GradedModules
  
  
  A homalg based package for the Abelian category of finitely presented graded
                     modules over a computable graded ring
  
  
                               Version 2017.09.10
  
  
                                 September 2015
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                             Markus Lange-Hegermann
  
                                Oleksandr Motsak
  
  
  
            (this manual is still under construction)
            This  manual  is  best  viewed  as an HTML document. The
            latest version is available online at:
            http://homalg.math.rwth-aachen.de/~markus/GradedModules/chap0.html
            An   offline   version   should   be   included  in  the
            documentation  subfolder of the package. This package is
            part of the homalg-project:
            http://homalg.math.rwth-aachen.de/index.php/unreleased/gradedmodules
  
  
  
  Mohamed Barakat
      Email:    mailto:barakat@mathematik.uni-kl.de
      Homepage: http://www.mathematik.uni-kl.de/~barakat
      Address:  Department of Mathematics,
                University of Kaiserslautern,
                67653 Kaiserslautern,
                Germany
  
  
  Sebastian Gutsche
      Email:    mailto:sebastian.gutsche@rwth-aachen.de
      Homepage: http://wwwb.math.rwth-aachen.de/~gutsche/
      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  Markus Lange-Hegermann
      Email:    mailto:markus.lange.hegermann@rwth-aachen.de
      Homepage: http://wwwb.math.rwth-aachen.de/~markus
      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  Oleksandr Motsak
      Email:    mailto:motsak@mathematik.uni-kl.de
      Homepage: http://www.mathematik.uni-kl.de/~motsak
      Address:  Department of Mathematics,
                University of Kaiserslautern,
                67653 Kaiserslautern,
                Germany
  
  
  
  -------------------------------------------------------
  Copyright
  ©   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.
  
  
  -------------------------------------------------------
  Acknowledgements
  
  -------------------------------------------------------
  
  
  Contents (GradedModules)
  
  1 Introduction
  2 Installation of the GradedModules Package
  3 Quick Start
  4 Ring Maps
    4.1 Ring Maps: Attributes
      4.1-1 KernelSubobject
    4.2 Ring Maps: Operations and Functions
      4.2-1 SegreMap
      4.2-2 PlueckerMap
      4.2-3 VeroneseMap
  5 GradedModules
    5.1 GradedModules: Category and Representations
    5.2 GradedModules: Constructors
    5.3 GradedModules: Properties
    5.4 GradedModules: Attributes
      5.4-1 BettiTable
      5.4-2 CastelnuovoMumfordRegularity
      5.4-3 CastelnuovoMumfordRegularityOfSheafification
    5.5 LISHV: Logical Implications for GradedModules
    5.6 GradedModules: Operations and Functions
      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 The Tate Resolution
    6.1 The Tate Resolution: Operations and Functions
      6.1-1 TateResolution
  7 Examples
    7.1 Betti Diagrams
      7.1-1 DE-2.2
      7.1-2 DE-Code
      7.1-3 Schenck-3.2
      7.1-4 Schenck-8.3
      7.1-5 Schenck-8.3.3
    7.2 Commutative Algebra
      7.2-1 Saturate
    7.3 Global Section Modules of the Induced Sheaves
      7.3-1 Examples of the ModuleOfGlobalSections Functor and Purity
      Filtrations
      7.3-2 Horrocks Mumford bundle
  A Overview of the GradedModules Package Source Code