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/a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chapA_mj.html" >A</a> <a href="chapB_mj.html" >B</a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >GradedRingForHomalg</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:gutsche@mathematik.uni-siegen.de" >gutsche@mathematik.uni-siegen.de</a></span >br />Homepage: <span class="URL" ><a href="https://sebasguts.github.io " >https://sebasguts.github.io</a></span >br />Address : <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57072 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:markus.kischmer@math.rwth-aachen.de" >markus.kischmer@math.rwth-aachen.de</a></span >br />Homepage: <span class="URL" ><a href="http://www.math.rwth-aachen.de/~Markus.Kirschmer/ " >http://www.math.rwth-aachen.de/~Markus.Kirschmer/</a></span >br />Address : <br />Markus Kirschmer<br /> Lehrstuhl D fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:sebastian.jambor@rwth-aachen.de" >sebastian.jambor@rwth-aachen.de</a></span >br />Homepage: <span class="URL" ><a href="http://wwwb.math.rwth-aachen.de/~sebastian/ " >http://wwwb.math.rwth-aachen.de/~sebastian/</a></span >br />Address : <br />Sebastian Jambor<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<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:daniel@momo.math.rwth-aachen.de" >daniel@momo.math.rwth-aachen.de</a></span >br />Homepage: <span class="URL" ><a href="http://wwwb.math.rwth-aachen.de/~daniel/ " >http://wwwb.math.rwth-aachen.de/~daniel/</a></span >br />Address : <br />Daniel Robertz<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X7F7255BA7A43157E" >1.1 <span class="Heading" >What is the Role of the <strong class="pkg" >GradedRingForHomalg</strong > Package instrong class="pkg" >homalg</strong > Project?</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X87F1120883F5B4D0" >1.2 <span class="Heading" >Functionality</span ></a>span >div >div >div class="ContChap" ><a href="chap2_mj.html#X83CA25F97F1EECDB" >2 <span class="Heading" >Installation of the <strong class="pkg" >GradedRingForHomalg</strong > Package</span ></a>div >div class="ContChap" ><a href="chap3_mj.html#X810D68A7794474F9" >3 <span class="Heading" >Graded Rings</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7A16AC227F0B7E6B" >3.1 <span class="Heading" >Graded Rings: Category and Representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8025623B822D44AF" >3.1-1 IsHomalgGradedRingRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84BC7F817BF737F7" >3.1-2 IsHomalgGradedRingElementRep</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8538A7C985FE0E46" >3.2 <span class="Heading" >Graded Rings: Constructors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X823140CE8286BA90" >3.2-1 HomalgGradedRingElement</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7CA805077B75EAAD" >3.3 <span class="Heading" >Graded Rings: Attributes and Properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79649FC47A744BD2" >3.3-1 DegreeGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X826C131D83796CC5" >3.3-2 CommonNonTrivialWeightOfIndeterminates</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E43637F8431FB69" >3.3-3 WeightsOfIndeterminates</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X807A4268816DD69D" >3.3-4 IsHomogeneousRingElement</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7B86A3DD7D2CE35F" >3.4 <span class="Heading" >Graded Rings: Operations and Functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DA1D14F87DE72D8" >3.4-1 UnderlyingNonGradedRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8708576B84997122" >3.4-2 UnderlyingNonGradedRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83971F1879017E3D" >3.4-3 Name</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X840864B38184FF3E" >3.4-4 HomogeneousPartOfRingElement</a></span >div ></div >div >div class="ContChap" ><a href="chap4_mj.html#X81274D247D293332" >4 <span class="Heading" >Homogeneous Matrices</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7912A7EE7DD9C130" >4.1 <span class="Heading" >Homogeneous Matrices: Category and Representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X860DABC0806C4064" >4.1-1 IsHomalgMatrixOverGradedRingRep</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7E3D72117F84D517" >4.2 <span class="Heading" >Homogeneous Matrices: Constructors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7AC02E03868CB664" >4.2-1 MatrixOverGradedRing</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7C1C5AA2813F4F73" >4.3 <span class="Heading" >Homogeneous Matrices: Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X8608086E82701204" >4.3-1 DegreesOfEntries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X86C3DD8479FDDB36" >4.3-2 NonTrivialDegreePerRow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X801EBD4D7DAB0672" >4.3-3 NonTrivialDegreePerColumn</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B109D738475FED4" >4.3-4 HomogeneousPartOfMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B28E6B97D1A5E09" >4.3-5 IsMatrixOverGradedRingWithHomogeneousEntries</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X81897DD8835ACE8C" >4.4 <span class="Heading" >Homogeneous Matrices: Operations and Functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7DC25A5E83DC3E85" >4.4-1 UnderlyingNonGradedRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7D0D1E1E784C3BC7" >4.4-2 SetMatElm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B56EC5E8545C1B6" >4.4-3 AddToMatElm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X865E51967E6D0AD3" >4.4-4 MatElmAsString</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X8028986083BEC896" >4.4-5 MatElm</a></span >div ></div >div >div class="ContChap" ><a href="chapA_mj.html#X7B2993CB7B012115" >A <span class="Heading" >The Matrix Tool Operations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7988F0AF7D87FD23" >A.1 <span class="Heading" >The Tool Operations <em >without</em > a Fallback Method</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7912E42C81296637" >A.2 <span class="Heading" >The Tool Operations with a Fallback Method</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X84C78C6B7C0890BF" >A.2-1 MonomialMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X7F9F9C978703E871" >A.2-2 RandomMatrixBetweenGradedFreeLeftModules</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X82E813D982331C0B" >A.2-3 RandomMatrixBetweenGradedFreeRightModules</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X7EA1DC07822DE322" >A.2-4 Diff</a></span >div ></div >div >div class="ContChap" ><a href="chapB_mj.html#X78C55DF7875560DD" >B <span class="Heading" >Overview of the <strong class="pkg" >GradedRingForHomalg</strong > Package Source Code </span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X87807E467C364A00" >B.1 <span class="Heading" >The generic Methods</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7D9FBBDE794DE447" >B.1-1 BasisOfRowModule</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X84C649FA7C820D49" >B.1-2 DecideZeroRows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X87D2B8748076B5DD" >B.1-3 SyzygiesGeneratorsOfRows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X8508AEF8845565A1" >B.2 <span class="Heading" >Tools</span ></a>span >div >div >div class="ContChap" ><a href="chapBib_mj.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a 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