Summary of New Features in Magma V2.13.pdf

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1、SummaryofNewFeaturesinMagmaV2.13July20061IntroductionThisdocumentprovidesatersesummaryofthenewfeaturesinstalledinMagmaforreleaseversionV2.13(July2006).PreviousreleasesofMagmawere:V2.12(June2005),V2.11(May2004),V2.10(April2003),V2.9(May2002),V2.8(July2001),V2.7(June2000),V2.6(November1999),

2、V2.5(July1999),V2.4(December1998),V2.3(January1998),V2.2(April1997),V2.1(October1996),V2.01(June1996)andV1.3(March1996).2SummaryGroups²Finitely-PresentedGroups:AnalgorithmduetoDerekHoltfortestingwhethertwo¯nitelypresentedgroupsareisomorphichasbeenimplementedinMagmabyDerek.Thealgorithmusest

3、heKnuth-Bendixproceduretoenumerateelements.²Finitely-PresentedGroups:Machineryforclassifyingmetacyclicp-groupsdevelopedbyEamonnO'BrienandMichaelVaughan-Leehasbeenincluded.²MatrixGroupsoverFiniteFields:ConstructiverecognitionofamatrixgroupasSL(3;q)hasbeenprovidedbyEamonnO'Brien.Thecorrespon

4、dingcodeforSL(2;q)hasbeenimproved.²MatrixGroupsoverFiniteFields:ItisnowpossibletorecognisetheSuzukiandReegroupsinvariousmatrixrepresentationsusingapackagedevelopedbyHendrikBÄaÄarnhielm.ThismakesuseofthecodeforrecognisingSL(2;q).ThepackagealsocontainsfunctionstocomputeSylowp-subgroupsforthe

5、setwofamiliesofgroups.²MatrixGroupsoverFiniteFields:ItisnowpossibletoconstructaSylowp-subgroupofanyclassicalgroupusingapackagedevelopedbyMarkStather.FunctionsarealsoincludedforcomputingnormalisersandsolvingtheconjugacyproblemforSylowsubgroups.1BasicRings²RealandComplexNumbers:Supportforrea

6、lnumbershasbeenimprovedinthisreleasebyintegratinginthelatestversionoftheMPFRlibrary.Thisincludesnewimplementationsofmanyfunctions(suchasthegammafunction)whicharefasterandmorestablethanthepreviousimplementations.LinearAlgebraandModuleTheory²LatticeReduction:AnewimplementationofLLLreductiono

7、fintegerlatticeshasbeenundertakenbyDamienStehlµeandisbasedontheNguyen{Stehl¶e°oating-pointalgorithm.TheLLLandLLLGramalgorithmsarenowguaranteedbothtocompleteandtoproduceLLL-reducedbases.Thenewalgorithmismoree±cientthanthepreviousone,sometimesdramaticallyso.²Ver