  
  
                       [1XThe [5XGaussForHomalg[0m[1X Package Manual[0m
  
  
                         [1X[5XGauss[0m[1X Functionality for [5Xhomalg[0m[1X[0m
  
  
                               Version 2009.11.09
  
  
                                 November 2009
  
  
                                 Simon Goertzen
  
  
  
  Simon Goertzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/goertzen/[0m
      Address:  Lehrstuhl B für Mathematik
                RWTH Aachen
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
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  [1XAbstract[0m
  This  document  explains  the  primary  uses  of the [5XGaussForHomalg[0m package.
  Included  in  this manual is a documented list of the most important methods
  and functions you will need.
  
  
  -------------------------------------------------------
  [1XCopyright[0m
  © 2007-2009 by Simon Goertzen
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0m
  Many  thanks  to  Mohamed Barakat and the Lehrstuhl B für Mathematik at RWTH
  Aachen  University  in  general  for  their support. It should be noted that
  [5XGaussForHomalg[0m is dependant on the [5XGAP[0m [5Xhomalg[0m package by M. Barakat [Bar09],
  as  well  as  the  [5XGauss[0m  package by myself [Gör08]. This should be clear as
  [5XGaussForHomalg[0m  presents  a link between these two packages. This manual was
  created  with  the help of the [5XGAPDoc[0m package by M. Neunhöffer and F. Lübeck
  [LN08].
  
  
  -------------------------------------------------------
  
  
  [1XContents (GaussForHomalg)[0X
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the [5XGaussForHomalg[0m Package
  2 Usage
  3 [5XGaussForHomalg[0m methods and functions
    3.1 The Tools
      3.1-1 ZeroMatrix
      3.1-2 IdentityMatrix
      3.1-3 CopyMatrix
      3.1-4 ImportMatrix
      3.1-5 Involution
      3.1-6 CertainRows
      3.1-7 CertainColumns
      3.1-8 UnionOfRows
      3.1-9 UnionOfColumns
      3.1-10 DiagMat
      3.1-11 KroneckerMat
      3.1-12 Compose
      3.1-13 NrRows
      3.1-14 NrColumns
      3.1-15 IsZeroMatrix
      3.1-16 IsDiagonalMatrix
      3.1-17 ZeroRows
      3.1-18 ZeroColumns
    3.2 The Basic Functions and [5Xhomalg[0m table creation
      3.2-1 DecideZeroRows
      3.2-2 DecideZeroRowsEffectively
      3.2-3 SyzygiesGeneratorsOfRows
      3.2-4 RelativeSyzygiesGeneratorsOfRows
      3.2-5 RowReducedEchelonForm
      3.2-6 CreateHomalgTable
    3.3 Matrix entry manipulation
      3.3-1 GetEntryOfHomalgMatrix
      3.3-2 SetEntryOfHomalgMatrix
      3.3-3 AddToEntryOfHomalgMatrix
  4 Example
    4.1 HomHom
  A An Overview of the [5XGaussForHomalg[0m package source code
  
  
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