  
  
                             [1X[5XLocalizeRingForHomalg[105X[101X
  
  
              [1XLocalize Commutative [5Xhomalg[105X Rings at Maximal Ideals[101X
  
  
                               Version 2020.10-02
  
  
                                 September 2015
  
  
                                Mohamed Barakat
  
                             Markus Lange-Hegermann
  
                                   Vinay Wagh
  
  
  
            [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/LocalizeRingForHomalg/doc/chap0.html[107X[133X
            [33X[0;10YAn   [12Xoffline[112X   version   should   be   included  in  the
            documentation subfolder of the package.[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
  
  
  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,  RWTH Aachen, Templergraben 64,
                52056 Aachen, Germany[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© 2009-2015 by Mohamed Barakat and Markus Lange-Hegermann[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
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YWe  would  like  to  thank the Aachen forest for being such a nice place for
  jogging.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (LocalizeRingForHomalg)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YWhat is the Role of the [5XLocalizeRingForHomalg[105X Package in the [5Xhomalg[105X
    Project?[133X
    1.2 [33X[0;0YFunctionality[133X
    1.3 [33X[0;0YThe Math Behind This Package[133X
    1.4 [33X[0;0YWhich Ring to Use?[133X
  2 [33X[0;0YInstallation of the [5XLocalizeRingForHomalg[105X Package[133X
  3 [33X[0;0YQuick Start[133X
    3.1 [33X[0;0YLocalization of ℤ[133X
  4 [33X[0;0YLocalize Rings[133X
    4.1 [33X[0;0YCategory and Representations[133X
      4.1-1 IsHomalgLocalRingRep
      4.1-2 IsHomalgLocalRingElementRep
      4.1-3 IsHomalgLocalMatrixRep
    4.2 [33X[0;0YRings: Attributes[133X
      4.2-1 GeneratorsOfMaximalLeftIdeal
      4.2-2 GeneratorsOfMaximalRightIdeal
    4.3 [33X[0;0YOperations and Functions[133X
      4.3-1 AssociatedGlobalRing
      4.3-2 AssociatedGlobalRing
      4.3-3 AssociatedGlobalRing
      4.3-4 Numerator
      4.3-5 Numerator
      4.3-6 Denominator
      4.3-7 Denominator
      4.3-8 Name
      4.3-9 SetMatElm
      4.3-10 AddToMatElm
      4.3-11 MatElmAsString
      4.3-12 MatElm
      4.3-13 Cancel
      4.3-14 LocalizeAt
      4.3-15 LocalizeAtZero
      4.3-16 LocalizePolynomialRingAtZeroWithMora
      4.3-17 HomalgLocalRingElement
      4.3-18 HomalgLocalMatrix
  5 [33X[0;0YExamples[133X
    5.1 [33X[0;0YAn Easy Polynomial Example[133X
    5.2 [33X[0;0YHom(Hom(-,Z128),Z16)[133X
    5.3 [33X[0;0YResidueClass[133X
    5.4 [33X[0;0YTesting the Intersection Formula[133X
  A [33X[0;0YOverview of the [5XLocalizeRingForHomalg[105X Package Source Code[133X
    A.1 [33X[0;0YThe generic Methods[133X
      A.1-1 BasisOfRowModule
      A.1-2 DecideZeroRows
      A.1-3 SyzygiesGeneratorsOfRows
    A.2 [33X[0;0YThe Local Decide Zero trick[133X
      A.2-1 DecideZeroRows
    A.3 [33X[0;0YTools[133X
  
  
  [32X
