  
  
                            [1X LocalizeRingForHomalg [101X
  
  
                [1X A Package for Localization of Polynomial Rings [101X
  
  
                                   2022.11-01
  
  
                                23 November 2022
  
  
                                Mohamed Barakat
  
                             Markus Lange-Hegermann
  
                                   Vinay Wagh
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:mohamed.barakat@uni-siegen.de[107X
      Homepage: [7Xhttps://mohamed-barakat.github.io[107X
      Address:  [33X[0;14YWalter-Flex-Str. 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange-hegermann@hs-owl.de[107X
      Homepage: [7Xhttps://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/[107X
      Address:  [33X[0;14YMarkus Lange-Hegermann[133X
                [33X[0;14YHochschule Ostwestfalen-Lippe[133X
                [33X[0;14YLiebigstraße 87[133X
                [33X[0;14Y32657 Lemgo[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
                [33X[0;14YIndia[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y©  2009-2015  by Mohamed Barakat and Markus Lange-Hegermann This 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 (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
