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  • 音像算代数论教程(英文版)(法)科恩
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    • 作者: (法)科恩著 | (法)科恩编 | (法)科恩译 | (法)科恩绘
    • 出版社: 世界图书出版公司
    • 出版时间:2015-07-01
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    • 作者: (法)科恩著| (法)科恩编| (法)科恩译| (法)科恩绘
    • 出版社:世界图书出版公司
    • 出版时间:2015-07-01
    • 版次:1
    • 印次:1
    • 印刷时间:2015-07-01
    • 开本:24开
    • ISBN:9787510097973
    • 版权提供:世界图书出版公司
    • 作者:(法)科恩
    • 著:(法)科恩
    • 装帧:暂无
    • 印次:1
    • 定价:95.00
    • ISBN:9787510097973
    • 出版社:世界图书出版公司
    • 开本:24开
    • 印刷时间:2015-07-01
    • 语种:暂无
    • 出版时间:2015-07-01
    • 页数:暂无
    • 外部编号:3382014
    • 版次:1
    • 成品尺寸:暂无

    Chapter 1 Fundamental Number-Theoretic Algorithms
    1.1 Introduction
    1.1.1 Algorithms
    1.1.2 Multi-precision
    1.1.3 Base Fields and Rings
    1.1.4 Notations
    1.2 The Powering Algorithms
    1.3 Euclid's Algorithms
    1.3.1 Euclid's and Lehmer's Algorithms
    1.3.2 Euclid's Extended Algorithms
    1.3.3 The Chinese Remainder Theorem
    1.3.4 Continued Fraction Expansions of Real Numbers
    1.4 The Legendre Symbol
    1.4.1 The Groups (Z/nZ)*
    1.4.2 The Legendre-Jacobi-Kronecker Symbol
    1.5 Computing Square Roots Modulo p
    1.5.1 The Algorithm of ToneUi and Shanks
    1.5.2 The Algorithm of Cornacchia
    1.6 Solving Polynomial Equations Modulo p
    1.7 Power Detection
    1.7.1 Integer Square Roots
    1.7.2 Square Detection
    1.7.3 Prime Power Detection
    1.8 Exercises for Chapter 1
    Chapter 2 Algorithms for Linear Algebra and Lattices
    2.1 Introduction
    2.2 Linear Algebra Algorithms on Square Matrices
    2.2.1 Generalities on Linear Algebra Algorithms
    2.2.2 Gaussian Elimination and Solving Linear Systems
    2.. Computing Determinants
    2.2.4 Computing the Characteristic Polynomial
    . Linear Algebra on General Matrices
    ..1 Kernel and Image
    ..2 Inverse Image and Supplement
    .. Oraios on Subspaces
    ..4 Remarks on Modules
    2.4 Z-Modules and the Hermite and Smith Normal Forms
    2.4.1 Introduction to Z-Modules
    2.4.2 The Hermite Normal Form
    2.4.3 Applications of the Hermite Normal Form
    2.4.4 The Smith Normal Form and Applications
    2.5 Generalities on Lattices
    2.5.1 Lattices and dratic Forms
    2.5.2 The Gram-Schmidt Orthogonalization Procedure
    2. Lattice Reduction Algorithms
    2.6.1 The LLL Algorithm
    2.6.2 The LLL Algorithm with Deep Insertions
    2.6.3 The Integral LLL Algorithm
    2.6.4 LLL Algorithms for Linearly Dependent Vectors
    2.7 Applications of the LLL Algorithm
    2.7.1 Computing the Integer Kernel and Image of a Matrix
    2.7.2 Linear and Algebraic Dependence Using LLL
    2.7.3 Finding Small Vectors in Lattices
    2.8 Exercises for Chapter 2
    Chapter 3 Algorithms on Polynomials
    3.1 Basic Algorithms
    3.1.1 Representation of Polynomials
    3.1.2 Multiplication of Polynomials
    3.1.3 Division of Polynomials
    3.2 Euclid's Algorithms for Polynomials
    3.2.1 Polynomials over a Field
    3.2.2 Unique Factorization Domains (UFD's)
    3.. Polynomials over Unique Factorization Domains
    ……
    Chapter 4 Algorithms for Algebraic Number Theory Ⅰ
    Chapter 5 Algorithms for dratic Fields
    Chapter 6 Algorithms—for Algebraic Number Theory Ⅱ
    Chapter 7 Introduction to Elliptic Curves
    Chapter 8 Factoring in the Dark Ages
    Chapter 9 Modern Primality Tests
    Chapter 10 Modern Factoring Methods
    Appendix A Packages for Number Theory
    Appendix B Some Useful Tables
    Bibliography
    Index
    Errata et Addenda

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