RingsForHomalg
  
  
           Dictionaries of External Rings for the GAP Package homalg
  
  
                               Version 2018.01.07
  
  
                                 September 2015
  
  
                                Mohamed Barakat
  
                                 Simon Goertzen
  
                                Markus Kirschmer
  
                             Markus Lange-Hegermann
  
                                Oleksandr Motsak
  
                                 Max Neunhöffer
  
                                 Daniel Robertz
  
                                Hans Schönemann
  
                                Andreas Steenpaß
  
                                   Vinay Wagh
  
  
  
            (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:    mailto:barakat@mathematik.uni-kl.de
      Homepage: http://www.mathematik.uni-kl.de/~barakat/
      Address:  Department of Mathematics,
                University of Kaiserslautern,
                67653 Kaiserslautern,
                Germany
  
  
  Simon Goertzen
      Email:    mailto: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:    mailto: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:    mailto: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:    mailto: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:    mailto: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:    mailto: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:    mailto: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:    mailto:steenpass@mathematik.uni-kl.de
      Homepage: 
      Address:  Department of Mathematics,
                University of Kaiserslautern,
                67653 Kaiserslautern,
                Germany
  
  
  Vinay Wagh
      Email:    mailto: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.
  
  
  -------------------------------------------------------
  
  
  Contents (RingsForHomalg)
  
  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