  
  
                                    [1X Gauss [101X
  
  
                     [1X Extended Gauss functionality for [5XGAP[105X [101X
  
  
                                   2022.11-01
  
  
                                3 November 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 [5XGauss[105X package. Included is a
  documented  list  of the most important methods and functions needed to work
  with sparse matrices and the algorithms provided by the [5XGauss[105X package.[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;0YThe  [5XGauss[105X  package  would  not  have  been  possible  without  the  helpful
  contributions by[133X
  
  [30X    [33X[0;6YMax Neunhöffer, University of St Andrews, and[133X
  
  [30X    [33X[0;6YMohamed Barakat, Lehrstuhl B für Mathematik, RWTH Aachen.[133X
  
  [33X[0;0YMany  thanks  to these two and the Lehrstuhl B für Mathematik in general. It
  should  be  noted  that  the  [5XGAP[105X  algorithms  for [10XSemiEchelonForm[110X and other
  methods formed an important and informative basis for the development of the
  extended  Gaussian  algorithms. This manual was created with the help of the
  [5XGAPDoc[105X package by F. Lübeck and M. Neunhöffer [LN08].[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Gauss)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview over this manual[133X
    1.2 [33X[0;0YInstallation of the [5XGauss[105X Package[133X
  2 [33X[0;0YExtending Gauss Functionality[133X
    2.1 [33X[0;0YThe need for extended functionality[133X
    2.2 [33X[0;0YThe applications of the [5XGauss[105X package algorithms[133X
  3 [33X[0;0YThe Sparse Matrix Data Type[133X
    3.1 [33X[0;0YThe inner workings of [5XGauss[105X sparse matrices[133X
      3.1-1 [33X[0;0YA special case: GF(2)[133X
    3.2 [33X[0;0YMethods and functions for sparse matrices[133X
      3.2-1 SparseMatrix
      3.2-2 ConvertSparseMatrixToMatrix
      3.2-3 CopyMat
      3.2-4 GetEntry
      3.2-5 SetEntry
      3.2-6 AddToEntry
      3.2-7 SparseZeroMatrix
      3.2-8 SparseIdentityMatrix
      3.2-9 TransposedSparseMat
      3.2-10 CertainRows
      3.2-11 CertainColumns
      3.2-12 SparseUnionOfRows
      3.2-13 SparseUnionOfColumns
      3.2-14 SparseDiagMat
      3.2-15 Nrows
      3.2-16 Ncols
      3.2-17 IndicesOfSparseMatrix
      3.2-18 EntriesOfSparseMatrix
      3.2-19 RingOfDefinition
  4 [33X[0;0YGaussian Algorithms[133X
    4.1 [33X[0;0YA list of the available algorithms[133X
    4.2 [33X[0;0YMethods and Functions for [5XGauss[105Xian algorithms[133X
      4.2-1 EchelonMat
      4.2-2 EchelonMatTransformation
      4.2-3 ReduceMat
      4.2-4 ReduceMatTransformation
      4.2-5 KernelMat
      4.2-6 Rank
  A [33X[0;0YAn Overview of the [5XGauss[105X package source code[133X
  
  
  [32X
