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1、AlgorithmsandComputationinMathematics•Volume10EditorsArjehM.CohenHenriCohenDavidEisenbudMichaelF.SingerBerndSturmfelsSaugataBasuRichardPollackMarie-FrançoiseRoyAlgorithmsinRealAlgebraicGeometrySecondEditionWith37Figures123SaugataBasuGeorgiaInstituteofTechnologySchoolofMathematicsAtlanta
2、,GA30332-0160USAe-mail:saugata@math.gatech.eduRichardPollackCourantInstituteofMathematicalSciences251MercerStreetNewYork,NY10012USAe-mail:pollack@cims.nyu.eduMarie-FrançoiseRoyIRMARCampusdeBeaulieuUniversitédeRennesI35042RennescedexFrancee-mail:Marie-Francoise.Roy@univ-rennes1.frLibrary
3、ofCongressControlNumber:2006927110MathematicsSubjectClassification(2000):14P10,68W30,03C10,68Q25,52C45ISSN1431-1550ISBN-103-540-33098-4SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-33098-1SpringerBerlinHeidelbergNewYorkISBN3-540-00973-61steditionSpringer-VerlagBerlinHeidelbergNewYorkTh
4、isworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofi
5、spermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.com©Springer-VerlagBerlinHe
6、idelberg2003,2006PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantpro-tectivelawsandregulationsandthereforefreeforgeneraluse.TypesetbytheauthorsusingaSpri
7、ngerLATEXmacropackageProduction:LE-TEXJelonek,Schmidt&VöcklerGbR,LeipzigCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaper46/3100YL-543210TableofContentsIntroduction....................................11AlgebraicallyClosedFields......................111.1Definit
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