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1、SolvingProblemswithMagmaWiebBosmaJohnCannonCatherinePlayoustAllanSteelSchoolofMathematicsandStatisticsUniversityofSydneyNSW2006,AustraliaCopyright°c1999.Allrightsreserved.Nopartofthisbookmaybereproducedwithoutwrittenpermission.TypesetbycomputerusingDonaldKnuth’sT
2、EX,andthedocumentpreparationsystemLATEXdevelopedbyLeslieLamport.IntroductionThisbookisneitheranintroductorymanualnorareferencemanualforMagma.ThoseneedsaremetbythebooksAnIntroductiontoMagmaandHandbookofMagmaFunctions.Eventhemostkeeninductivelearnerswillnotlearnall
3、thereistoknowaboutMagmafromthepresentwork.WhatSolvingProblemswithMagmadoeso?erisalargecollectionofreal-worldalgebraicproblems,solvedusingtheMagmalanguageandintrinsics.Itishopedthatbystudyingtheseexamples,especiallythoseinyourspecialty,youwillgainapracticalunderst
4、andingofhowtoexpressmath-ematicalproblemsinMagmaterms.Mostoftheexampleshavearisenfromgenuineresearchquestions,someofwhichtheothercomputeralgebrasystemsonthemarketcannothandlewell,andafewwhichstretchMagmatoitslimittoo.IfyouaretryingtheexamplesonyourownMagma,bewarn
5、edthatsomeoftheexamplesrequiresigni?cantCPUtimeand/orstoragespacetocompletetheirexecution.Wethankallthosewhohavecontributedexamples.Someareolderproblems,solvedwithMagma’spredecessorCayley.OthersarenewonesthatexploitMagma’sabilitytostraddleallaspectsofalgebra.Wewe
6、lcomecommentsonthisbookandsubmissionsofnewapproachesthatyouthinkmightadvantageothermathematicians.iiiContentsIntroductioniii1Language11.1Puzzle-solving:::::::::::::::::::::::::::::::::::::::11.1.1DogDaze:::::::::::::::::::::::::::::::::::::11.1.2Lettersstandingfo
7、rdigits::::::::::::::::::::::::::::21.2Sets,sequencesandfunctions::::::::::::::::::::::::::::::51.2.1Fareysequence::::::::::::::::::::::::::::::::::51.2.2Theknapsackproblem::::::::::::::::::::::::::::::71.2.3Simulationofacellularautomaton:::::::::::::::::::::::72
8、TheIntegers112.1Introduction::::::::::::::::::::::::::::::::::::::::112.2ArithmeticandArithmeticFunctions::::::::::::::::::::::::::112.2.1Example:Amicablenumbe
