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# RingsForHomalg

## Dictionaries of external rings

2023.11-02

4 November 2023

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Walter-Flex-Str. 3
57072 Siegen
Germany

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

Markus Kirschmer
Email: markus.kirschmer@math.rwth-aachen.de
Homepage: http://www.math.rwth-aachen.de/~Markus.Kirschmer/
Address:
Markus Kirschmer
Lehrstuhl D fuer Mathematik, RWTH Aachen
Templergraben 64
52062 Aachen
Germany

Markus Lange-Hegermann
Email: markus.lange-hegermann@hs-owl.de
Homepage: https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/
Address:
Markus Lange-Hegermann
Hochschule Ostwestfalen-Lippe
Liebigstraße 87
32657 Lemgo
Germany

Oleksandr Motsak
Email: motsak@mathematik.uni-kl.de
Homepage: http://www.mathematik.uni-kl.de/~motsak/
Address:
Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern
Germany

Daniel Robertz
Email: daniel@momo.math.rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~daniel/
Address:
Daniel Robertz
Lehrstuhl B fuer Mathematik, RWTH Aachen
Templergraben 64
52062 Aachen
Germany

Hans Schönemann
Email: hannes@mathematik.uni-kl.de
Homepage: http://www.mathematik.uni-kl.de/~hannes/
Address:
Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern
Germany

Andreas Steenpaß
Email: steenpass@mathematik.uni-kl.de
Address:
Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern
Germany

Vinay Wagh
Email: waghoba@gmail.com
Homepage: http://www.iitg.ernet.in/vinay.wagh/
Address:
E-102, Department of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati, Assam, India.
PIN: 781 039.
India

### Copyright

© 2007-2015 by Mohamed Barakat, Simon Görtzen, Markus Kirschmer, Markus Lange-Hegermann, Oleksandr Motsak, Max Neunhöffer, Daniel Robertz, and Hans Schönemann. This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.

### Contents

1 Introduction
1.1 Ring Constructions for Supported External Computer Algebra Systems
1.1-1 external GAP
1.1-2 Singular
1.1-3 MAGMA
1.1-4 Macaulay2
1.1-5 Sage
1.1-6 Maple
2 Installation of the RingsForHomalg Package
3 The Ring Table
3.1 An Example for a Ring Table - Singular
3.1-1 BasisOfRowModule
3.1-2 BasisOfRowModule
3.1-3 BasisOfColumnModule
3.1-4 BasisOfColumnModule
3.1-5 DecideZeroRows
3.1-6 DecideZeroRows
3.1-7 DecideZeroColumns
3.1-8 DecideZeroColumns
3.1-9 SyzygiesGeneratorsOfRows
3.1-10 SyzygiesGeneratorsOfRows
3.1-11 SyzygiesGeneratorsOfColumns
3.1-12 SyzygiesGeneratorsOfColumns
3.1-13 BasisOfRowsCoeff
3.1-14 BasisOfRowsCoeff
3.1-15 BasisOfColumnsCoeff
3.1-16 BasisOfColumnsCoeff
3.1-17 DecideZeroRowsEffectively
3.1-18 DecideZeroRowsEffectively
3.1-19 DecideZeroColumnsEffectively
3.1-20 DecideZeroColumnsEffectively
3.1-21 RelativeSyzygiesGeneratorsOfRows
3.1-22 RelativeSyzygiesGeneratorsOfRows
3.1-23 RelativeSyzygiesGeneratorsOfColumns
3.1-24 RelativeSyzygiesGeneratorsOfColumns
3.1-25 ReducedSyzygiesGeneratorsOfRows
3.1-26 ReducedSyzygiesGeneratorsOfRows
3.1-27 ReducedSyzygiesGeneratorsOfColumns
3.1-28 ReducedSyzygiesGeneratorsOfColumns
References
Index
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