计算不变量理论

(荷) 德克森 (Derksen,H.) 等, 著

出版社：科学出版社

年代：2008

定价：66.0

书籍简介:

本书内容全面而且前沿，包含了最新的研究成果，图文并茂，例题丰富。

书籍目录:

Introduction

1ConstructiveIdealTheory

1.1IdealsandGrSbnerBases

1.2EliminationIdeals

1.3SyzygyModules

1.4HilbertSeries

1.5TheRadicalIdeal

1.6Normalization

2InvariantTheory

2.1InvariantRings

2.2ReductiveGroups

2.3CategoricalQuotients

2.4HomogeneousSystemsofParameters

2.5TheCohen-MacaulayPropertyofInvariantRings

2.6HilbertSeriesofInvariantRings

3InvariantTheoryofFiniteGroups

3.1HomogeneousComponents

3.2MoliensFormula..

3.3PrimaryInvariants

3.4Cohen-Macaulayness

3.5SecondaryInvariants

3.6MinimalAlgebraGeneratorsandSyzygies

3.7PropertiesofInvariantRings

3.8NoethersDegreeBound

3.9DegreeBoundsintheModularCase

3.10PermutationGroups

3.11AdHocMethods

4InvariantTheoryofReductiveGroups

4.1ComputingInvariantsofLinearlyReductiveGroups

4.2ImprovementsandGeneralizations

4.3InvariantsofTori

4.4InvariantsofSLnandGLn

4.5TheReynoldsOperator

4.6ComputingHilbertSeries

4.7DegreeBoundsforInvariants

4.8PropertiesofInvariantRings

5ApplicationsofInvariantTheory

5.1CohomologyofFiniteGroups

5.2GaloisGroupComputation

5.3NoethersProblemandGenericPolynomials

5.4SystemsofAlgebraicEquationswithSymmetries

5.5GraphTheory

5.6Combinatorics

5.7CodingTheory

5.8EquivariantDynamicalSystems

5.9MaterialScience

5.10ComputerVision

ALinearAlgebraicGroups

A.1LinearAlgebraicGroups

A.2TheLieAlgebraofaLinearAlgebraicGroup

A.3ReductiveandSemi-simpleGroups

A.4Roots

A.5RepresentationTheory

References

Notation

Index

内容摘要:

　　Thisbookisaboutthecomputationalaspectsofinvarianttheory.Thenalgorithmsforcomputinginvariantsoffiniteandreductivegroupsarediscussed.Thetextisenrichedwithnumerousexplicitexampleswhichillustratethetheoiwandshouldbeofmorethanpassinginterest.　　Thisbookisaboutthecomputationalaspectsofinvarianttheory.Ofcentralinterestisthequestionhowtheinvariantringofagivengroupactioncanbecalculated.Algorithmsforthispurposeformthemainpillarsaroundwhichthebookisbuilt.Therearetwointroductorychapters,oneonGrObnerbasismethodsandoneonthebasicconceptsofinvarianttheory,whichpreparethegroundforthealgorithms.Thenalgorithmsforcomputinginvariantsoffiniteandreductivegroupsarediscussed.Particularemphasisliesoninterrelationsbetweenstructuralpropertiesofinvariantringsandcomputationalmethods.Finally,thebookcontainsachapteronapplicationsofinvarianttheory,coveringfieldsasdisparateasgraphtheory,codingtheory,dynamicalsystems,andcomputervision.　　Thebookisintendedforpostgraduatestudentsaswellasresearchersingeometry,computeralgebra,and,ofcourse,invarianttheory.Thetextisenrichedwithnumerousexplicitexampleswhichillustratethetheoiwandshouldbeofmorethanpassinginterest.

书籍规格:

书籍详细信息
书名	计算不变量理论站内查询相似图书
丛书名	国外数学名著系列
	9787030234926 如需购买下载《计算不变量理论》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
出版地	北京	出版单位	科学出版社
版次	影印本	印次	1
定价(元)	66.0	语种	英文
尺寸	24	装帧	精装
页数		印数

全网搜索试读资源

书籍信息归属:

计算不变量理论是科学出版社于2008.出版的中图分类号为 O174 的主题关于不变量－理论－英文的书籍。