  
  
                                 [1X[5XRingsForHomalg[0m[1X[0m
  
  
     [1XRings in External Computer Algebra Systems for the GAP-Package homalg[0m
  
  
                               Version 2009.11.09
  
  
                                 November 2009
  
  
                                Mohamed Barakat
  
                                 Simon Goertzen
  
                                Markus Kirschmer
  
                             Markus Lange-Hegermann
  
                                 Max Neunhöffer
  
                                 Daniel Robertz
  
  
  
            ([13Xthis manual is still under construction[0m)
            This  manual  is  best  viewed  as an [12XHTML[0m document. The
            latest version is available [12Xonline[0m at:
            [7Xhttp://homalg.math.rwth-aachen.de/~barakat/RingsForHomalg/chap0.html[0m
            An   [12Xoffline[0m   version   should   be   included  in  the
            documentation  subfolder of the package. This package is
            part of the [5Xhomalg[0m-project:
            [7Xhttp://homalg.math.rwth-aachen.de/index.php/core-packages/ringsforhomalg[0m
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:barakat@mathematik.uni-kl.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~barakat/[0m
      Address:  Department of Mathematics,
                University of Kaiserslautern,
                67653 Kaiserslautern,
                Germany
  
  
  Simon Goertzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~simon[0m
      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  Markus Kirschmer
      Email:    [7Xmailto:markus.kirschmer@math.rwth-aachen.de[0m
      Homepage: [7Xhttp://www.math.rwth-aachen.de/~Markus.Kirschmer[0m
      Address:  Lehrstuhl  D  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange-hegermann@rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~markus[0m
      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  Max Neunhöffer
      Email:    [7Xmailto:daniel@momo.math.rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~daniel[0m
      Address:  St  Andrews  University, School of Mathematics and Statistics,
                Mathematical  Institute,  North  Haugh,  St Andrews, Fife KY16
                9SS, Scotland, UK
  
  
  Daniel Robertz
      Email:    [7Xmailto:daniel@momo.math.rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~daniel[0m
      Address:  Lehrstuhl  B  für  Mathematik,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany
  
  
  
  -------------------------------------------------------
  [1XCopyright[0m
  ©  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.
  
  
  -------------------------------------------------------
  
  
  [1XContents (RingsForHomalg)[0X
  
  1 Introduction
    1.1 Ring Constructions for Supported External Computer Algebra Systems
      1.1-1 external [5XGAP[0m
      1.1-2 [5XSingular[0m
      1.1-3 [5XMAGMA[0m
      1.1-4 [5XMacaulay2[0m
      1.1-5 [5XSage[0m
      1.1-6 [5XMaple[0m
  2 Installation of the [5XRingsForHomalg[0m 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
  
  
  -------------------------------------------------------
