  
  
                                [1X GaussForHomalg [101X
  
  
                  [1X Gauss functionality for the homalg project [101X
  
  
                                   2022.08-03
  
  
                                 26 August 2022
  
  
                                 Simon Görtzen
  
  
  
  Simon Görtzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[107X
      Homepage: [7Xhttps://www.linkedin.com/in/simongoertzen/[107X
      Address:  [33X[0;14YSimon Görtzen[133X
                [33X[0;14YLehrstuhl B fuer Mathematik, RWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis  document  explains  the  primary  uses  of the [5XGaussForHomalg[105X package.
  Included  in  this manual is a documented list of the most important methods
  and functions you will need.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2007-2013 by Simon Goertzen[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or (at your option) any later version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YMany  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[105X  is  dependant  on  the  [5XGAP[105X  [5XMatricesForHomalg[105X package by M.
  Barakat et al. [Bar20], as well as the [5XGauss[105X package by myself [Gör08]. This
  should  be  clear  as  [5XGaussForHomalg[105X  presents  a  link  between  these two
  packages.  This manual was created with the help of the [5XGAPDoc[105X package by M.
  Neunhöffer and F. Lübeck [LN08].[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (GaussForHomalg)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview over this manual[133X
    1.2 [33X[0;0YInstallation of the [5XGaussForHomalg[105X Package[133X
  2 [33X[0;0YUsage[133X
  3 [33X[0;0Y[5XGaussForHomalg[105X methods and functions[133X
    3.1 [33X[0;0YThe field of rationals[133X
      3.1-1 HomalgFieldOfRationals
    3.2 [33X[0;0YThe Tools[133X
      3.2-1 ZeroMatrix
      3.2-2 IdentityMatrix
      3.2-3 CopyMatrix
      3.2-4 ImportMatrix
      3.2-5 Involution
      3.2-6 CertainRows
      3.2-7 CertainColumns
      3.2-8 UnionOfRows
      3.2-9 UnionOfColumns
      3.2-10 DiagMat
      3.2-11 KroneckerMat
      3.2-12 DualKroneckerMat
      3.2-13 Compose
      3.2-14 NrRows
      3.2-15 NrColumns
      3.2-16 IsZeroMatrix
      3.2-17 IsDiagonalMatrix
      3.2-18 ZeroRows
      3.2-19 ZeroColumns
    3.3 [33X[0;0YThe Basic Functions and [5Xhomalg[105X table creation[133X
      3.3-1 ReducedRowEchelonForm
      3.3-2 CreateHomalgTable
    3.4 [33X[0;0YMatrix entry manipulation[133X
      3.4-1 MatElm
      3.4-2 SetMatElm
      3.4-3 AddToMatElm
  4 [33X[0;0YExample[133X
    4.1 [33X[0;0YHomHom[133X
  A [33X[0;0YAn Overview of the [5XGaussForHomalg[105X package source code[133X
  
  
  [32X
