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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="chap6.html" >6 </a> <a href="chapA.html" >A</a> <a href="chapB.html" >B</a> <a href="chapC.html" >C</a> <a href="chapD.html" >D</a> <a href="chapE.html" >E</a> <a href="chapF.html" >F</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="chapBib.html" >[Previous Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chapInd_mj.html" >[MathJax on]</a></p>"X83A0356F839C696F" name="X83A0356F839C696F" ></a></p>div class="index" >strong class="pkg" >MatricesForHomalg</strong > <a href="chap0.html#X8537FEB07AF2BEC8" >.-1 </a> <br />code class="func" >\*</code >, copy a matrix over a different ring <a href="chap5.html#X81225377833C4644" >5 .2 -11 </a> <br />"chap5.html#X81225377833C4644" >5 .2 -11 </a> <br "chap5.html#X7F5961D78754157B" >5 .5 -22 </a> <br />"chap5.html#X7D1A074278B415BE" >5 .5 -19 </a> <br />code class="func" >\+</code >, for matrices <a href="chap5.html#X87C773DA85B21ADF" >5 .5 -20 </a> <br />code class="func" >\-</code >, for matrices <a href="chap5.html#X784B57617B24208C" >5 .5 -21 </a> <br />code class="func" >\/</code >, constructor for residue class rings <a href="chap3.html#X85D9DDE384304BAB" >3 .2 -2 </a> <br />code class="func" >\=</code >, for matrices <a href="chap5.html#X7E2074A77AFF518A" >5 .5 -23 </a> <br />code class="func" >AddMat</code >, homalgTable entry <a href="chapB.html#X7B0B12F080A90039" >B.1 -17 </a> <br />"chapD.html#X83E1AEC781AE1274" >D.2 -15 </a> <br />code class="func" >AffineDegree</code > <a href="chap5.html#X87C428A079000336" >5 .4 -21 </a> <br />code class="func" >AffineDimension</code > <a href="chap5.html#X7BC36CC67CB09858" >5 .4 -20 </a> <br code class="func" >AreEqualMatrices</code >, homalgTable entry <a href="chapB.html#X7871FE5478BFC167" >B.2 -1 </a> <br />"chapD.html#X848EB509816E8A7D" >D.3 -1 </a> <br />code class="func" >AreUnitsCentral</code > <a href="chap3.html#X781617F678CC0BA8" >3 .3 -54 </a> <br code class="func" >AssociatedGradedRing</code > <a href="chap3.html#X826BE1E87EE023B2" >3 .4 -28 </a> <br />code class="func" >BasisAlgorithmRespectsPrincipalIdeals</code > <a href="chap3.html#X803259617B5F89AE" >3 .3 -53 </a> <br />code class="func" >BasisOfColumnModule</code >, for matrices <a href="chap5.html#X868CDA327D6C8DDC" >5 .5 -29 </a> <br />"chapD.html#X7F2B3332793FACA3" >D.1 -2 </a> <br />code class="func" >BasisOfColumns</code >, for matrices <a href="chap5.html#X83A5B51980FFDE53" >5 .5 -45 </a> <br />"chap5.html#X83A5B51980FFDE53" >5 .5 -45 </a> <br />code class="func" >BasisOfColumnsCoeff</code >, for matrices <a href="chap5.html#X7BBC885F7C24DEC2" >5 .5 -41 </a> <br />"chapD.html#X7D2E9D797877FFBD" >D.1 -8 </a> <br />code class="func" >BasisOfRowModule</code >, for matrices <a href="chap5.html#X80ADBE0D82CC6E85" >5 .5 -28 </a> <br />"chapD.html#X7AB980C5791BA204" >D.1 -1 </a> <br />code class="func" >BasisOfRows</code >, for matrices <a href="chap5.html#X81ABDA3E7D94C661" >5 5 -44 </a> <br />"chap5.html#X81ABDA3E7D94C661" >5 .5 -44 </a> <br />code class="func" >BasisOfRowsCoeff</code >, for matrices <a href="chap5.html#X7D9DEC6081AF0003" >5 .5 -40 </a> <br />"chapD.html#X78BC2E8E7A78CC82" >D.1 -7 </a> <br />code class="func" >CanBeUsedToDecideZero</code > <a href="chap6.html#X835DF250790EF863" >6 .3 1 </a> <br />code class="func" >CertainColumns</code >, for matrices <a href="chap5.html#X8256AF2A840B19C4" >5 .5 -9 </a> <br />"chapB.html#X78EADFC67D17CF04" >B.1 -8 </a> <br />"chapD.html#X84CBE51981BA2C77" >D.2 -8 </a> <br />code class="func" >CertainRows</code >, for matrices <a href="chap5.html#X7CF5CE79796001F6" >5 5 -8 </a> <br />"chapB.html#X7B6FC3267CD9EE9D" >B.1 -7 </a> <br />"chapD.html#X7C5B29A37B13A53D" >D.2 -7 </a> <br />code class="func" >CoefficientsOfNumeratorOfHilbertPoincareSeries</code > <a href="chap5.html#X7938E13A7EF4ADB1" >5 .4 -15 </a> <br />code class="func" >CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries</code > <a href="chap5.html#X7809E0507E882674" >5 .4 -14 </a> <br />code class="func" >CoefficientsRing</code > <a href="chap3.html#X8235D10781BE8003" >3 .4 -20 </a> <br />code class="func" >CoefficientsWithGivenMonomials</code >, for two homalg matrices <a href="chap5.html#X7EEFD7887E96714F" >5 .5 -64 </a> <br />"chapB.html#X8450E904787CBD35" >B.1 -24 </a> <br />code class="func" >CoercedMatrix</code >, copy