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1、MartinKreuzerandLorenzoRobbianoComputationalCommutativeAlgebra1July3,2000Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestForewordHofstadter’sLaw:Italwaystakeslongerthanyouthinkitwilltake,evenifyoutakeintoaccountHofstadter’sLaw.(DouglasR.Hofstadter)DearReader,wh
2、atyouareholdinginyourhandsnowisforyouabook.Butforus,forourfamiliesandfriends,ithasbeenknownasthebookoverthelastthreeyears.Threeyearsofintenseworkjusttofillthreecentimetersofyourbookshelf!Thisamountstoaboutonecentimeterperyear,orroughlytwo-fifthsofaninchperyearifyouarenon-metric.Clearlywehadamp
3、leopportunitytoexperiencethefullforceofHofstadter’sLaw.WritingabookaboutComputationalCommutativeAlgebraisnotun-likecomputingaGr¨obnerbasis:youneedunshakeablefaithtobelievethattheprojectwilleverend;likewise,youmusttrustintheNoetherianityofpolynomialringstobelievethatBuchberger’sAlgorithmwille
4、verterminate.Naturally,wehopethatthefinalresultprovesoureffortsworthwhile.Thisisabookforlearning,teaching,reading,and,mostofall,enjoyingthetopicathand.SinceneitherofusisanativeEnglishspeaker,theliteraryqualityofthisworkisnecessarilyalittlelimited.Worriesaboutourlackoflinguis-ticsophisticationg
5、rewconsiderablyuponreadingthefollowingpartoftheintroductionof“TheRandomHouseCollegeDictionary”Aneducatedspeakerwilltransferfrominformalhaven’ttoformalhavenot.TheuneducatedspeakerwhoinformallyusesIseenorIdonegonemayadjusttotheformalmodewithIhavesawandIhavewent.Quiteapartfrombeingunabletodisti
6、nguishbetweentheinformalandformalmodes,wewerefrequentlypuzzledbysuchelementaryquestionsas:isthereanotherwordforsynonym?Luckily,wewereabletoextricateour-selvesfromtheworstmiresthankstothegenerousaidofJohnAbbottandTonyGeramita.TheyprovideduswithmuchinsightintoBritishEnglishandAmericanEnglish,r
7、espectively.However,notwithstandingtheirilluminatinghelp,weweresometimesunabletodiscovertheultimatetruth:shouldIbeanidealinaringRoranidealofaringR?Finally,wedecidedtobenon-partisananduseboth.VIHavingrevealedthenamesoftwoofourmainaides,wenowabandona
