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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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 The Gauss Package Manual
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Extended Gauss Functionality for GAP
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Version 2017.12.07
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March 2013
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Simon Goertzen
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Simon Goertzen
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Email: mailto:[email protected]
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Homepage: http://wwwb.math.rwth-aachen.de/goertzen/
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Address: Lehrstuhl B für Mathematik
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Templergraben 64
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52062 Aachen
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(Germany)
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Abstract
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This document explains the primary uses of the Gauss package. Included is a
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documented list of the most important methods and functions needed to work
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with sparse matrices and the algorithms provided by the Gauss package.
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Copyright
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© 2007-2013 by Simon Goertzen
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This package may be distributed under the terms and conditions of the GNU
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Public License Version 2.
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Acknowledgements
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The Gauss package would not have been possible without the helpful
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contributions by
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 Max Neunhöffer, University of St Andrews, and
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 Mohamed Barakat, Lehrstuhl B für Mathematik, RWTH Aachen.
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Many thanks to these two and the Lehrstuhl B für Mathematik in general. It
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should be noted that the GAP algorithms for SemiEchelonForm and other
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methods formed an important and informative basis for the development of the
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extended Gaussian algorithms. This manual was created with the help of the
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GAPDoc package by F. Lübeck and M. Neunhöffer [LN08].
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Contents (Gauss)
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1 Introduction
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1.1 Overview over this manual
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1.2 Installation of the Gauss Package
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2 Extending Gauss Functionality
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2.1 The need for extended functionality
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2.2 The applications of the Gauss package algorithms
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3 The Sparse Matrix Data Type
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3.1 The inner workings of Gauss sparse matrices
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3.1-1 A special case: GF(2)
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3.2 Methods and functions for sparse matrices
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3.2-1 SparseMatrix
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3.2-2 ConvertSparseMatrixToMatrix
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3.2-3 CopyMat
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3.2-4 GetEntry
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3.2-5 SetEntry
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3.2-6 AddToEntry
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3.2-7 SparseZeroMatrix
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3.2-8 SparseIdentityMatrix
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3.2-9 TransposedSparseMat
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3.2-10 CertainRows
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3.2-11 CertainColumns
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3.2-12 UnionOfRows
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3.2-13 UnionOfColumns
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3.2-14 SparseDiagMat
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3.2-15 Nrows
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3.2-16 Ncols
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3.2-17 IndicesOfSparseMatrix
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3.2-18 EntriesOfSparseMatrix
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3.2-19 RingOfDefinition
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4 Gaussian Algorithms
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4.1 A list of the available algorithms
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4.2 Methods and Functions for Gaussian algorithms
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4.2-1 EchelonMat
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4.2-2 EchelonMatTransformation
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4.2-3 ReduceMat
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4.2-4 ReduceMatTransformation
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4.2-5 KernelMat
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4.2-6 Rank
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A An Overview of the Gauss package source code
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