a matrix over a different ring <a href="chap5.html#X7C4E49D287011DCD" >5 .2 -12 </a> <br />"chap5.html#X7C4E49D287011DCD" >5 .2 12 </a> <br />code class="func" >ColumnRankOfMatrix</code > <a href="chap5.html#X7C61862E81CABD51" >5 .4 -11 </a> <br />code class="func" >Compose</code >, homalgTable entry <a href="chapB.html#X7D491D957E63C3A4" >B.1 -19 </a> <br />"chapD.html#X875447A686949D59" >D.2 -17 </a> <br />code class="func" >ConstantTermOfHilbertPolynomialn</code > <a href="chap5.html#X791B772A7E368A88" >5 .4 -23 </a> <br />code class="func" >ConstructorForHomalgMatrices</code > <a href="chap3.html#X80504BE983BD1A70" >3 .4 -5 </a> <br />code class="func" >ContainsAField</code > <a href="chap3.html#X84F3040687E68338" >3 .3 -3 </a> <br />code class="func" >ConvertColumnToMatrix</code >, for matrices <a href="chap5.html#X853EA6C87EDDF6EF" >5 .5 -13 </a> <br />code class="func" >ConvertMatrixToColumn</code >, for matrices <a href="chap5.html#X84C7C1D07DB6FBAA" >5 .5 -15 </a> <br />code class="func" >ConvertMatrixToRow</code >, for matrices <a href="chap5.html#X7ED5C86379A647F2" >5 .5 -14 </a> <br />code class="func" >ConvertRowToMatrix</code >, for matrices <a href="chap5.html#X7E61390E79B663E8" >5 .5 -12 </a> <br />code class="func" >CoordinateRingOfGraph</code >, for ring maps <a href="chap4.html#X785155EE844A98BD" >4 .4 -4 </a> <br />code class="func" >DecideZero</code >, for matrices and relations <a href="chap5.html#X85C980288304B4AC" >5 .5 -46 </a> <br />code class="func" >DecideZeroColumns</code >, for pairs of matrices <a href="chap5.html#X86C97DBB787BAD6D" >5 .5 -31 </a> <br />"chapD.html#X841426A87A1A20E4" >D.1 -4 </a> <br />code class="func" >DecideZeroColumnsEffectively</code >, for pairs of matrices <a href="chap5.html#X7A06BF7779830815" >5 .5 -43 </a> <br />"chapD.html#X7B68B9F27BC02520" >D.1 -10 </a> <br />code class="func" >DecideZeroRows</code >, for pairs of matrices <a href="chap5.html#X7F851EC7861170D1" >5 .5 -30 </a> <br />"chapD.html#X83E072E1790A7D38" >D.1 -3 </a> <br />code class="func" >DecideZeroRowsEffectively</code >, for pairs of matrices <a href="chap5.html#X8513963C84A9F8CB" >5 .5 -42 </a> <br />"chapD.html#X7F10DC697D2B828D" >D.1 -9 </a> <br />code class="func" >DegreeOfMorphism</code >, for ring maps <a href="chap4.html#X7C4F3F0F82C6EB88" >4 .4 -3 </a> <br />code class="func" >Determinant</code >, homalgTable entry <a href="chapB.html#X80A573257D7F2E1A" >B.1 -23 </a> <br />"chapD.html#X80831B287AB565BA" >D.2 -21 </a> <br />code class="func" >DeterminantMat</code > <a href="chap5.html#X83045F6F82C180E1" >5 .4 -3 </a> <br />code class="func" >DiagMat</code >, for a homalg ring and a list of homalg matrices <a href="chap5.html#X7C7830BE847D84B4" >5 .5 -16 </a> <br />"chapB.html#X86C5B86981FA1F9A" >B.1 -13 </a> <br />"chapD.html#X802BEBF5790D4167" >D.2 -11 </a> <br />code class="func" >DualKroneckerMat</code >, for matrices <a href="chap5.html#X7ECF744B7DE82BED" >5 .5 -18 </a> <br />"chapB.html#X87E0747D7FEEAC76" >B.1 -15 </a> <br />"chapD.html#X7E996A50863FE76C" >D.2 -13 </a> <br />code class="func" >ElementaryRank</code > <a href="chap3.html#X79BCB23D873268CB" >3 .4 -26 </a> <br />code class="func" >Eliminate</code > <a href="chap5.html#X781B1C0C80529B09" >5 .5 -27 </a> <br />code class="func" >Eval</code >, for matrices created with AddMat <a href="chapC.html#X85971C16868BD83C" >C.4 -18 </a> <br />"chapC.html#X835F6F2E7D590F3D" >C.4 -11 </a> <br "chapC.html#X852DCBD57A742FA5" >C.4 -10 </a> <br />"chapC.html#X848FE4F07BAF89DB" >C.4 -21 </a> <br />"chapC.html#X87BF7FD083D0EE88" >C.4 -9 </a> <br />"chapC.html#X7F7682FC86F602C2" >C.4 -20 </a> <br />"chapC.html#X7FD68F43831046B6" >C.4 -14 </a> <br />"chapC.html#X78ADE5C879583E7B" >C.4 -16 </a> <br />"chapC.html#X78CCA57B84E51834" >C.4 4 </a> <br />"chapC.html#X7B619CA885024F0F" >C.4 -2 </a> <br />"chapC.html#X7EEAADA6807A5A45" >C.4 -1 </a> <br />"chapC.html#X7EADAA3180A84318" >C.4 -3 </a> <br />"chapC.html#X7928991E8768FA72" >C.4 -7 </a> <br />"chapC.html#X84F45FB4854A079C" >C.4 -15 </a> <br />"chapC.html#X8362669D87FD667B" >C.4 -5 </a> <br "chapC.html#X7B68797C7EA79B10" >C.4 -17 </a> <br />"chapC.html#X84D72DF482F70AD5" >C.4 -6 </a> <br />"chapC.html#X86F848318791595C" >C.4 -19 </a> <br />"chapC.html#X78D5359480EFC5AC" >C.4 -8 </a> <br />"chapC.html#X7EDE6095820F8128" >C.4 -13 </a> <br "chapC.html#X7F35A61C8522A1B0" >C.4 -12 </a> <br />code class="func" >GeneralLinearRank</code > <a href="chap3.html#X792D56C278E346B1" >3 .4 -25 </a> <br />code class="func" >GenerateSameColumnModule</code >, for pairs of matrices <a href="chap5.html#X867A947682754A9A" >5 .5 -60 </a> <br />code class="func" >GenerateSameRowModule</code >, for pairs of matrices <a href="chap5.html#X82B2C4987D6D5BD3" >5 .5 -59 </a> <br />code class="func" >GetColumnIndependentUnitPositions</code >, for matrices <a href="chap5.html#X85887BBB86F0A08B" >5 .5 -24 </a> <br />"chapB.html#X7BCBACDB79C96FBF" >B.2 -6 </a> <br />code class="func" >GetRowIndependentUnitPositions</code >, for matrices <a href="chap5.html#X824AB44184DD63B0" >5 .5 -25 </a> <br />"chapB.html#X855C57B6822E7A98" >B.2 -7 </a> <br />code class="func" >GetUnitPosition</code >, for matrices <a href="chap5.html#X7A1969A17979FC49" >5 .5 -26 </a> <br />"chapB.html#X876495AA79063CDE" >B.2 -8 </a> <br />code class="func" >GlobalDimension</code > <a href="chap3.html#X7D511B3E7A50AB2A" >3 .4 -24 </a> <br code class="func" >HasInvariantBasisProperty</code > <a href="chap3.html#X81269E1881D45163" >3 .3 -21 </a> <br />code class="func" >HilbertPoincareSeries</code > <a href="chap5.html#X7B93B7D082A50E61" >5 .4 18 </a> <br />code class="func" >HilbertPolynomial</code > <a href="chap5.html#X84299BAB807A1E13" >5 .4 -19 </a> <br />code class="func" >HomalgColumnVector</code >, constructor for matrices with a single column <a href="chap5.html#X871AF271843FF2B5" >5 .2 -9 </a> <br />code class="func" >HomalgDiagonalMatrix</code >, constructor for diagonal matrices <a href="chap5.html#X872D39C678D0C4AE" >5 .2 -10 </a> <br />code class="func" >HomalgIdentityMatrix</code >, constructor for identity matrices <a href="chap5.html#X83266B9D7BE740D8" >5 .2 -4 </a> <br />code class="func" >HomalgInitialIdentityMatrix</code >, constructor for initial quadratic matrices with ones on the diagonal <a href="chap5.html#X7CB77009868D369A" >5 .2 -2 </a> <br />code class="func" >HomalgInitialMatrix</code >, constructor for initial matrices filled with zeros <a href="chap5.html#X86D290B084AC6638" >5 .2 -1 </a> <br />code class="func" >HomalgMatrix</code >, constructor for matrices using a list <a href="chap5.html#X864ACCB08094F0B7" >5 .2 -6 </a> <br />"chap5.html#X864ACCB08094F0B7" >5 .2 -6 </a> <br />"chap5.html#X864ACCB08094F0B7" >5 .2 -6 </a> <br />"chap5.html#X864ACCB08094F0B7" >5 .2 -6 </a> <br />"chap5.html#X864ACCB08094F0B7" >5 .2 -6 </a> <br />code class="func" >HomalgMatrixListList</code >, constructor for matrices using a listlist with given dimensions <a href="chap5.html#X8246E1D17F96DAE7" >5 .2 -7 </a> <br />code class="func" >homalgMode</code > <a href="chapE.html#X7D07F29F7EB515EE" >E.2 -1 </a> <br />code class="func" >HomalgRing</code >, for matrices <a href="chap5.html#X81BBF79C79C3B6DF" >5 .5 -1 </a> <br />code class="func" >HomalgRingOfIntegers</code >, constructor for the integers <a href="chap3.html#X78AC74CB802A8A49" >3 .2 -1 </a> <br />"chap3.html#X78AC74CB802A8A49" >3 .2 -1 </a> <br />code class="func" >HomalgRowVector</code >, constructor for matrices with a single row <a href="chap5.html#X7B127B5584CD012D" >5 .2 -8 </a> <br />code class="func" >homalgTable</code > <a href="chap3.html#X7AFD26D480AA9323" >3 .4 -2 </a> <br />code class="func" >HomalgVoidMatrix</code >, constructor for void matrices <a href="chap5.html#X7D2E3472879E28AB" >5 .2 -5 </a> <br />code class="func" >HomalgZeroMatrix</code >, constructor for zero matrices <a href="chap5.html#X8309EB7B86953A23" >5 .2 -3 </a> <br />code class="func" >IdentityMatrix</code >, homalgTable entry <a href="chapB.html#X87BFF3567DEEBEF4" >B.1 -4 </a> <br />"chapD.html#X811B306C81435D87" >D.2 -4 </a> <br />code class="func" >IndeterminateAntiCommutingVariablesOfExteriorRing</code > <a href="chap3.html#X7C15E6647945C0E3" >3 .4 -17 </a> <br />code class="func" >IndeterminateCoordinatesOfRingOfDerivations</code > <a href="chap3.html#X7F4A050A87C042E5" >3 .4 -13 </a> <br />code class="func" >IndeterminateDerivationsOfRingOfDerivations</code > <a href="chap3.html#X78776EBA7DC179B4" >3 .4 -15 </a> <br />code class="func" >IndeterminatesOfExteriorRing</code > <a href="chap3.html#X7BBEF7097B459D33" >3 .4 -19 </a> <br />code class="func" >IndeterminatesOfPolynomialRing</code > <a href="chap3.html#X80D585E1793D4552" >3 .4 -11 </a> <br />code class="func" >InitialIdentityMatrix</code >, homalgTable entry for initial identity matrices <a href="chapB.html#X84179BE87E7DCE76" >B.1 -2 </a> <br />"chapD.html#X7D0F99857E280142" >D.2 -2 </a> <br />code class="func" >InitialMatrix</code >, homalgTable entry for initial matrices <a href="chapB.html#X7DBA33F083A317B5" >B.1 -1 </a> <br />"chapD.html#X81CD6BAB7CA73AFC" >D.2 -1 </a> <br />code class="func" >Inverse</code >, for homalg ring elements <a href="chap3.html#X8066502785A109B8" >3 .4 -1 </a> <br />code class="func" >Involution</code >, for matrices <a href="chap5.html#X800FA81F7C42BFEA" >5 .5 -6 </a> <br />"chapB.html#X85884C3178473521" >B.1 -5 </a> <br />"chapD.html#X7B322C637FC26E2D" >D.2 -5 </a> <br />code class="func" >IsArtinian</code >, for rings <a href="chap3.html#X7AF81F6383F5CFCA" >3 .3 -37 br />code class="func" >IsAutomorphism</code >, for ring maps <a href="chap4.html#X790E34C5802D0F54" >4 .3 -6 </a> <br />code class="func" >IsBasisOfColumnsMatrix</code > <a href="chap5.html#X7D46613983DC5302" >5 .3 -23 </a> <br />code class="func" >IsBasisOfRowsMatrix</code > <a href="chap5.html#X7F520F89821A8602" >5 .3 -22 br />code class="func" >IsBezoutRing</code > <a href="chap3.html#X7F9F59B5857F19A3" >3 .3 -9 </a> <br />code class="func" >IsCohenMacaulay</code > <a href="chap3.html#X8373421F7E085763" >3 .3 -34 </a> <br code class="func" >IsDedekindDomain</code > <a href="chap3.html#X86C625EF7E417AA6" >3 .3 -13 </a> <br />code class="func" >IsDiagonalMatrix</code > <a href="chap5.html#X7EEC8E768178696E" >5 .3 -13 </a> <br />"chapB.html#X7B6420E88418316B" >B.2 -3 </a> <br />"chapD.html#X87B8E7137DC97A71" >D.3 -3 </a> <br />code class="func" >IsDiscreteValuationRing</code > <a href="chap3.html#X855E560A7F40B2BF" >3 3 -14 </a> <br />code class="func" >IsDivisionRingForHomalg</code > <a href="chap3.html#X805112347CF99F02" >3 3 -6 </a> <br />code class="func" >IsEmptyMatrix</code > <a href="chap5.html#X7BFC9266823F2C15" >5 .3 -12 </a> <br />code class="func" >IsEpimorphism</code >, for ring maps <a href="chap4.html#X849F620C824F4078" >4 .3 -4 </a> <br />code class="func" >IsFieldForHomalg</code > <a href="chap3.html#X86221E0E8416F1CF" >3 .3 -5 </a> <br code class="func" >IsFiniteFreePresentationRing</code > <a href="chap3.html#X7FB92D467B9B6707" >3 .3 -47 </a> <br />code class="func" >IsFreePolynomialRing</code > <a href="chap3.html#X80E0C8B28039B8F0" >3 .3 -15 </a> <br />code class="func" >IsGlobalDimensionFinite</code > <a href="chap3.html#X86558C9F8474DA39" >3 3 -18 </a> <br />code class="func" >IsGorenstein</code > <a href="chap3.html#X83CBA38E81DC4A72" >3 .3 -35 </a> <br />code class="func" >IsHereditary</code > <a href="chap3.html#X7FEB8A337CC92955" >3 .3 -25 </a> <br />code class="func" >IsHermite</code > <a href="chap3.html#X783ACC147A7F82AA" >3 .3 -28 </a> <br />code class="func" >IsHomalgInternalMatrixRep</code > <a href="chap5.html#X7FE94FC47F460E35" >5 .1 -2 </a> <br />code class="func" >IsHomalgInternalRingRep</code > <a href="chap3.html#X8097E89E7B6EF731" >3 1 -4 </a> <br />code class="func" >IsHomalgMatrix</code > <a href="chap5.html#X7B68E1057F5F011F" >5 .1 -1 </a> <br />code class="func" >IsHomalgRing</code > <a href="chap3.html#X85E217C67DD633AB" >3 .1 -1 </a> <br />code class="func" >IsHomalgRingElement</code > <a href="chap3.html#X80A410ED8500DA7E" >3 .1 -3 br />code class="func" >IsHomalgRingMap</code > <a href="chap4.html#X7E084D947E3AEFE6" >4 .1 -1 </a> <br />code class="func" >IsHomalgRingMapRep</code > <a href="chap4.html#X7DFD1CBA83E63737" >4 .1 -3 </a> <br />code class="func" >IsHomalgRingRelations</code > <a href="chap6.html#X7D50E3AD82087AE6" >6 .1 1 </a> <br />code class="func" >IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</code > <a href="chap6.html#X7DECADD683403C65" >6 .1 -2 </a> <br />code class="func" >IsHomalgRingRelationsAsGeneratorsOfRightIdeal</code > <a href="chap6.html#X78746A217FEEB058" >6 .1 -3 </a> <br />code class="func" >IsHomalgRingSelfMap</code > <a href="chap4.html#X87DB79AF83F17FB6" >4 .1 -2 br />code class="func" >IsIdentityMatrix</code >, homalgTable entry <a href="chapB.html#X80C1856D82172268" >B.2 -2 </a> <br />code class="func" >IsIdentityMorphism</code >, for ring maps <a href="chap4.html#X832893897FD3744D" >4 .3 -2 </a> <br />code class="func" >IsInitialIdentityMatrix</code > <a href="chap5.html#X7EE624707ACEC26E" >5 3 -27 </a> <br />code class="func" >IsInitialMatrix</code > <a