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# RingsForHomalg

## Dictionaries of External Rings for the GAP Package homalg

Version 2019.12.08

September 2015

(this manual is still under construction)
This manual is best viewed as an HTML document. The latest version is available online at:
http://homalg.math.rwth-aachen.de/~barakat/homalg-project/RingsForHomalg/chap0.html
An offline version should be included in the documentation subfolder of the package. This package is part of the homalg-project:
http://homalg.math.rwth-aachen.de/index.php/core-packages/ringsforhomalg

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Department of Mathematics,
University of Siegen,
57072 Siegen,
Germany

Simon Goertzen
Email: simon.goertzen@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~simon/
Address:
Lehrstuhl B für Mathematik,
RWTH Aachen,
Templergraben 64,
52056 Aachen,
Germany

Markus Kirschmer
Email: markus.kirschmer@math.rwth-aachen.de
Homepage: http://www.math.rwth-aachen.de/~Markus.Kirschmer/
Address:
Lehrstuhl D für Mathematik,
RWTH Aachen,
Templergraben 64,
52056 Aachen,
Germany

Markus Lange-Hegermann
Email: markus.lange-hegermann@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~markus/
Address:
Lehrstuhl B für Mathematik,
RWTH Aachen,
Templergraben 64,
52056 Aachen,
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

Max Neunhöffer
Email: neunhoef@mcs.st-and.ac.uk
Homepage: http://www-groups.mcs.st-and.ac.uk/~neunhoef/
Address:
St Andrews University,
School of Mathematics and Statistics,
Mathematical Institute,
North Haugh,
St Andrews, Fife KY16 9SS,
Scotland, UK

Daniel Robertz
Email: daniel@momo.math.rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~daniel
Address:
Lehrstuhl B für Mathematik,
RWTH Aachen,
Templergraben 64,
52056 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
Homepage:
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.

### 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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