The Gauss Package Manual
  
  
                      Extended Gauss Functionality for GAP
  
  
                               Version 2017.12.07
  
  
                                   March 2013
  
  
                                 Simon Goertzen
  
  
  
  Simon Goertzen
      Email:    mailto:simon.goertzen@rwth-aachen.de
      Homepage: http://wwwb.math.rwth-aachen.de/goertzen/
      Address:  Lehrstuhl B für Mathematik
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
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  Abstract
  This  document explains the primary uses of the Gauss 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 Gauss package.
  
  
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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.
  
  
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  Acknowledgements
  The  Gauss  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  GAP  algorithms  for SemiEchelonForm 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
  GAPDoc package by F. Lübeck and M. Neunhöffer [LN08].
  
  
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  Contents (Gauss)
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the Gauss Package
  2 Extending Gauss Functionality
    2.1 The need for extended functionality
    2.2 The applications of the Gauss package algorithms
  3 The Sparse Matrix Data Type
    3.1 The inner workings of Gauss 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 Gaussian 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 Gauss package source code