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# GaussForHomalg

## Gauss functionality for the homalg project

2022.08-02

17 August 2022

Simon Görtzen
Email: simon.goertzen@rwth-aachen.de
Homepage: https://www.linkedin.com/in/simongoertzen/
Address:
Simon Görtzen
Lehrstuhl B fuer 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

© 2007-2013 by Simon Goertzen

This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.

### 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 MatricesForHomalg package by M. Barakat et al. [Bar20], 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 field of rationals
3.1-1 HomalgFieldOfRationals
3.2 The Tools
3.2-1 ZeroMatrix
3.2-2 IdentityMatrix
3.2-3 CopyMatrix
3.2-4 ImportMatrix
3.2-5 Involution
3.2-6 CertainRows
3.2-7 CertainColumns
3.2-8 UnionOfRows
3.2-9 UnionOfColumns
3.2-10 DiagMat
3.2-11 KroneckerMat
3.2-12 DualKroneckerMat
3.2-13 Compose
3.2-14 NrRows
3.2-15 NrColumns
3.2-16 IsZeroMatrix
3.2-17 IsDiagonalMatrix
3.2-18 ZeroRows
3.2-19 ZeroColumns
3.3 The Basic Functions and homalg table creation
3.3-1 ReducedRowEchelonForm
3.3-2 CreateHomalgTable
3.4 Matrix entry manipulation
3.4-1 MatElm
3.4-2 SetMatElm
3.4-3 AddToMatElm
4 Example
4.1 HomHom
A An Overview of the GaussForHomalg package source code
References
Index
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