理想、簇与算法 第3版：Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra 3rd ed.

图书标准信息

• 作者 [美]D.考克斯（David Cox） 著
• 出版社 世界图书出版公司
• 出版时间 2013-03
• 版次 3
• ISBN 9787510058400
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 551页
• 正文语种 英语

【内容简介】

　　Thebookassumesthatthestudentswillhaveaccesstoacomputeralgebrasystem.AppendixCdescribesthefeaturesofAXIOM，Maple，Mathematica，andREDUCEthataremostrelevanttothetext.Wedonotassumeanypriorexperiencewithacom-puter.However，manyofthealgorithmsinthebookaredescribedinpseudocode，whichmaybeunfamiliartostudentswithnobackgroundinprogramming.AppendixBcon-tainsacarefuldescripLionofthepseudocodethatweuseinthetext.

【目录】

PrefacetotheFirstEdition
PrefacetotheSecondEdition
PrefacetotheThirdEdition
1Geometry,Algebra,andAlgoritlnns
1.PolynomialsandAffineSpace
2.AffineVarieties
3.ParametrizationsofAffineVarieties
4.Ideals
5.PolynomialsofOneVariable
2.GroebnerBases

2.OrderingsontheMonomialsink[xlxn]
1.Introduction
3.ADivisionAlgorithmink[xlXn]
4.MonomialIdealsandDickson'sLemma
5.TheHilbertBasisTheoremandGroebnerBases
6.PropertiesofGroebnerBases
7.Buchberger'sAlgorithm
8.FirstApplicationsofGroebnerBases
9.(Optional)ImprovementsonBuchberger'sAlgorithm
3.EliminationTheory
1.TheEliminationandExtensionTheorems
2.TheGeometryofElimination
3.Implicitization
4.SingularPointsandEnvelopes
5.UniqueFactorizationandResultants
6.ResultantsandtheExtensionTheorem
……
3.EliminationTheory
4.TheAlgebra-GeometryDictionary
5.PolynomialandRationalFunctionsonaVariety
6.RoboticsandAutomaticGeometricTheoremProving
7.InvariantTheoryofFiniteGroups
8.ProjectiveAlgebraicGeometry
9.TheDimensionofaVariety
AppendixA.SomeConceptsFromAlgebra
AppendixB.Pseudocode
AppendixC.ComputerAlgebraSystems
AppendixD.IndependentProjects
References
Index