  
  
                                 [1X[5XRingsForHomalg[105X[101X
  
  
           [1XDictionaries of External Rings for the [5XGAP[105X Package [5Xhomalg[105X[101X
  
  
                               Version 2020.11-01
  
  
                                 September 2015
  
  
                                Mohamed Barakat
  
                                 Simon Goertzen
  
                                Markus Kirschmer
  
                             Markus Lange-Hegermann
  
                                Oleksandr Motsak
  
                                 Max Neunhöffer
  
                                 Daniel Robertz
  
                                Hans Schönemann
  
                                Andreas Steenpaß
  
                                   Vinay Wagh
  
  
  
            [33X[0;10Y([13Xthis manual is still under construction[113X)[133X
            [33X[0;10YThis  manual  is  best  viewed  as an [12XHTML[112X document. The
            latest version is available [12Xonline[112X at:[133X
            [33X[0;10Y[7Xhttps://homalg-project.github.io/homalg_project/RingsForHomalg/doc/chap0.html[107X[133X
            [33X[0;10YAn   [12Xoffline[112X   version   should   be   included  in  the
            documentation  subfolder of the package. This package is
            part of the [5Xhomalg[105X-project:[133X
            [33X[0;10Y[7Xhttp://homalg.math.rwth-aachen.de/index.php/core-packages/ringsforhomalg[107X[133X
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:mohamed.barakat@uni-siegen.de[107X
      Homepage: [7Xhttps://mohamed-barakat.github.io[107X
      Address:  [33X[0;14YDepartment of Mathematics,[133X
                [33X[0;14YUniversity of Siegen,[133X
                [33X[0;14Y57072 Siegen,[133X
                [33X[0;14YGermany[133X
  
  
  Simon Goertzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~simon/[107X
      Address:  [33X[0;14YLehrstuhl B für Mathematik,[133X
                [33X[0;14YRWTH Aachen,[133X
                [33X[0;14YTemplergraben 64,[133X
                [33X[0;14Y52056 Aachen,[133X
                [33X[0;14YGermany[133X
  
  
  Markus Kirschmer
      Email:    [7Xmailto:markus.kirschmer@math.rwth-aachen.de[107X
      Homepage: [7Xhttp://www.math.rwth-aachen.de/~Markus.Kirschmer/[107X
      Address:  [33X[0;14YLehrstuhl D für Mathematik,[133X
                [33X[0;14YRWTH Aachen,[133X
                [33X[0;14YTemplergraben 64,[133X
                [33X[0;14Y52056 Aachen,[133X
                [33X[0;14YGermany[133X
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange-hegermann@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~markus/[107X
      Address:  [33X[0;14YLehrstuhl B für Mathematik,[133X
                [33X[0;14YRWTH Aachen,[133X
                [33X[0;14YTemplergraben 64,[133X
                [33X[0;14Y52056 Aachen,[133X
                [33X[0;14YGermany[133X
  
  
  Oleksandr Motsak
      Email:    [7Xmailto:motsak@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://www.mathematik.uni-kl.de/~motsak/[107X
      Address:  [33X[0;14YDepartment of Mathematics,[133X
                [33X[0;14YUniversity of Kaiserslautern,[133X
                [33X[0;14Y67653 Kaiserslautern,[133X
                [33X[0;14YGermany[133X
  
  
  Max Neunhöffer
      Email:    [7Xmailto:neunhoef@mcs.st-and.ac.uk[107X
      Homepage: [7Xhttp://www-groups.mcs.st-and.ac.uk/~neunhoef/[107X
      Address:  [33X[0;14YSt Andrews University,[133X
                [33X[0;14YSchool of Mathematics and Statistics,[133X
                [33X[0;14YMathematical Institute,[133X
                [33X[0;14YNorth Haugh,[133X
                [33X[0;14YSt Andrews, Fife KY16 9SS,[133X
                [33X[0;14YScotland, UK[133X
  
  
  Daniel Robertz
      Email:    [7Xmailto:daniel@momo.math.rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~daniel[107X
      Address:  [33X[0;14YLehrstuhl B für Mathematik,[133X
                [33X[0;14YRWTH Aachen,[133X
                [33X[0;14YTemplergraben 64,[133X
                [33X[0;14Y52056 Aachen,[133X
                [33X[0;14YGermany[133X
  
  
  Hans Schönemann
      Email:    [7Xmailto:hannes@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://www.mathematik.uni-kl.de/~hannes/[107X
      Address:  [33X[0;14YDepartment of Mathematics,[133X
                [33X[0;14YUniversity of Kaiserslautern,[133X
                [33X[0;14Y67653 Kaiserslautern,[133X
                [33X[0;14YGermany[133X
  
  
  Andreas Steenpaß
      Email:    [7Xmailto:steenpass@mathematik.uni-kl.de[107X
      Homepage: [7X[107X
      Address:  [33X[0;14YDepartment of Mathematics,[133X
                [33X[0;14YUniversity of Kaiserslautern,[133X
                [33X[0;14Y67653 Kaiserslautern,[133X
                [33X[0;14YGermany[133X
  
  
  Vinay Wagh
      Email:    [7Xmailto:waghoba@gmail.com[107X
      Homepage: [7Xhttp://www.iitg.ernet.in/vinay.wagh/[107X
      Address:  [33X[0;14YE-102, Department of Mathematics,[133X
                [33X[0;14YIndian Institute of Technology Guwahati,[133X
                [33X[0;14YGuwahati, Assam, India.[133X
                [33X[0;14YPIN: 781 039.[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y©  2007-2015  by  Mohamed  Barakat,  Simon Görtzen, Markus Kirschmer, Markus
  Lange-Hegermann,  Oleksandr Motsak, Max Neunhöffer, Daniel Robertz, and Hans
  Schönemann.[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or (at your option) any later version.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (RingsForHomalg)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YRing Constructions for Supported External Computer Algebra Systems[133X
      1.1-1 [33X[0;0Yexternal [5XGAP[105X[133X
      1.1-2 [33X[0;0Y[5XSingular[105X[133X
      1.1-3 [33X[0;0Y[5XMAGMA[105X[133X
      1.1-4 [33X[0;0Y[5XMacaulay2[105X[133X
      1.1-5 [33X[0;0Y[5XSage[105X[133X
      1.1-6 [33X[0;0Y[5XMaple[105X[133X
  2 [33X[0;0YInstallation of the [5XRingsForHomalg[105X Package[133X
  3 [33X[0;0YThe Ring Table[133X
    3.1 [33X[0;0YAn Example for a Ring Table - Singular[133X
      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
  
  
  [32X
