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1、SaugataBasuRichardPollackMarie-FrançoiseRoyAlgorithmsinRealAlgebraicGeometrySecondEditionWith37Figures123SaugataBasuGeorgiaInstituteofTechnologySchoolofMathematicsAtlanta,GA30332-0160USAe-mail:saugata@math.gatech.eduRichardPollackCourantInstituteofMathematicalSciences251MercerStreetNewYo
2、rk,NY10012USAe-mail:pollack@cims.nyu.eduMarie-FrançoiseRoyIRMARCampusdeBeaulieuUniversitédeRennesI35042RennescedexFrancee-mail:Marie-Francoise.Roy@univ-rennes1.frLibraryofCongressControlNumber:2006927110MathematicsSubjectClassification(2000):14P10,68W30,03C10,68Q25,52C45ISSN1431-1550ISBN-
3、103-540-33098-4SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-33098-1SpringerBerlinHeidelbergNewYorkISBN3-540-00973-61steditionSpringer-VerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftran
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5、sbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.com©Springer-VerlagBerlinHeidelberg2003,2006PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotim
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7、onacid-freepaper46/3100YL-543210TableofContentsIntroduction....................................11AlgebraicallyClosedFields......................111.1DefinitionsandFirstProperties..................111.2EuclideanDivisionandGreatestCommonDivisor......141.3ProjectionTheoremfor
