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# The GaussForHomalg Package Manual

## Gauss Functionality for homalg

Version 2009.11.09

November 2009

Simon Goertzen
Email: simon.goertzen@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/goertzen/
Address:
Lehrstuhl B für Mathematik
RWTH Aachen
Templergraben 64
52062 Aachen
(Germany)

### Abstract

This document explains the primary uses of the GaussForHomalg package. Included in this manual is a documented list of the most important methods and functions you will need.

### Copyright

© 2007-2009 by Simon Goertzen

This package may be distributed under the terms and conditions of the GNU Public License Version 2.

### Acknowledgements

Many thanks to Mohamed Barakat and the Lehrstuhl B für Mathematik at RWTH Aachen University in general for their support. It should be noted that GaussForHomalg is dependant on the GAP homalg package by M. Barakat [Bar09], as well as the Gauss package by myself [Gör08]. This should be clear as GaussForHomalg presents a link between these two packages. This manual was created with the help of the GAPDoc package by M. Neunhöffer and F. Lübeck [LN08].

### Contents

1 Introduction
1.1 Overview over this manual
1.2 Installation of the GaussForHomalg Package
2 Usage
3 GaussForHomalg methods and functions
3.1 The Tools
3.1-1 ZeroMatrix
3.1-2 IdentityMatrix
3.1-3 CopyMatrix
3.1-4 ImportMatrix
3.1-5 Involution
3.1-6 CertainRows
3.1-7 CertainColumns
3.1-8 UnionOfRows
3.1-9 UnionOfColumns
3.1-10 DiagMat
3.1-11 KroneckerMat
3.1-12 Compose
3.1-13 NrRows
3.1-14 NrColumns
3.1-15 IsZeroMatrix
3.1-16 IsDiagonalMatrix
3.1-17 ZeroRows
3.1-18 ZeroColumns
3.2 The Basic Functions and homalg table creation
3.2-1 DecideZeroRows
3.2-2 DecideZeroRowsEffectively
3.2-3 SyzygiesGeneratorsOfRows
3.2-4 RelativeSyzygiesGeneratorsOfRows
3.2-5 RowReducedEchelonForm
3.2-6 CreateHomalgTable
3.3 Matrix entry manipulation
3.3-1 GetEntryOfHomalgMatrix
3.3-2 SetEntryOfHomalgMatrix
3.3-3 AddToEntryOfHomalgMatrix
4 Example
4.1 HomHom
A An Overview of the GaussForHomalg package source code
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