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<h1>NormalizInterface</h1>


<h2><strong class="pkg">GAP</strong> wrapper for Normaliz</h2>

<p>
    1.4.1</p>

<p>
    20 June 2025
  </p>

</div>
<p><b>
    Sebastian Gutsche


  </b>
<br />Email: <span class="URL"><a href="mailto:gutsche@mathematik.uni-siegen.de">gutsche@mathematik.uni-siegen.de</a></span>
</p><p><b>
    Max Horn




  </b>
<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 />
</p><p><b>
    Christof Söger


  </b>
<br />Email: <span class="URL"><a href="mailto:csoeger@uos.de">csoeger@uos.de</a></span>
</p>

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<h3>Contents<a id="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>
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</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>
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<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>
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<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>
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