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ID:14317974
大小:13.36 MB
页数:534页
时间:2018-07-27
《a computational introduction to number theory and algebra - victor shoup》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、TEAMLinGAComputationalIntroductiontoNumberTheoryandAlgebra(Version1)VictorShoupTEAMLinGTEAMLinGThisPDFdocumentcontainshyperlinks,andonemaynavigatethroughitbyclickingontheorem,definition,lemma,equation,andpagenumbers,aswellasURLs,andchapterandsectiontitlesinthet
2、ableofcontents;mostPDFviewersshouldalsodisplayalistof“bookmarks”thatallowdirectaccesstochaptersandsections.TEAMLinGCopyrightc2005byVictorShoupAllrightsreserved.TherighttopublishordistributethisworkinprintformbelongsexclusivelytoCambridgeUniv
3、ersityPress;however,thiselectronicversionisdistributedunderthetermsandconditionsofaCreativeCommonslicense(Attribution-NonCommercial-NoDerivs2.0):Youarefreetocopy,distribute,anddisplaythiselectronicversionunderthefollowingconditions:Attribution.Youmustgivetheor
4、iginalauthorcredit.Noncommercial.Youmaynotusethiselectronicversionforcommercialpurposes.NoDerivativeWorks.Youmaynotalter,transform,orbuilduponthiselectronicversion.Foranyreuseordistribution,youmustmakecleartoothersthelicensetermsofthiswork.Anyoftheseconditions
5、canbewaivedifyougetpermissionfromtheauthor.Formoreinformationaboutthelicense,visitcreativecommons.org/licenses/by-nd-nc/2.0.TEAMLinGContentsPrefacepagexPreliminariesxiv1Basicpropertiesoftheintegers11.1Divisibilityandprimality11.2Idealsandgreatestcommondivisors
6、41.3Someconsequencesofuniquefactorization82Congruences132.1Definitionsandbasicproperties132.2Solvinglinearcongruences152.3Residueclasses202.4Euler’sphifunction242.5Fermat’slittletheorem252.6ArithmeticfunctionsandM¨obiusinversion283Computingwithlargeintegers333.
7、1Asymptoticnotation333.2Machinemodelsandcomplexitytheory363.3Basicintegerarithmetic393.4ComputinginZn483.5Fasterintegerarithmetic(∗)513.6Notes524Euclid’salgorithm554.1ThebasicEuclideanalgorithm554.2TheextendedEuclideanalgorithm584.3ComputingmodularinversesandC
8、hineseremaindering624.4Speedingupalgorithmsviamodularcomputation634.5Rationalreconstructionandapplications664.6Notes73vTEAMLinGviContents5Thedistributionofprimes745.1Chebyshev’sthe
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