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1、MartinKreuzerandLorenzoRobbianoComputationalCommutativeAlgebra1July3,2000Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestForewordHofstadter’sLaw:Italwaystakeslongerthanyouthinkitwilltake,evenifyoutakeintoaccountHofstadter’sLaw.(DouglasR.Hofstadter)Dear
2、Reader,whatyouareholdinginyourhandsnowisforyouabook.Butforus,forourfamiliesandfriends,ithasbeenknownasthebookoverthelastthreeyears.Threeyearsofintenseworkjusttofillthreecentimetersofyourbookshelf!Thisamountstoaboutonecentimeterperyear,orroughlytwo-fifthsofaninchperyearifyouarenon-metr
3、ic.ClearlywehadampleopportunitytoexperiencethefullforceofHofstadter’sLaw.WritingabookaboutComputationalCommutativeAlgebraisnotun-likecomputingaGr¨obnerbasis:youneedunshakeablefaithtobelievethattheprojectwilleverend;likewise,youmusttrustintheNoetherianityofpolynomialringstobelievetha
4、tBuchberger’sAlgorithmwilleverterminate.Naturally,wehopethatthefinalresultprovesoureffortsworthwhile.Thisisabookforlearning,teaching,reading,and,mostofall,enjoyingthetopicathand.SinceneitherofusisanativeEnglishspeaker,theliteraryqualityofthisworkisnecessarilyalittlelimited.Worriesabou
5、tourlackoflinguis-ticsophisticationgrewconsiderablyuponreadingthefollowingpartoftheintroductionof“TheRandomHouseCollegeDictionary”Aneducatedspeakerwilltransferfrominformalhaven’ttoformalhavenot.TheuneducatedspeakerwhoinformallyusesIseenorIdonegonemayadjusttotheformalmodewithIhavesaw
6、andIhavewent.Quiteapartfrombeingunabletodistinguishbetweentheinformalandformalmodes,wewerefrequentlypuzzledbysuchelementaryquestionsas:isthereanotherwordforsynonym?Luckily,wewereabletoextricateour-selvesfromtheworstmiresthankstothegenerousaidofJohnAbbottandTonyGeramita.Theyprovidedu
7、swithmuchinsightintoBritishEnglishandAmericanEnglish,respectively.However,notwithstandingtheirilluminatinghelp,weweresometimesunabletodiscovertheultimatetruth:shouldIbeanidealinaringRoranidealofaringR?Finally,wedecidedtobenon-partisananduseboth.VIHavingrevealedthenamesoftwoofourmain
8、aides,wenowabandona