<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (NormalizInterface) - Contents</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap0" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</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="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 >NormalizInterface</h1 >strong class="pkg" >GAP</strong > wrapper for Normaliz</h2>div >br />Email: <span class="URL" ><a href="mailto:gutsche@mathematik.uni-siegen.de" >gutsche@mathematik.uni-siegen.de</a></span >br />Email: <span class="URL" ><a href="mailto:mhorn@rptu.de" >mhorn@rptu.de</a></span >br />Homepage: <span class="URL" ><a href="https://www.quendi.de/math " >https://www.quendi.de/math</a></span >br />Address : <br />Fachbereich Mathematik<br /> RPTU Kaiserslautern-Landau<br /> Gottlieb-Daimler-Straße 48<br /> 67663 Kaiserslautern<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:csoeger@uos.de" >csoeger@uos.de</a></span >"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#X86B6D8F583923CB5" >1.1 <span class="Heading" >What is the purpose of the this package?</span ></a>span >div >div >div class="ContChap" ><a href="chap2_mj.html#X86FA580F8055B274" >2 <span class="Heading" >Functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X788BCD4B87853B34" >2.1 <span class="Heading" >Create a NmzCone</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7DBDE20A8515FF5D" >2.1-1 NmzCone</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7D0D9BF983F5DABB" >2.2 <span class="Heading" >Use a NmzCone</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87E0E6967E47394E" >2.2-1 NmzHasConeProperty</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8488EAA478AA3706" >2.2-2 NmzKnownConeProperties</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7AD4C81887308070" >2.2-3 NmzSetVerboseDefault</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84A5129078C5D198" >2.2-4 NmzSetVerbose</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82752899822ED2F0" >2.2-5 NmzCompute</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78ED435078E3E377" >2.2-6 NmzConeProperty</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87C644A6861CFCD9" >2.2-7 NmzPrintConeProperties</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X81EC46D08211949E" >2.3 <span class="Heading" >Cone properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79232A2D7B1CAFC2" >2.3-1 NmzAffineDim</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X872772CB78B4E2E8" >2.3-2 NmzAllGeneratorsTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CCFE4FE84145C13" >2.3-3 NmzAmbientAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D0B2A4978D88CD9" >2.3-4 NmzApproximate</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78CB11547A7EF6C0" >2.3-5 NmzAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F80B01C7F6760B9" >2.3-6 NmzAxesScaling</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X802E37267CCB35EB" >2.3-7 NmzBasicStanleyDec</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C49ED54861542CF" >2.3-8 NmzBasicTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C1A8AE178FC3315" >2.3-9 NmzBigInt</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83485BC4780CA904" >2.3-10 NmzBottomDecomposition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B12EE3D7ED4F9EB" >2.3-11 NmzClassGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E49A40886FF88D1" >2.3-12 NmzCombinatorialAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B2BD880858784A9" >2.3-13 NmzConeDecomposition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C7798F8847FE06F" >2.3-14 NmzCongruences</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7999AC97819BF6EC" >2.3-15 NmzCoveringFace</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CE49A02802DE038" >2.3-16 NmzDefaultMode</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X804F0A437C267569" >2.3-17 NmzDeg1Elements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X81909669839E5AC5" >2.3-18 NmzDehomogenization</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X818A93CB81759F9B" >2.3-19 NmzDescent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X85F7F7287C5F7E11" >2.3-20 NmzDistributedComp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82FF327E7D6109A7" >2.3-21 NmzDualFVector</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83E125847D34529B" >2.3-22 NmzDualFaceLattice</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X820B11A286A19E8E" >2.3-23 NmzDualIncidence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83D8B1647A5E4C6E" >2.3-24 NmzDualMode</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79C452757E8686FB" >2.3-25 NmzDynamic</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7A2C84F0822015AF" >2.3-26 NmzEhrhartQuasiPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X796F86A078BB2E13" >2.3-27 NmzEhrhartSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D96A251809EC941" >2.3-28 NmzEmbeddingDimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7DA58BB08657810D" >2.3-29 NmzEquations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X865B138A80CD79B9" >2.3-30 NmzEuclideanAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87919D897817F584" >2.3-31 NmzEuclideanIntegral</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E55AF3678F4EC46" >2.3-32 