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1、AlgorithmsandComputationinMathematics•Volume20EditorsArjehM.CohenHenriCohenDavidEisenbudMichaelF.SingerBerndSturmfelsJohannesBuchmannUlrichVollmerBinaryQuadraticFormsAnAlgorithmicApproachWith17Figuresand5TablesABCAuthorsJohannesBuchmannUlrichVollmerTechnicalUnivers
2、ityDepartmentofComputerScienceHochschulstraße1064289DarmstadtGermanyE-mail:buchmann@cdc.informatik.tu-darmstadt.deuvollmer@cdc.informatik.tu-darmstadt.deLibraryofCongressControlNumber:2006938722MathematicsSubjectClassification(2000):11-01,11Y40,11E12,11R29ISSN1431-1
3、550ISBN-103-540-46367-4SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-46367-2SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustra
4、tions,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtained
5、fromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,even
6、intheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandtechbooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN
7、:1052165046/techbooks543210ContentsIntroduction...................................................11BinaryQuadraticForms...................................91.1Computationalproblems.................................91.1.1Findingrepresentations........................
8、....91.1.2Findingtheminimum..............................111.2Discriminant............................................121.2.1Definition...........
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