href="chap5.html#X7E6E51517822CB3F" >5 .3 -26 </a> <br code class="func" >IsInjectivePresentation</code > <a href="chap6.html#X7B9398827AEEA2E6" >6 3 -2 </a> <br />code class="func" >IsIntegersForHomalg</code > <a href="chap3.html#X799A9A9F7A26C6B2" >3 .3 -7 br />code class="func" >IsIntegralDomain</code > <a href="chap3.html#X7EE2F1C187131E19" >3 .3 -24 </a> <br />code class="func" >IsIntegrallyClosedDomain</code > <a href="chap3.html#X79D8752F78215FC1" >3 .3 -10 </a> <br />code class="func" >IsInvertibleMatrix</code > <a href="chap5.html#X856E1D217A47EE8C" >5 .3 -9 </a> <br />code class="func" >IsIsomorphism</code >, for ring maps <a href="chap4.html#X82B9422D7B01BA4A" >4 .3 -5 </a> <br />code class="func" >IsKaplanskyHermite</code > <a href="chap3.html#X86EF914787EB5572" >3 .3 -12 </a> <br />code class="func" >IsKoszul</code > <a href="chap3.html#X7E7AEFBE7801F196" >3 .3 -36 </a> <br />code class="func" >IsLeftArtinian</code > <a href="chap3.html#X7E000F5780A17602" >3 .3 -38 </a> <br />code class="func" >IsLeftFiniteFreePresentationRing</code > <a href="chap3.html#X7B0EE3BF8402793B" >3 .3 -48 </a> <br />code class="func" >IsLeftGlobalDimensionFinite</code > <a href="chap3.html#X7AE1C7297A66F116" >3 .3 -19 </a> <br />code class="func" >IsLeftHereditary</code > <a href="chap3.html#X7D4AC0177C6D85A8" >3 .3 -26 </a> <br />code class="func" >IsLeftHermite</code > <a href="chap3.html#X7A33BCFE7B6C6817" >3 .3 -29 </a> <br />code class="func" >IsLeftInvertibleMatrix</code > <a href="chap5.html#X7A4FA27C80BC42D1" >5 .3 -10 </a> <br />code class="func" >IsLeftNoetherian</code > <a href="chap3.html#X7803DB3A7E6689B6" >3 .3 -32 </a> <br />code class="func" >IsLeftOreDomain</code > <a href="chap3.html#X8528CA397BC76826" >3 .3 -41 </a> <br code class="func" >IsLeftPrincipalIdealRing</code > <a href="chap3.html#X7BF4EFB67DCEBF6D" >3 .3 -44 </a> <br />code class="func" >IsLeftRegular</code > <a href="chap5.html#X7EF95CAD78BDE12F" >5 .3 -7 </a> <br />"chap3.html#X811A01D5803ADCA3" >3 .3 -58 </a> <br />code class="func" >IsLocal</code > <a href="chap3.html#X8758DFD57E83925D" >3 .3 -22 </a> <br />code class="func" >IsLocalizedWeylRing</code > <a href="chap3.html#X7EFB456286B4F9DB" >3 .3 -17 br />code class="func" >IsLowerStairCaseMatrix</code > <a href="chap5.html#X7B3A5DE1860373F0" >5 .3 -20 </a> <br />code class="func" >IsLowerTriangularMatrix</code > <a href="chap5.html#X853A5B988306DBFE" >5 3 -16 </a> <br />code class="func" >IsMinusOne</code > <a href="chap3.html#X85B6710082984863" >3 .3 -55 </a> <br />code class="func" >IsMonic</code >, for homalg ring elements <a href="chap3.html#X7A0A3A927BE3F352" >3 .3 -56 </a> <br />code class="func" >IsMonicUptoUnit</code >, for homalg ring elements <a href="chap3.html#X785EF83B8054D2FF" >3 .3 -57 </a> <br />code class="func" >IsMonomorphism</code >, for ring maps <a href="chap4.html#X87F79EA381E3E34F" >4 .3 -3 </a> <br />code class="func" >IsMorphism</code >, for ring maps <a href="chap4.html#X8555A4DF84C9165B" >4 .3 -1 </a> <br />code class="func" >IsNoetherian</code > <a href="chap3.html#X7AA2911E802BE73D" >3 .3 -31 </a> <br />code class="func" >IsNonZeroRing</code >, for rings <a href="chap3.html#X7F80A53387A0C23D" >3 .3 -2 </a> <br />code class="func" >IsOne</code > <a href="chap5.html#X814D78347858EC13" >5 .3 -2 </a> <br />"chapD.html#X80122FB3846A6BA5" >D.3 -2 </a> <br />code class="func" >IsOreDomain</code > <a href="chap3.html#X8290570679F86CE8" >3 .3 -40 </a> <br />code class="func" >IsPermutationMatrix</code > <a href="chap5.html#X8612CB4A82D6D79E" >5 .3 -4 br />code class="func" >IsPreHomalgRing</code > <a href="chap3.html#X81DC249883163C01" >3 .1 -2 </a> <br />code class="func" >IsPrincipalIdealRing</code > <a href="chap3.html#X85F1485F840E2354" >3 .3 -43 </a> <br />code class="func" >IsRationalsForHomalg</code > <a href="chap3.html#X7C337D0F8413FE38" >3 .3 -4 </a> <br />code class="func" >IsReducedBasisOfColumnsMatrix</code > <a href="chap5.html#X7E6BB540865C0344" >5 .3 -25 </a> <br />code class="func" >IsReducedBasisOfRowsMatrix</code > <a href="chap5.html#X86445AD281024339" >5 .3 -24 </a> <br />code class="func" >IsRegular</code > <a href="chap3.html#X7CF02C4785F0EAB5" >3 .3 -46 </a> <br />"chap3.html#X80A3294C834D8F21" >3 .3 -60 </a> <br />code class="func" >IsResidueClassRingOfTheIntegers</code > <a href="chap3.html#X8548FE4E8283ACC6" >3 .3 -8 </a> <br />code