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href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chap5.html" >5</a> <a href="chapA.html" >A</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >LocalizeRingForHomalg</h1 >div >br />Email: <span class="URL" ><a href="mailto:mohamed.barakat@uni-siegen.de" >mohamed.barakat@uni-siegen.de</a></span >br />Homepage: <span class="URL" ><a href="https://mohamed-barakat.github.io " >https://mohamed-barakat.github.io</a></span >br />Address : <br />Walter-Flex-Str. 3<br /> 57072 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:markus.lange-hegermann@hs-owl.de" >markus.lange-hegermann@hs-owl.de</a></span >br />Homepage: <span class="URL" ><a href="https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/ " >https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/</a></span >br />Address : <br />Markus Lange-Hegermann<br /> Hochschule Ostwestfalen-Lippe<br /> Liebigstraße 87<br /> 32657 Lemgo<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:waghoba@gmail.com" >waghoba@gmail.com</a></span >br />Homepage: <span class="URL" ><a href="http://www.iitg.ernet.in/vinay.wagh/ " >http://www.iitg.ernet.in/vinay.wagh/</a></span >br />Address : <br />E-102, Department of Mathematics,<br /> Indian Institute of Technology Guwahati,<br /> Guwahati, Assam, India.<br /> PIN: 781 039.<br /> India<br />"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>er the terms and conditions of the GNU Public License Version 2 or (at your option ) any later version.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7AC2A9FA80501972" >1.1 <span class="Heading" >What is the Role of the <strong class="pkg" >LocalizeRingForHomalg</strong > Package in the <strong class="pkg" >homalg</strong > Project?</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X87F1120883F5B4D0" >1.2 <span class="Heading" >Functionality</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7845DA5685210CC3" >1.3 <span class="Heading" >The Math Behind This Package</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X795ABF907CEB327F" >1.4 <span class="Heading" >Which Ring to Use?</span ></a>span >div >div >div class="ContChap" ><a href="chap2.html#X7E6144A47929DD91" >2 <span class="Heading" >Installation of the <strong class="pkg" >LocalizeRingForHomalg</strong > Package</span ></a>div >div class="ContChap" ><a href="chap3.html#X7EB860EC84DFC71E" >3 <span class="Heading" >Quick Start</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X799572BF810091BC" >3.1 <span class="Heading" >Localization of ℤ</span ></a>span >div >div >div class="ContChap" ><a href="chap4.html#X86CBDDB082295E5F" >4 <span class="Heading" >Localize Rings</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X826B3EF37FB188A8" >4.1 <span class="Heading" >Category and Representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7AEE9D7F85CD25DD" >4.1-1 IsHomalgLocalRingRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E2AD9FF82990735" >4.1-2 IsHomalgLocalRingElementRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80AB357F7883ACF3" >4.1-3 IsHomalgLocalMatrixRep</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X867290E7847A5101" >4.2 <span class="Heading" >Rings: Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EAE00247B717A0F" >4.2-1 GeneratorsOfMaximalLeftIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X85BA4850780569D7" >4.2-2 GeneratorsOfMaximalRightIdeal</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X81CFB50085A4E12F" >4.3 <span class="Heading" >Operations and Functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D8C5E8B8533EE2D" >4.3-1 AssociatedGlobalRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8612432F81364A90" >4.3-2 AssociatedGlobalRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X78AE3B5187FC5B24" >4.3-3 AssociatedGlobalRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X86B86F85831145D0" >4.3-4 Numerator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8613D7A27D3D770D" >4.3-5 Numerator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83E87130831148A4" >4.3-6 Denominator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X863DB91A7DEDEA22" >4.3-7 Denominator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7FA0CC577E97B6E8" >4.3-8 Name</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80F936B786454DD0" >4.3-9 SetMatElm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X87689354873E0B14" >4.3-10 AddToMatElm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8789D7998407AD36" >4.3-11 MatElmAsString</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EFD740F87ADB6E0" >4.3-12 MatElm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F0196827D195F88" >4.3-13 Cancel</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E4E70FE82978F9C" >4.3-14 LocalizeAt</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D910AA785CEED34" >4.3-15 LocalizeAtZero</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F790F3B852C1A5C" >4.3-16 LocalizePolynomialRingAtZeroWithMora</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8741B0AE787624CB" >4.3-17 HomalgLocalRingElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X808317A88773E967" >4.3-18 HomalgLocalMatrix</a></span >div ></div >div >div class="ContChap" ><a href="chap5.html#X7A489A5D79DA9E5C" >5 <span class="Heading" >Examples</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X8426A658837B4911" >5.1 <span class="Heading" >An Easy Polynomial Example</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7820475F7C884EA5" >5.2 <span class="Heading" >Hom(Hom(-,Z128),Z16)</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7CC8EA507E7AABA4" >5.3 <span class="Heading" >ResidueClass</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7958E7417BB312F0" >5.4 <span class="Heading" >Testing the Intersection Formula</span ></a>span >div >div >div class="ContChap" ><a href="chapA.html#X7C7697867CBF79C9" >A <span class="Heading" >Overview of the <strong class="pkg" >LocalizeRingForHomalg</strong > Package Source Code </span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA.html#X87807E467C364A00" >A.1 <span class="Heading" >The generic Methods</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA.html#X7B04DAB47BAB9165" >A.1-1 BasisOfRowModule</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA.html#X8196F11E7FD3201C" >A.1-2 DecideZeroRows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA.html#X7B1B3662863726EE" >A.1-3 SyzygiesGeneratorsOfRows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA.html#X85822F1B7E006A87" >A.2 <span class="Heading" >The Local Decide Zero trick</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA.html#X790256E88417752F" >A.2-1 DecideZeroRows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA.html#X8508AEF8845565A1" >A.3 <span class="Heading" >Tools</span ></a>span >div >div >div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a 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