chap0.txt

  
  
                       The GaussForHomalg Package Manual
  
  
                         Gauss Functionality for homalg
  
  
                               Version 2017.09.10
  
  
                                 September 2013
  
  
                                 Simon Goertzen
  
  
  
  Simon Goertzen
      Email:    mailto:[email protected]
      Homepage: http://wwwb.math.rwth-aachen.de/goertzen/
      Address:  Lehrstuhl B für Mathematik
                RWTH Aachen
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
  -------------------------------------------------------
  Abstract
  This  document  explains  the  primary  uses  of the GaussForHomalg package.
  Included  in  this manual is a documented list of the most important methods
  and functions you will need.
  
  
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  Copyright
  © 2007-2013 by Simon Goertzen
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.
  
  
  -------------------------------------------------------
  Acknowledgements
  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
  GaussForHomalg  is  dependant  on  the  GAP  MatricesForHomalg package by M.
  Barakat et al. [Bar09], as well as the Gauss package by myself [Gör08]. This
  should  be  clear  as  GaussForHomalg  presents  a  link  between  these two
  packages.  This manual was created with the help of the GAPDoc package by M.
  Neunhöffer and F. Lübeck [LN08].
  
  
  -------------------------------------------------------
  
  
  Contents (GaussForHomalg)
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the GaussForHomalg Package
  2 Usage
  3 GaussForHomalg 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 homalg 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 MatElm
      3.3-2 SetMatElm
      3.3-3 AddToMatElm
  4 Example
    4.1 HomHom
  A An Overview of the GaussForHomalg package source code