NmzEuclideanVolume</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8606AB57813797E5" >2.3-33 NmzExcludedFaces</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79E3505A782163F4" >2.3-34 NmzExploitAutomsVectors</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X862AFE757A5DD829" >2.3-35 NmzExploitIsosMult</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BEA1D007DE03002" >2.3-36 NmzExternalIndex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X855CB6B5820F28FC" >2.3-37 NmzExtremeRays</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FB459597A3A1787" >2.3-38 NmzExtremeRaysFloat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8084862B7E5EB685" >2.3-39 NmzFVector</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87916CA882C9B4CC" >2.3-40 NmzFaceLattice</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X836BB3CE7C97B141" >2.3-41 NmzFixedPrecision</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CA11F1787307478" >2.3-42 NmzFullConeDynamic</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8782055C7F394B20" >2.3-43 NmzGeneratorOfInterior</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87E77F007E199FCA" >2.3-44 NmzGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83DC150E7C7A3AF7" >2.3-45 NmzGrading</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X812A9E21823DCC42" >2.3-46 NmzGradingDenom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X804F6DF27FA1FD5E" >2.3-47 NmzGradingIsPositive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86D252817DDF4689" >2.3-48 NmzHSOP</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7A11497282B4831D" >2.3-49 NmzHilbertBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8405B3167F4ED99C" >2.3-50 NmzHilbertQuasiPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FC3F68185D5E220" >2.3-51 NmzHilbertSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X81B24C9187682ACC" >2.3-52 NmzIncidence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8491B203791F0526" >2.3-53 NmzInclusionExclusionData</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C6C9DAE843CC8B4" >2.3-54 NmzInputAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83425BF67C13B187" >2.3-55 NmzIntegerHull</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E2B4A657D716227" >2.3-56 NmzIntegral</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C73E21E87B75DDB" >2.3-57 NmzInternalIndex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X847176FE85D292D5" >2.3-58 NmzIsDeg1ExtremeRays</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7846999882E09FBC" >2.3-59 NmzIsDeg1HilbertBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84A71139794B76F9" >2.3-60 NmzIsEmptySemiOpen</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X848E74AA86BAA5B9" >2.3-61 NmzIsGorenstein</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82EF925E7CF91FDD" >2.3-62 NmzIsInhomogeneous</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8315ACBC797CF531" >2.3-63 NmzIsIntegrallyClosed</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X863887AA852ACA6F" >2.3-64 NmzIsPointed</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X80CAC21686223F6F" >2.3-65 NmzIsReesPrimary</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7EEE4D2F86463F21" >2.3-66 NmzIsTriangulationNested</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8159CF6885A164E1" >2.3-67 NmzIsTriangulationPartial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84DB162079D98024" >2.3-68 NmzKeepOrder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X870368D0819E8170" >2.3-69 NmzLatticePointTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78E297A8795F0074" >2.3-70 NmzLatticePoints</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79D80E6081737899" >2.3-71 NmzMaximalSubspace</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CDCEC40814035A8" >2.3-72 NmzModuleGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X871D59BC83D7CADA" >2.3-73 NmzModuleGeneratorsOverOriginalMonoid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X81CD718A78E72475" >2.3-74 NmzModuleRank</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BEE5536807AD064" >2.3-75 NmzMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D14D7D17BC476ED" >2.3-76 NmzNoBottomDec</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8256AFFA7AD3DB1D" >2.3-77 NmzNoDescent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E2A036A78414435" >2.3-78 NmzNoGradingDenom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B6047317EDBB5F2" >2.3-79 NmzNoLLL</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7ADD635981E04C15" >2.3-80 NmzNoNestedTri</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X802E5F2C84870D9A" >2.3-81 NmzNoPeriodBound</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X844FFA72847DEF0D" >2.3-82 NmzNoProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X784B65D984012D39" >2.3-83 NmzNoRelax</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86F5AD227B0A8DAB" >2.3-84 NmzNoSignedDec</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8274F8F57816A9B5" >2.3-85 NmzNoSubdivision</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87BEBC4883D9E4CF" >2.3-86 NmzNoSymmetrization</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X812E448A7C49CCD3" >2.3-87 