  
  
                                 [1X[5XGradedModules[105X[101X
  
  
  [1XA [5Xhomalg[105X based package for the Abelian category of finitely presented graded
                     modules over a computable graded ring[101X
  
  
                               Version 2015.12.04
  
  
                                 September 2015
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                             Markus Lange-Hegermann
  
                                Oleksandr Motsak
  
  
  
            [33X[0;10Y([13Xthis manual is still under construction[113X)[133X
            [33X[0;10YThis  manual  is  best  viewed  as an [12XHTML[112X document. The
            latest version is available [12Xonline[112X at:[133X
            [33X[0;10Y[7Xhttp://homalg.math.rwth-aachen.de/~markus/GradedModules/chap0.html[107X[133X
            [33X[0;10YAn   [12Xoffline[112X   version   should   be   included  in  the
            documentation  subfolder of the package. This package is
            part of the [5Xhomalg[105X-project:[133X
            [33X[0;10Y[7Xhttp://homalg.math.rwth-aachen.de/index.php/unreleased/gradedmodules[107X[133X
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:barakat@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://www.mathematik.uni-kl.de/~barakat[107X
      Address:  [33X[0;14YDepartment of Mathematics,[133X
                [33X[0;14YUniversity of Kaiserslautern,[133X
                [33X[0;14Y67653 Kaiserslautern,[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:sebastian.gutsche@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~gutsche/[107X
      Address:  [33X[0;14YLehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany[133X
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange.hegermann@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~markus[107X
      Address:  [33X[0;14YLehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany[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[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  
  -------------------------------------------------------
  
  
  [1XContents (GradedModules)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YInstallation of the [5XGradedModules[105X Package[133X
  3 [33X[0;0YQuick Start[133X
  4 [33X[0;0YRing Maps[133X
    4.1 [33X[0;0YRing Maps: Attributes[133X
      4.1-1 KernelSubobject
    4.2 [33X[0;0YRing Maps: Operations and Functions[133X
      4.2-1 SegreMap
      4.2-2 PlueckerMap
      4.2-3 VeroneseMap
  5 [33X[0;0YGradedModules[133X
    5.1 [33X[0;0YGradedModules: Category and Representations[133X
    5.2 [33X[0;0YGradedModules: Constructors[133X
    5.3 [33X[0;0YGradedModules: Properties[133X
    5.4 [33X[0;0YGradedModules: Attributes[133X
      5.4-1 BettiTable
      5.4-2 CastelnuovoMumfordRegularity
      5.4-3 CastelnuovoMumfordRegularityOfSheafification
    5.5 [33X[0;0Y[5XLISHV[105X: Logical Implications for GradedModules[133X
    5.6 [33X[0;0YGradedModules: Operations and Functions[133X
      5.6-1 MonomialMap
      5.6-2 RandomMatrix
      5.6-3 GeneratorsOfHomogeneousPart
      5.6-4 SubmoduleGeneratedByHomogeneousPart
      5.6-5 RepresentationMapOfRingElement
      5.6-6 RepresentationMatrixOfKoszulId
      5.6-7 RepresentationMapOfKoszulId
      5.6-8 KoszulRightAdjoint
      5.6-9 HomogeneousPartOverCoefficientsRing
  6 [33X[0;0YThe Tate Resolution[133X
    6.1 [33X[0;0YThe Tate Resolution: Operations and Functions[133X
      6.1-1 TateResolution
  7 [33X[0;0YExamples[133X
    7.1 [33X[0;0YBetti Diagrams[133X
      7.1-1 [33X[0;0YDE-2.2[133X
      7.1-2 [33X[0;0YDE-Code[133X
      7.1-3 [33X[0;0YSchenck-3.2[133X
      7.1-4 [33X[0;0YSchenck-8.3[133X
      7.1-5 [33X[0;0YSchenck-8.3.3[133X
    7.2 [33X[0;0YCommutative Algebra[133X
      7.2-1 [33X[0;0YSaturate[133X
    7.3 [33X[0;0YGlobal Section Modules of the Induced Sheaves[133X
      7.3-1 [33X[0;0YExamples of the ModuleOfGlobalSections Functor and Purity
      Filtrations[133X
      7.3-2 [33X[0;0YHorrocks Mumford bundle[133X
  A [33X[0;0YOverview of the [5XGradedModules[105X Package Source Code[133X
  
  
  [32X
