国外数学名著系列（续1）（影印版）49：计算不变量理论

图书标准信息

• 作者 [美]德克森（Derksen H.） 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030234926
• 定价 66.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 268页
• 字数 338千字
• 正文语种 英语

【内容简介】

《国外数学名著系列（续1）（影印版）49：计算不变量理论》isaboutthecomputationalaspectsofinvarianttheory.Ofcentralinterestisthequestionhowtheinvariantringofagivengroupactioncanbecalculated.Algorithmsforthispurposeformthemainpillarsaroundwhichthebookisbuilt.Therearetwointroductorychapters，oneonGrObnerbasismethodsandoneonthebasicconceptsofinvarianttheory，whichpreparethegroundforthealgorithms.Thenalgorithmsforcomputinginvariantsoffiniteandreductivegroupsarediscussed.Particularemphasisliesoninterrelationsbetweenstructuralpropertiesofinvariantringsandcomputationalmethods.Finally，thebookcontainsachapteronapplicationsofinvarianttheory，coveringfieldsasdisparateasgraphtheory，codingtheory，dynamicalsystems，andcomputervision.
Thebookisintendedforpostgraduatestudentsaswellasresearchersingeometry，computeralgebra，and，ofcourse，invarianttheory.Thetextisenrichedwithnumerousexplicitexampleswhichillustratethetheoiwandshouldbeofmorethanpassinginterest.

【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