《国外数学厚金置名著系列49:计算不变量理论》是由科学所门及庆议它知学出版社出版编著的实体书。主要讲述怎样计算不变量理论。
出版社: 科学出版社; 第1版 (2009年1月1日)
外文书名: Computational Invariant Theory
丛书名: 国外数学名著系列(续一)(影印版)49
精装: 268页
正文语种: 英语
开本: 16
ISBN: 978703023492界责皮拉6
条形码: 9787030234926
尺寸: 23.8 x 17 x 2 cm
重量: 58做他入1 g
作者:(美国)德克森 (harm derksen)
《国外数学名著系列(续1)(影印版)49:计算不变量理论》is about the computational aspects of invariant 族充theory.Of central interest is the question how the invariant ring of a given group action can be calculated. Algor来自ithms for this p突消比什厂举剂件林异那urpose form the main pillars around which the book is built院划氧座爱发. There are two introductory 备析阿甚精果密宣chapters, one on GrObner basis methods an则普观态杨侵计d one on the basic concepts 360百科of invari五往或批论精限ant theory, which prepare the ground for the a委持约农附奏组职型lgorithms. Th别带统事更原en algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural propertie象样保s of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph t便否环heory, coding theor越陆古都矛十鸡根状后y, dynamical systems, and computer vision.
The book is intended for postgr李际村同aduate students as well as researchers in geometry, computer algebra, and, of cours维程维九耐连印目城e, invariant theory. The text is enriched with numerous explicit examples which illustrate the t少解后初衣愿heoiw and should be of more than passing interest.
Introdu没ction
1 Con规协海和structive Ideal T就括heory
1.1 Ideals and GrSbner Bases
1.可双2 Elimination Ideals
1.3 Syzygy Modules
1.4 Hilbert Series
1.5 The Radical Ideal
1.6 Normalization
2 Invariant Theory
2.1 Invariant Rings
2.2 Reductive Groups
2.3 Categorical Quotients
2.4 Homogeneous Systems of Parameters
2.5 The Cohen-Macaulay Property of Invariant Rings
2.6 Hilbert Series of Invariant Rings
3 Invariant Theory of Finite Groups
3.1 Homogeneous Components
3.2 Molien's Formula..
3.3 Primary Invariants
3.4 Cohen-Macaulayness
3.5 Secondary Invariants
3.6 Minimal Algebra Generators and Syzygies
3.7 Properties of Invariant Rings
3.8 Noether's Degree Bound
3.9 Degree Bounds in the Modular Case
3.10 Permutation Groups
3.11 Ad Hoc Methods
4 Invariant Theory of Reductive Groups
4.1 Computing Invariants of Linearly Reductive Groups
4.2 Improvements and Generalizations
4.3 Invariants of Tori
4.4 Invariants of SLn and GLn
4.5 The Reynolds Operator
4.6 Computing Hilbert Series
4.7 Degree Bounds for Invariants
4.8 Properties of Invariant Rings
5 Applications of Invariant Theory
5.1 Cohomology of Finite Groups
5.2 Galois Group Computation
5.3 Noether's Problem and Generic Polynomials
5.4 Systems of Algebraic Equations with Symmetries
5.5 Graph Theory
5.6 Combinatorics
5.7 Coding Theory
5.8 Equivariant Dynamical Systems
5.9 Material Science
5.10 Computer Vision
A Linear Algebraic Groups
A.1 Linear Algebraic Groups
A.2 The Lie Algebra of a Linear Algebraic Group
A.3 Reductive and Semi-simple Groups
A.4 Roots
A.5 Representation Theory
References
Notation
Index
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