  
  
                           [1X The [5XGauss[0m[1X Package Manual[0m
  
  
                      [1XExtended Gauss Functionality for [5XGAP[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
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
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  [1XAbstract[0m
  This  document explains the primary uses of the [5XGauss[0m 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[0m package.
  
  
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  [1XCopyright[0m
  © 2007-2009 by Simon Goertzen
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.
  
  
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  [1XAcknowledgements[0m
  The  [5XGauss[0m  package  would  not  have  been  possible  without  the  helpful
  contributions by
  
  --    Max Neunhöffer, University of St Andrews, and
  
  --    Mohamed Barakat, Lehrstuhl B für Mathematik, RWTH Aachen.
  
  Many  thanks  to these two and the Lehrstuhl B für Mathematik in general. It
  should  be  noted  that  the  [5XGAP[0m  algorithms  for [10XSemiEchelonForm[0m 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[0m package by F. Lübeck and M. Neunhöffer [LN08].
  
  
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  [1XContents (Gauss)[0X
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the [5XGauss[0m Package
  2 Extending Gauss Functionality
    2.1 The need for extended functionality
    2.2 The applications of the [5XGauss[0m package algorithms
  3 The Sparse Matrix Data Type
    3.1 The inner workings of [5XGauss[0m sparse matrices
      3.1-1 A special case: GF(2)
    3.2 Methods and functions for sparse matrices
      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 UnionOfRows
      3.2-13 UnionOfColumns
      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 Gaussian Algorithms
    4.1 A list of the available algorithms
    4.2 Methods and Functions for [5XGauss[0mian algorithms
      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 An Overview of the [5XGauss[0m package source code
  
  
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