Some tapas of computer algebra.计算机代数一些Tapas
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： Arjeh M. Cohen著
出 版 社： 广东教育出版社
出版时间： 1998-12-1字数：版次：页数： 352印刷时间： 1998/12/01开本： 16开印次：纸张： 胶版纸I S B N ： 9783540634805包装： 精装内容简介
This book arose from a series of courses on computer algebra which were given at Eindhoven Technical University. Its chapters present a variety of topics in computer algebra at an accessible (upper undergraduate/graduate) level with a view towards recent developments. For those wanting to acquaint themselves somewhat further with the material, the book also contains seven 'projects', which could serve as practical sessions related to one or more chapters.
The contributions focus on topics like Gröbner bases, real algebraic geometry, Lie algebras, factorisation of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry.
This book is a must-read for everybody interested in computer algebra.
目录
Chapter 1. GrSbner Bases, an Introduction
Arjeh M. Cohen
1. Introduction
2. Monomials
3. The Buchberger Algorithm
4. Standard Monomials
5. Solving Polynomial Equations
6. Effectiveness of Polynomial Rings
Chapter 2. Symbolic Recipes for Polynomial System Solving
Laureano Gonzalez-Vega, Fabrice Rouillier,and Marie-Frangoise Roy
1. Introduction
2. General Systems of Equations
2.1 Algebraic Preliminaries
2.2 First Recipes for Polynomial System Solving
3. Linear Algebra, Traces, and Polynomial Systems
3.1 Eigenvalues and Polynomial Systems
3.2 Counting Solutions and Removing Multiplicities
3.3 Rational Univariate Representation
4. As Many Equations as Variables
4.1 Generalities on Complete Intersection Polynomial Systems
4.2 Recipes for Polynomial System Solving When the Number of Equations Equals the Number of Unknowns
5. GrSbner Bases and Numerical Approximations
Chapter 3. Lattice Reduction
Frits Beukers
1. Introduction
2. Lattices
3. Lattice Reduction in Dimension 2
4. Lattice Reduction in Any Dimension
5. Implementations of the LLL-Algorithm
6. Small Linear Forms
Chapter 4. Factorisation of Polynomials
Frits Beukers
1. Introduction
2. Berlekamp's Algorithm
3. Additional Algorithms
4. Polynomials with Integer Coefficients
5. Factorisation of Polynomials with Integer Coefficients, I
6. Factorisation of Polynomials with Integer Coefficients, II
7. Factorisation in K[X], K Algebraic Number Field
Chapter 5. Computations in Associative and Lie Algebras Ggbor Ivanyos and Lajos Rdnyai
1. Introduction
2. Basic Definitions and Structure Theorems
3. Computing the Radical
4. Applications to Lie Algebras
5. Finding the Simple Components of Semisimple Algebras
6. Zero Divisors in Finite Algebras
Chapter 6. Symbolic Recipes for Real Solutions
Laureano Gonzalez-Vega, Fabrice Rouillier, Marie-Frangoise Roy,and Guadalupe Trujillo
1. Introduction
2. Real Root Counting: The Univariate Case.
2.1 Computing the Number of Real Roots
2.2 Sylvester Sequence
2.3 Sylvester-Habicht Sequence
2.4 Some Recipes for Counting Real Roots
3. Real Root Counting: The Multivariate Case
4. Tile Sign Determination Scheme
5. Real Algebraic Numbers and Thorn Codes
6. Quantifier Elimination
7. Appendix: Properties of the Polynomials in the Sylvester-Habicht Sequence
7.1 Definition and the Structure Theorem
7.2 Proof of the Structure Theorem
7.3 Sylvester-Habicht Sequences and Cauchy Index
Chapter 7. GrSbner Bases and Integer Programming Giinter M. Ziegler
1. Introduction
2. What is Integer Programming?
3. A Buchberger Algorithm for Integer Programming
……
Chapter 8. Working with Finite Groups
Chapter 9. Symbolic Analysis of Differential Equations
Chapter 10. Grobner Bases for Codes
Chapter 11. Grobner Bases for Decoding
Project 1. Automatic Geometry Theorem Proving
Project 2. The Birkhoff INterpolation Problem
Project 3. The Inverse Kinematics Problem in Robotics
Project 4. Quaternion Algebras
Project 5. Explorations with the Icosahedral Group
Project 6. The Small Mathieu Groups
Project 7. The Golay Codes
Index
