  
  
                                [1X GradedModules [101X
  
  
     [1X A homalg based package for the Abelian category of finitely presented
                  graded modules over computable graded rings [101X
  
  
                                   2022.09-02
  
  
                               28 September 2022
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                                Sebastian Jambor
  
                             Markus Lange-Hegermann
  
                                  Arne Lorenz
  
                                Oleksandr Motsak
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:mohamed.barakat@uni-siegen.de[107X
      Homepage: [7Xhttps://mohamed-barakat.github.io[107X
      Address:  [33X[0;14YWalter-Flex-Str. 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Jambor
      Email:    [7Xmailto:sebastian.jambor@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~sebastian/[107X
      Address:  [33X[0;14YSebastian Jambor[133X
                [33X[0;14YLehrstuhl B fuer Mathematik, RWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14YGermany[133X
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange-hegermann@hs-owl.de[107X
      Homepage: [7Xhttps://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/[107X
      Address:  [33X[0;14YMarkus Lange-Hegermann[133X
                [33X[0;14YHochschule Ostwestfalen-Lippe[133X
                [33X[0;14YLiebigstraße 87[133X
                [33X[0;14Y32657 Lemgo[133X
                [33X[0;14YGermany[133X
  
  
  Arne Lorenz
      Email:    [7Xmailto:arne.lorenz@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~arne/[107X
      Address:  [33X[0;14YArne Lorenz[133X
                [33X[0;14YLehrstuhl B fuer Mathematik, RWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14YGermany[133X
  
  
  Oleksandr Motsak
      Email:    [7Xmailto:motsak@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://www.mathematik.uni-kl.de/~motsak/[107X
      Address:  [33X[0;14YDepartment of Mathematics[133X
                [33X[0;14YUniversity of Kaiserslautern[133X
                [33X[0;14Y67653 Kaiserslautern[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y©   2008-2015   by   Mohamed   Barakat,   Sebastian   Gutsche,   and  Markus
  Lange-Hegermann  This  package  may  be  distributed  under  the  terms  and
  conditions of the GNU Public License Version 2 or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (GradedModules)[101X
  
  1 [33X[0;0YInstallation of the [5XGradedModules[105X Package[133X
  2 [33X[0;0YRing Maps[133X
    2.1 [33X[0;0YRing Maps: Attributes[133X
      2.1-1 KernelSubobject
    2.2 [33X[0;0YRing Maps: Operations and Functions[133X
      2.2-1 SegreMap
      2.2-2 PlueckerMap
      2.2-3 VeroneseMap
  3 [33X[0;0YGradedModules[133X
    3.1 [33X[0;0YGradedModules: Category and Representations[133X
    3.2 [33X[0;0YGradedModules: Constructors[133X
    3.3 [33X[0;0YGradedModules: Properties[133X
    3.4 [33X[0;0YGradedModules: Attributes[133X
      3.4-1 BettiTable
      3.4-2 CastelnuovoMumfordRegularity
      3.4-3 CastelnuovoMumfordRegularityOfSheafification
    3.5 [33X[0;0Y[5XLISHV[105X: Logical Implications for GradedModules[133X
    3.6 [33X[0;0YGradedModules: Operations and Functions[133X
      3.6-1 MonomialMap
      3.6-2 RandomMatrix
      3.6-3 GeneratorsOfHomogeneousPart
      3.6-4 SubmoduleGeneratedByHomogeneousPart
      3.6-5 RepresentationMapOfRingElement
      3.6-6 RepresentationMatrixOfKoszulId
      3.6-7 RepresentationMapOfKoszulId
      3.6-8 KoszulRightAdjoint
      3.6-9 HomogeneousPartOverCoefficientsRing
  4 [33X[0;0YThe Tate Resolution[133X
    4.1 [33X[0;0YThe Tate Resolution: Operations and Functions[133X
      4.1-1 TateResolution
  5 [33X[0;0YExamples[133X
    5.1 [33X[0;0YBetti Diagrams[133X
      5.1-1 [33X[0;0YDE-2.2[133X
      5.1-2 [33X[0;0YDE-Code[133X
      5.1-3 [33X[0;0YSchenck-3.2[133X
      5.1-4 [33X[0;0YSchenck-8.3[133X
      5.1-5 [33X[0;0YSchenck-8.3.3[133X
    5.2 [33X[0;0YCommutative Algebra[133X
      5.2-1 [33X[0;0YSaturate[133X
    5.3 [33X[0;0YGlobal Section Modules of the Induced Sheaves[133X
      5.3-1 [33X[0;0YExamples of the ModuleOfGlobalSections Functor and Purity
      Filtrations[133X
      5.3-2 [33X[0;0YHorrocks Mumford bundle[133X
  
  
  [32X