class="func" >IsRightArtinian</code > <a href="chap3.html#X7C34A319827FFDDB" >3 .3 -39 </a> <br code class="func" >IsRightFiniteFreePresentationRing</code > <a href="chap3.html#X839A82AC7D0D7BA1" >3 .3 -49 </a> <br />code class="func" >IsRightGlobalDimensionFinite</code > <a href="chap3.html#X799A94467B8EC416" >3 .3 -20 </a> <br />code class="func" >IsRightHereditary</code > <a href="chap3.html#X7DE025D781FEBD04" >3 .3 -27 </a> <br />code class="func" >IsRightHermite</code > <a href="chap3.html#X830989817DC97403" >3 .3 -30 </a> <br />code class="func" >IsRightInvertibleMatrix</code > <a href="chap5.html#X7E43FDE57E8449B6" >5 3 -11 </a> <br />code class="func" >IsRightNoetherian</code > <a href="chap3.html#X78A93EFA7B677CED" >3 .3 -33 </a> <br />code class="func" >IsRightOreDomain</code > <a href="chap3.html#X7FC7E8317BF9B9CE" >3 .3 -42 </a> <br />code class="func" >IsRightPrincipalIdealRing</code > <a href="chap3.html#X83858198873F7760" >3 .3 -45 </a> <br />code class="func" >IsRightRegular</code > <a href="chap5.html#X87C369D27D6AAF68" >5 .3 -8 </a> <br />"chap3.html#X7E99731F83A41777" >3 .3 -59 </a> <br />code class="func" >IsRingRelationsRep</code > <a href="chap6.html#X86CA83A081B8C8EA" >6 .1 -4 </a> <br />code class="func" >IsScalarMatrix</code > <a href="chap5.html#X7848E6A0783B7428" >5 .3 -14 </a> <br />code class="func" >IsSemiLocalRing</code > <a href="chap3.html#X7AAF0A3178E23B09" >3 .3 -23 </a> <br code class="func" >IsSemiSimpleRing</code > <a href="chap3.html#X847DEBCF872F5175" >3 .3 -51 </a> <br />code class="func" >IsSimpleRing</code > <a href="chap3.html#X8491CBBE862D4FFB" >3 .3 -50 </a> <br />code class="func" >IsSpecialSubidentityMatrix</code > <a href="chap5.html#X7EEE3E9780EBA607" >5 .3 -5 </a> <br />code class="func" >IsStrictLowerTriangularMatrix</code > <a href="chap5.html#X7B0C78AF8056D650" >5 .3 -18 </a> <br />code class="func" >IsStrictUpperTriangularMatrix</code > <a href="chap5.html#X7976C42B7FA905EC" >5 .3 -17 </a> <br />code class="func" >IsSubidentityMatrix</code > <a href="chap5.html#X8672364D79EBCC5D" >5 .3 -6 br />code class="func" >IsSuperCommutative</code > <a href="chap3.html#X842C9ABA807DB431" >3 .3 -52 </a> <br />code class="func" >IsTriangularMatrix</code > <a href="chap5.html#X7BAAE75A8660D7A5" >5 .3 -21 </a> <br />code class="func" >IsUniqueFactorizationDomain</code > <a href="chap3.html#X864BF29E7B5D3305" >3 .3 -11 </a> <br />code class="func" >IsUnitFree</code > <a href="chap5.html#X7813653578F174AB" >5 .3 -3 </a> <br />code class="func" >IsUpperStairCaseMatrix</code > <a href="chap5.html#X81A2C3F67C99A3C2" >5 .3 -19 </a> <br />code class="func" >IsUpperTriangularMatrix</code > <a href="chap5.html#X8740E71C799C0BCC" >5 3 -15 </a> <br />code class="func" >IsVoidMatrix</code > <a href="chap5.html#X802794217F56DE51" >5 .3 -28 </a> <br />code class="func" >IsWeylRing</code > <a href="chap3.html#X850A0EAB7E017D5E" >3 .3 -16 </a> <br />code class="func" >IsZero</code >, for matrices <a href="chap5.html#X858B5AF57D5BC90A" >5 .3 -1 </a> <br />"chap3.html#X7C48437187E668F3" >3 .3 -1 </a> <br />code class="func" >IsZeroMatrix</code >, homalgTable entry <a href="chapB.html#X849BB912798A01EB" >B.1 -20 </a> <br />"chapD.html#X78D7BABE806B82FA" >D.2 -18 </a> <br />code class="func" >KroneckerMat</code >, for matrices <a href="chap5.html#X7CDA5D848468A0AA" >5 .5 -17 </a> <br />"chapB.html#X82202A6A7FAB7174" >B.1 -14 </a> <br />"chapD.html#X85F1DDDB864AF265" >D.2 -12 </a> <br />code class="func" >KrullDimension</code > <a href="chap3.html#X789CF8B778A0C58D" >3 .4 -21 </a> <br />code class="func" >LeftDivide</code >, for pairs of matrices <a href="chap5.html#X7D0EAF527F8514E0" >5 .5 -52 </a> <br />"chap5.html#X86CEB1FC7C358777" >5 .5 -54 </a> <br />code class="func" >LeftGlobalDimension</code > <a href="chap3.html#X8735C56B7BEBC86E" >3 .4 -22 br />code class="func" >LeftInverse</code > <a href="chap5.html#X7EFCE38281AE60F9" >5 .4 -12 </a> <br />"chap5.html#X7FBAA11B8008D936" >5 .5 -2 </a> <br />code class="func" >LeftInverseLazy</code >, for matrices <a href="chap5.html#X7A7E42C179142727" >5 .5 -4 </a> <br />code class="func" >MatrixOfSymbols</code > <a href="chap5.html#X835972A77F02C5BB" >5 .4 -24 </a> <br code class="func" >MinusOne</code > <a href="chap3.html#X810D03AA827BD128" >3 .4 -8 </a> <br />code class="func" >MulMat</code >, homalgTable entry <a href="chapB.html#X828F8C7785EEC3D1" >B.1 -16 </a> <br />"chapD.html#X7A5D229384E9D19C" >D.2 -14 </a> <br />code class="func" >NonZeroColumns</code > <a href="chap5.html#X7F335DCB7B8781E4" >5 .4 -7 </a> <br />code class="func" >NonZeroRows</code > <a href="chap5.html#X7991ED337C73065A" >5 .4 -6 </a> <br />code class="func" >NumberColumns</code > <a href="chap5.html#X847D45BF7F2BC67C" >5 .4 -2 </a> <br />"chapB.html#X7DFA534B7AFA2E17" >B.1 -22 </a> <br />"chapD.html#X79A76B1A7CB57518" >D.2 -20 </a> <br />code class="func" >NumberRows</code > <a href="chap5.html#X7C72971F7D0CA3C8" >5 .4 -1 </a> <br />"chapB.html#X7F4D7FAF821DA1C2" >B.1 -21 </a> <br />"chapD.html#X85CE26418598FACE" >D.2 -19 </a> <br />code class="func" >NumeratorOfHilbertPoincareSeries</code > <a href="chap5.html#X7C44039382DD5D91" >5 .4 -17 </a> <br />code class="func" >One</code >, for homalg rings <a href="chap3.html#X84701329860750C3" >3 .4 -7 </a> <br />code class="func" >PositionOfFirstNonZeroEntryPerColumn</code > <a href="chap5.html#X83B389A97A703E42" >5 .4 -9 </a> <br />"chapB.html#X833B384278492266" >B.2 -10 </a> <br />code class="func" >PositionOfFirstNonZeroEntryPerRow</code > <a href="chap5.html#X7B7A073D7E1FAEA4" >5 .4 -8 </a> <br />"chapB.html#X7F40B57079CF80ED" >B.2 -9 </a> <br />code class="func" >ProductOfIndeterminates</code > <a href="chap3.html#X7CC4312578DC42B6" >3 4 -9 </a> <br />code class="func" >ProjectiveDegree</code > <a href="chap5.html#X82A1B55879AB1742" >5 .4 -22 </a> <br />code class="func" >Range</code >, for ring maps <a href="chap4.html#X7EBE68567900396A" >4 .4 -2 </a> <br />code class="func" >RationalParameters</code > <a href="chap3.html#X7DF4F71C86835DCF" >3 .4 -10 </a> <br />code class="func" >ReducedBasisOfColumnModule</code >, for matrices <a href="chap5.html#X84CED11F7A633BDA" >5 .5 -37 </a> <br />code class="func" >ReducedBasisOfRowModule</code >, for matrices <a href="chap5.html#X82E0FF517DC38040" >5 .5 -36 </a> <br />code class="func" >ReducedSyzygiesGeneratorsOfColumns</code >, for matrices <a href="chap5.html#X8699114D7A865C11" >5 .5 -39 </a> <br />code class="func" >ReducedSyzygiesGeneratorsOfRows</code >, for matrices <a href="chap5.html#X7DE458D67B9B85BF" >5 .5 -38 </a> <br />code class="func" >ReducedSyzygiesOfColumns</code >, for matrices <a href="chap5.html#X8766BBD578557D15" >5 .5 -50 </a> <br />"chap5.html#X8766BBD578557D15" >5 .5 -50 </a> <br />code class="func" >ReducedSyzygiesOfRows</code >, for matrices <a href="chap5.html#X86A798D4850BF9E8" >5 .5 -49 </a> <br />"chap5.html#X86A798D4850BF9E8" >5 .5 -49 </a> <br />code class="func" >RelativeIndeterminateAntiCommutingVariablesOfExteriorRing</code > <a href="chap3.html#X7C63673A80911044" >3 .4 -18 </a> <br />code class="func" >RelativeIndeterminateCoordinatesOfRingOfDerivations</code > <a href="chap3.html#X821FCC287E4FB92F" >3 .4 -14 </a> <br />code class="func" >RelativeIndeterminateDerivationsOfRingOfDerivations</code > <a href="chap3.html#X8522A7987C6483ED" >3 .4 -16 </a> <br />code class="func" >RelativeIndeterminatesOfPolynomialRing</code > <a href="chap3.html#X84CE78E379A34C56" >3 .4 -12 </a> <br />code class="func" >RelativeSyzygiesGeneratorsOfColumns</code >, ResidueClassRing <a href="chapD.html#X852F9FD8837D97A5" >D.1 -12 </a> <br />code class="func" >RelativeSyzygiesGeneratorsOfRows</code >, ResidueClassRing <a href="chapD.html#X7DF62C5D7D2E6A6E" >D.1 -11 </a> <br />code class="func" >RightDivide</code >, for pairs of matrices <a href="chap5.html#X850AEC9C7C00AFF5" >5 .5 -51 </a> <br />"chap5.html#X7A8546EA87E3AE67" >5 .5 -53 </a> <br />code class="func" >RightGlobalDimension</code > <a href="chap3.html#X7E6C5B5781EF78C5" >3 .4 -23 </a> <br />code class="func" >RightInverse</code > <a href="chap5.html#X87614CA48493B63F" >5 .4 -13 </a> <br />"chap5.html#X7AAD17D47839BCAE" >5 .5 -3 </a> <br />code class="func" >RightInverseLazy</code >, for matrices <a href="chap5.html#X7FA3E7617EED7E1E" >5 .5 -5 </a> <br />code class="func" >RingElementConstructor</code > <a href="chap3.html#X816D807781E8F854" >3 .4 -3 </a> <br />code class="func" >RingMap</code >, constructor for ring maps <a href="chap4.html#X7F21AB318507FF83" >4 .2 -1 </a> <br />code class="func" >RowRankOfMatrix</code > <a href="chap5.html#X862841E68674FA2A" >5 .4 -10 </a> <br code class="func" >SafeLeftDivide</code >, for pairs of matrices <a href="chap5.html#X85B64BD47F0379C5" >5 .5 -56 </a> <br />code class="func" >SafeRightDivide</code >, for pairs of matrices <a href="chap5.html#X86DFDD25824E2F35" >5 .5 -55 </a> <br />code class="func" >SimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices</code >, for matrices <a href="chap5.html#X81CDBBBE878DC1E5" >5 .5 -61 </a> <br />code class="func" >SimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix</code >, for matrices <a href="chap5.html#X85DA10C07E7E5A3D" >5 .5 -62 </a> <br />code class="func" >SimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix</code >, for matrices <a href="chap5.html#X79C124318588F37F" >5 .5 -63 </a> <br />code class="func" >Source </code >, for ring maps <a href="chap4.html#X83678DEC78394702" >4 .4 -1 </a> <br />code class="func" >StableRank</code > <a href="chap3.html#X822907CB7919EEF2" >3 .4 -27 </a> <br />code class="func" >SubMat</code >, homalgTable entry <a href="chapB.html#X7FE11AA27AE7D2D7" >B.1 -18 </a> <br />"chapD.html#X79A1C9297BE0C09A" >D.2 -16 </a> <br />code class="func" >SyzygiesGeneratorsOfColumns</code >, for matrices <a href="chap5.html#X86504B757F6DC990" >5 .5 -33 </a> <br />"chap5.html#X7D3FC0CE7B63AAF1" >5 .5 -35 </a> <br />"chapD.html#X7899768C8304A59E" >D.1 -6 </a> <br />code class="func" >SyzygiesGeneratorsOfRows</code >, for matrices <a href="chap5.html#X86ECEA9B7A4AE578" >5 .5 -32 </a> <br />"chap5.html#X84A93458804F16F6" >5 .5 -34 </a> <br />"chapD.html#X80F4836F7F175B12" >D.1 -5 </a> <br />code class="func" >SyzygiesOfColumns</code >, for matrices <a href="chap5.html#X80325CAD7CE56F4F" >5 .5 -48 </a> <br />"chap5.html#X80325CAD7CE56F4F" >5 .5 -48 </a> <br />code class="func" >SyzygiesOfRows</code >, for matrices <a href="chap5.html#X86C93ABD857447F8" >5 .5 -47 </a> <br />"chap5.html#X86C93ABD857447F8" >5 .5 -47 </a> <br />code class="func" >TransposedMatrix</code >, for matrices <a href="chap5.html#X7D0D35B582D9C0B0" >5 .5 -7 </a> <br />"chapB.html#X7AD2EEE680DF472B" >B.1 -6 </a> <br />"chapD.html#X816CBEA6790E0C31" >D.2 -6 </a> <br />code class="func" >TypeOfHomalgMatrix</code > <a href="chap3.html#X7E5426C67AA9A6E5" >3 .4 -4 </a> <br />code class="func" >UnionOfColumns</code >, for a homalg ring, an integer and a list of homalg matrices <a href="chap5.html#X7FF9661D85EC46B1" >5 .5 -11 </a> <br />"chapB.html#X7DF5DB55836D13A7" >B.1 -11 </a> <br />"chapD.html#X862F756A7FC0F0D4" >D.2 -10 </a> <br />code class="func" >UnionOfColumnsPair</code >, homalgTable entry <a href="chapB.html#X8092789C87E37020" >B.1 -12 </a> <br />code class="func" >UnionOfRows</code >, for a homalg ring, an integer and a list of homalg matrices <a href="chap5.html#X7D6D0BDF854C9EBC" >5 .5 -10 </a> <br />"chapB.html#X7DEB535782A3323E" >B.1 -9 </a> <br />"chapD.html#X8510678E8569799E" >D.2 -9 </a> <br />code class="func" >UnionOfRowsPair</code >, homalgTable entry <a href="chapB.html#X86C345CE82AAB220" >B.1 -10 </a> <br />code class="func" >UniqueLeftDivide</code >, for pairs of matrices <a href="chap5.html#X8788CB987A8A18A7" >5 .5 -58 </a> <br />code class="func" >UniqueRightDivide</code >, for pairs of matrices <a href="chap5.html#X7F6BAF8E7F2343EA" >5 .5 -57 </a> <br />code class="func" >UnreducedNumeratorOfHilbertPoincareSeries</code > <a href="chap5.html#X781E2CDB8743B1C6" >5 .4 -16 </a> <br />code class="func" >Zero</code >, for homalg rings <a href="chap3.html#X799B5F797F809EE5" >3 .4 -6 br />code class="func" >ZeroColumns</code > <a href="chap5.html#X870D761F7AB96D12" >5 .4 -5 </a> <br />"chapB.html#X7A469E6D7EA63BB6" >B.2 -5 </a> <br />"chapD.html#X7E78F7D6796C7016" >D.3 -5 </a> <br />code class="func" >ZeroMatrix</code >, homalgTable entry <a href="chapB.html#X785390E38396CAEB" >B.1 -3 </a> <br />"chapD.html#X80393225841391E7" >D.2 -3 </a> <br />code class="func" >ZeroRows</code > <a href="chap5.html#X828225E0857B1FDA" >5 .4 -4 </a> <br />"chapB.html#X872B70367F412945" >B.2 -4 </a> <br />"chapD.html#X7EFC928C7E59CEAE" >D.3 -4 </a> <br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chapBib.html" >[Previous Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a 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="chap6.html" >6 </a> <a href="chapA.html" >A</a> <a href="chapB.html" >B</a> <a href="chapC.html" >C</a> <a href="chapD.html" >D</a> <a href="chapE.html" >E</a> <a href="chapF.html" >F</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html > Messung V0.5 in Prozent 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