作者：(美)盖里·L.马伦(Gary L. M
页数：29,1041页
出版社：哈尔滨工业大学出版社
出版日期：2022
ISBN：9787560398167
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的数学工具书，中文书名可译为《有限域手册》。
本书旨在成为领域内领先的参考文献，该书着重介绍了有限域的理论与应用。这本权威手册中汇集了80余位国际贡献者编写的最新研究报告。本书由两位知名的研究者主编，使用了标准的形式和架构，每一章都是自洽的并由同行评审。
目录
Part I: Introduction
1 History of finite fields
1.1 Finite fields in the 18-th and 19-th centuries Roderick Gow
1.1.1 Introduction
1.1.2 Early anticipations of finite fields
1.1.3 Gauss’s Disquisitiones Arithmeticae
1.1.4 Gauss’s Disquisitiones Generales de Congruentiis
1.1.5 Galois’s Sur la theorie des nombres
1.1.6 Serret’s Cours d’algebre superieure
1.1.7 Contributions of SchSnemann and Dedekind
1.1.8 Moore’s characterization of abstract finite fields
1.1.9 Later developments
2 Introduction to finite fields
2.1 Basic properties of finite fields Gary L. Mullen and Daniel Panario
2.1.1 Basic definitions
2.1.2 Fundamental properties of finite fields
2.1.3 Extension fields
2.1.4 Trace and norm functions
2.1.5 Bases
2.1.6 Linearized polynomials
2.1.7 Miscellaneous results
2.1.7.1 The finite field polynomial Φ function
2.1.7.2 Cyclotomic polynomials
2.1.7.3 Lagrange interpolation
2.1.7.4 Discriminants
2.1.7.5 Jacobi logarithms
2.1.7.6 Field-like structures
2.1.7.7 Galois rings
2.1.8 Finite field related books
2.1.8.1 Textbooks
2.1.8.2 Finite field theory
2.1.8.3 Applications
2.1.8.4 Algorithms
2.1.8.5 Conference proceedings
2.2 Tables David Thomson
2.2.1 Low-weight irreducible and primitive polynomials
2.2.2 Low-complexity normal bases
2.2.2.1 Exhaustive search for low complexity normal bases
2.2.2.2 Minimum type of a Gauss period admitting a normal basis of F2n over F2
2.2.2.3 Minimum-known complexity of a normal basis of F2n over F2, n ≥ 40
2.2.3 Resources and standards
Part II: Theoretical Properties
3 Irreducible polynomials
3.1 Counting irreducible polynomials Joseph L. Yucas
3.1.1 Prescribed trace or norm
3.1.2 Prescribed coefficients over the binary field
3.1.3 Self-reciprocal polynomials
3.1.4 Compositions of powers
3.1.5 Translation invariant polynomials
3.1.6 Normal replicators
1 History of finite fields
1.1 Finite fields in the 18-th and 19-th centuries Roderick Gow
1.1.1 Introduction
1.1.2 Early anticipations of finite fields
1.1.3 Gauss’s Disquisitiones Arithmeticae
1.1.4 Gauss’s Disquisitiones Generales de Congruentiis
1.1.5 Galois’s Sur la theorie des nombres
1.1.6 Serret’s Cours d’algebre superieure
1.1.7 Contributions of SchSnemann and Dedekind
1.1.8 Moore’s characterization of abstract finite fields
1.1.9 Later developments
2 Introduction to finite fields
2.1 Basic properties of finite fields Gary L. Mullen and Daniel Panario
2.1.1 Basic definitions
2.1.2 Fundamental properties of finite fields
2.1.3 Extension fields
2.1.4 Trace and norm functions
2.1.5 Bases
2.1.6 Linearized polynomials
2.1.7 Miscellaneous results
2.1.7.1 The finite field polynomial Φ function
2.1.7.2 Cyclotomic polynomials
2.1.7.3 Lagrange interpolation
2.1.7.4 Discriminants
2.1.7.5 Jacobi logarithms
2.1.7.6 Field-like structures
2.1.7.7 Galois rings
2.1.8 Finite field related books
2.1.8.1 Textbooks
2.1.8.2 Finite field theory
2.1.8.3 Applications
2.1.8.4 Algorithms
2.1.8.5 Conference proceedings
2.2 Tables David Thomson
2.2.1 Low-weight irreducible and primitive polynomials
2.2.2 Low-complexity normal bases
2.2.2.1 Exhaustive search for low complexity normal bases
2.2.2.2 Minimum type of a Gauss period admitting a normal basis of F2n over F2
2.2.2.3 Minimum-known complexity of a normal basis of F2n over F2, n ≥ 40
2.2.3 Resources and standards
Part II: Theoretical Properties
3 Irreducible polynomials
3.1 Counting irreducible polynomials Joseph L. Yucas
3.1.1 Prescribed trace or norm
3.1.2 Prescribed coefficients over the binary field
3.1.3 Self-reciprocal polynomials
3.1.4 Compositions of powers
3.1.5 Translation invariant polynomials
3.1.6 Normal replicators