NmzNumberLatticePoints</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87F31DFA823B6D55" >2.3-88 NmzOriginalMonoidGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E9C4CC7878CF096" >2.3-89 NmzPlacingTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F201AE47FF7AEC6" >2.3-90 NmzPrimalMode</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X868659657E1463E3" >2.3-91 NmzProjectCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B5B2286812228B1" >2.3-92 NmzProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7913B00279250F90" >2.3-93 NmzProjectionFloat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X811EC96985FE99FA" >2.3-94 NmzPullingTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8372059D783BA911" >2.3-95 NmzPullingTriangulationInternal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7DE5D105856F5001" >2.3-96 NmzRank</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7982136F865B148A" >2.3-97 NmzRationalAutomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7EE7F2F6841E3390" >2.3-98 NmzRecessionRank</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X860FDA0D81BF641C" >2.3-99 NmzReesPrimaryMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8172BBE57E970C22" >2.3-100 NmzRenfVolume</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F637D5F86E4B500" >2.3-101 NmzSignedDec</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X81AF9A717BEB6B83" >2.3-102 NmzStanleyDec</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86C5550E7ED226A2" >2.3-103 NmzStatic</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F7C052E805BCE42" >2.3-104 NmzStrictIsoTypeCheck</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B0074147C3D10D6" >2.3-105 NmzSublattice</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X870DD7FB85D80425" >2.3-106 NmzSuppHypsFloat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87E51DB27D9007B1" >2.3-107 NmzSupportHyperplanes</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X80C9E1F9849E5F0D" >2.3-108 NmzSymmetrize</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X85F2376580CED5C2" >2.3-109 NmzTestArithOverflowDescent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X804CF2FC7CFC9367" >2.3-110 NmzTestArithOverflowDualMode</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E044A4D7E8D1207" >2.3-111 NmzTestArithOverflowFullCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82EC0B237F742AC9" >2.3-112 NmzTestArithOverflowProjAndLift</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FEAF6A278552948" >2.3-113 NmzTestLargePyramids</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B6557CF84E93CA0" >2.3-114 NmzTestLibNormaliz</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84412ABE84D42065" >2.3-115 NmzTestLinearAlgebraGMP</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CD00A81833E1899" >2.3-116 NmzTestSimplexParallel</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X80B85BB27B4ECC32" >2.3-117 NmzTestSmallPyramids</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79E934EA873F442B" >2.3-118 NmzTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X85BE26AF83A5BD27" >2.3-119 NmzTriangulationDetSum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X869840DC816DF323" >2.3-120 NmzTriangulationSize</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C5DC23D7BD1DEEB" >2.3-121 NmzUnimodularTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CDAD83D7FE1D02A" >2.3-122 NmzUnitGroupIndex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FF8BB22787FA222" >2.3-123 NmzVerticesFloat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84AB87777844250D" >2.3-124 NmzVerticesOfPolyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X878AE417839ACF89" >2.3-125 NmzVirtualMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8550FB5182075539" >2.3-126 NmzVolume</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X873956267E1EB3BD" >2.3-127 NmzWeightedEhrhartQuasiPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F7C11FD7C996E74" >2.3-128 NmzWeightedEhrhartSeries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7944885884E7368D" >2.3-129 NmzWitnessNotIntegrallyClosed</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84D0AADB7BAF0328" >2.3-130 NmzBasisChange</a></span >div ></div >div >div class="ContChap" ><a href="chap3_mj.html#X7A489A5D79DA9E5C" >3 <span class="Heading" >Examples</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7BD5B55C802805B4" >3.1 <span class="Heading" >Generators</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X872A3FB37D6D7DFE" >3.2 <span class="Heading" >System of equations</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8570F3C87B5B7DD7" >3.3 <span class="Heading" >System of inhomogeneous equations</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7B191A1778012C1D" >3.4 <span class="Heading" >Combined input </span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8406B01578B99D14" >3.5 <span class="Heading" >Using the dual mode</span ></a>span >div >div >div class="ContChap" ><a href="chap4_mj.html#X7DA4E7697F7D5F0C" >4 <span class="Heading" >Installing NormalizInterface</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7CD1A8937DFB78BF" >4.1 <span class="Heading" >Compiling</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 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