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                                 GradedModules

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  A homalg based package for the Abelian category of finitely presented graded

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                     modules over a computable graded ring

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                               Version 2017.09.10

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                                 September 2015

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                                Mohamed Barakat

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                               Sebastian Gutsche

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                             Markus Lange-Hegermann

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                                Oleksandr Motsak

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            (this manual is still under construction)

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            This  manual  is  best  viewed  as an HTML document. The

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            latest version is available online at:

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            http://homalg.math.rwth-aachen.de/~markus/GradedModules/chap0.html

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            An   offline   version   should   be   included  in  the

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            documentation  subfolder of the package. This package is

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            part of the homalg-project:

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            http://homalg.math.rwth-aachen.de/index.php/unreleased/gradedmodules

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  Mohamed Barakat

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      Email:    mailto:[email protected]

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      Homepage: http://www.mathematik.uni-kl.de/~barakat

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      Address:  Department of Mathematics,

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                University of Kaiserslautern,

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                67653 Kaiserslautern,

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                Germany

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  Sebastian Gutsche

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      Email:    mailto:[email protected]

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      Homepage: http://wwwb.math.rwth-aachen.de/~gutsche/

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      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,

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                52056 Aachen, Germany

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  Markus Lange-Hegermann

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      Email:    mailto:[email protected]

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      Homepage: http://wwwb.math.rwth-aachen.de/~markus

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      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,

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                52056 Aachen, Germany

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  Oleksandr Motsak

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      Email:    mailto:[email protected]

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      Homepage: http://www.mathematik.uni-kl.de/~motsak

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      Address:  Department of Mathematics,

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                University of Kaiserslautern,

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                67653 Kaiserslautern,

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                Germany

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  -------------------------------------------------------

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  Copyright

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  ©   2008-2015   by   Mohamed   Barakat,   Sebastian   Gutsche,   and  Markus

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  Lange-Hegermann

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  This  package  may  be distributed under the terms and conditions of the GNU

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  Public License Version 2.

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  -------------------------------------------------------

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  Acknowledgements

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  -------------------------------------------------------

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  Contents (GradedModules)

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  1 Introduction

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  2 Installation of the GradedModules Package

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  3 Quick Start

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  4 Ring Maps

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    4.1 Ring Maps: Attributes

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      4.1-1 KernelSubobject

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    4.2 Ring Maps: Operations and Functions

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      4.2-1 SegreMap

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      4.2-2 PlueckerMap

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      4.2-3 VeroneseMap

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  5 GradedModules

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    5.1 GradedModules: Category and Representations

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    5.2 GradedModules: Constructors

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    5.3 GradedModules: Properties

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    5.4 GradedModules: Attributes

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      5.4-1 BettiTable

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      5.4-2 CastelnuovoMumfordRegularity

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      5.4-3 CastelnuovoMumfordRegularityOfSheafification

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    5.5 LISHV: Logical Implications for GradedModules

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    5.6 GradedModules: Operations and Functions

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      5.6-1 MonomialMap

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      5.6-2 RandomMatrix

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      5.6-3 GeneratorsOfHomogeneousPart

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      5.6-4 SubmoduleGeneratedByHomogeneousPart

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      5.6-5 RepresentationMapOfRingElement

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      5.6-6 RepresentationMatrixOfKoszulId

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      5.6-7 RepresentationMapOfKoszulId

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      5.6-8 KoszulRightAdjoint

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      5.6-9 HomogeneousPartOverCoefficientsRing

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  6 The Tate Resolution

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    6.1 The Tate Resolution: Operations and Functions

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      6.1-1 TateResolution

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  7 Examples

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    7.1 Betti Diagrams

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      7.1-1 DE-2.2

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      7.1-2 DE-Code

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      7.1-3 Schenck-3.2

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      7.1-4 Schenck-8.3

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      7.1-5 Schenck-8.3.3

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    7.2 Commutative Algebra

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      7.2-1 Saturate

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    7.3 Global Section Modules of the Induced Sheaves

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      7.3-1 Examples of the ModuleOfGlobalSections Functor and Purity

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      Filtrations

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      7.3-2 Horrocks Mumford bundle

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  A Overview of the GradedModules Package Source Code

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