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1、MartinKreuzerandLorenzoRobbianoComputationalCommutativeAlgebra1July3,2000Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestForewordHofstadter’sLaw:Italwaystakeslongerthanyouthinkitwilltake,evenifyoutakeintoaccountHofstadter’sLaw.(DouglasR.Hofstadter)DearReader,
2、whatyouareholdinginyourhandsnowisforyouabook.Butforus,forourfamiliesandfriends,ithasbeenknownasthebookoverthelastthreeyears.Threeyearsofintenseworkjusttofillthreecentimetersofyourbookshelf!Thisamountstoaboutonecentimeterperyear,orroughlytwo-fifthsofaninchperyearifyouarenon-metric.Clearlyweha
3、dampleopportunitytoexperiencethefullforceofHofstadter’sLaw.WritingabookaboutComputationalCommutativeAlgebraisnotun-likecomputingaGr¨obnerbasis:youneedunshakeablefaithtobelievethattheprojectwilleverend;likewise,youmusttrustintheNoetherianityofpolynomialringstobelievethatBuchberger’sAlgorith
4、mwilleverterminate.Naturally,wehopethatthefinalresultprovesoureffortsworthwhile.Thisisabookforlearning,teaching,reading,and,mostofall,enjoyingthetopicathand.SinceneitherofusisanativeEnglishspeaker,theliteraryqualityofthisworkisnecessarilyalittlelimited.Worriesaboutourlackoflinguis-ticsophist
5、icationgrewconsiderablyuponreadingthefollowingpartoftheintroductionof“TheRandomHouseCollegeDictionary”Aneducatedspeakerwilltransferfrominformalhaven’ttoformalhavenot.TheuneducatedspeakerwhoinformallyusesIseenorIdonegonemayadjusttotheformalmodewithIhavesawandIhavewent.Quiteapartfrombeinguna
6、bletodistinguishbetweentheinformalandformalmodes,wewerefrequentlypuzzledbysuchelementaryquestionsas:isthereanotherwordforsynonym?Luckily,wewereabletoextricateour-selvesfromtheworstmiresthankstothegenerousaidofJohnAbbottandTonyGeramita.TheyprovideduswithmuchinsightintoBritishEnglishandAmeri
7、canEnglish,respectively.However,notwithstandingtheirilluminatinghelp,weweresometimesunabletodiscovertheultimatetruth:shouldIbeanidealinaringRoranidealofaringR?Finally,wedecidedtobenon-partisananduseboth.VIHavingrevealedthenamesoftwoofourmainaides,wenowabandona
