Edition Preface to the Second Edition Preface to the Third Edition 1. Geometry， Algebra， and Algorithms 1. Polynomials and Affine Space 2. Affine Varieties 3. Parametrizations of Affine Varieties 4. Ideals 5. Polynomials of One Variable 2. Groebner Bases 1. Introduction 2. Orderings on the Monomials in k[x1...，xn] 3. A Division Algorithm in k[x1..xn] 4. Monomial Ideals and Dickson's Lemma 5. The Hilbert Basis Theorem and Groebner Bases 6. Properties of Groebner Bases 7. Buchberger's Algorithm 8. First Applications of G-roebner Bases 9. (Optional) Improvements on Buchberger's Algorithm 3. Elimination Theory 1. The Elimination and Extension Theorems 2. The Geometry of Elimination 3. Implicitization 4. Singular Points and Envelopes 5. Unique Factorization and Resultants 6. Resultants and the Extension Theorem 4. The Algebra-Geometry Dictionary 1. Hilbert's Nullstellensatz 2. Radical Ideals and the Ideal-Variety Correspondence 3. Sums， Products， and Intersections of Ideals 4. Zariski Closure and Quotients of Ideals 5. Irreducible Varieties and Prime Ideals 6. Decomposition of a Variety into Irreducibles 7. (Optional) Primary Decomposition of Ideals 8. Summary 5. Polynomial and Rational Functions on a Variety 1. Polynomial Mappings 2. Quotients of Polynomial Rings 3. Algorithmic Computations in k[x1..xn]/1 4. The Coordinate Ring of an Affine Variety 5. Rational Functions on a Variety 6. (Optional) Proof of the Closure Theorem 6. Robotics and Automatic Geometric Theorem Proving 1. Geometric Description of Robots 2. The Forward Kinematic Problem 3. The Inverse Kinematic Problem and Motion Planning 4. Automatic Geometric Theorem Proving 5. Wu's Method 7. Invariant Theory of Finite Groups 1. Symmetric Polynomials 2. Finite Matrix Groups and Rings of Invariants 3. Generators for the Ring of Invariants 4. Relations Among Generators and the Geometry of Orbits 8. Projective Algebraic Geometry 1. The Projective Plane 2. Projective Space and Projective Varieties 3. The Projective Algebra-Geometry Dictionary 4. The Projective Closure of an Affine Variety 5. Projective Elimination Theory 6. The Geometry of Quadric Hypersurfaces 7. Bezout's Theorem 9. The Dimension of a Variety 1. The Variety of a Monomial Ideal 2. The Complement of a Monomial Ideal 3. The Hilbert Function and the Dimension of a Variety 4. Elementary Properties of Dimension 5. Dimension and Algebraic Independence 6. Dimension and Nonsingularity 7. The Tangent Cone Appendix A. Some Concepts from Algebra 1. Fields and Rings 2. Groups 3. Determinants Appendix B. Pseudocode 1. Inputs， Outputs， Variables， and Constants 2. Assignment Statements 3. Looping Structures 4. Branching Structures Appendix C. Computer Algebra Systems 1. AXIOM 2. Maple 3. Mathematica 4. REDUCE 5. Other Systems Appendix D. Independent Projects 1. General Comments 2. Suggested Projects References Index '
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