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# RingsForHomalg

## Rings in External Computer Algebra Systems for the GAP-Package homalg

Version 2009.11.09

November 2009

(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/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: barakat@mathematik.uni-kl.de
Homepage: http://wwwb.math.rwth-aachen.de/~barakat/
Address:
Department of Mathematics,
University of Kaiserslautern,
67653 Kaiserslautern,
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

Max Neunhöffer
Email: daniel@momo.math.rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~daniel
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

### Copyright

© 2007-2009 by Mohamed Barakat, Simon Görtzen, Markus Kirschmer, Markus Lange-Hegermann, Max Neunhöffer, and Daniel Robertz.

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

### 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
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