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<h1>NConvex</h1>


<h2>A Gap package to perform polyhedral computations</h2>

<p>
    2024.12-01</p>

<p>
    28 December 2024
  </p>

</div>
<p><b>
    Kamal Saleh




  </b>
<br />Email: <span class="URL"><a href="mailto:kamal.saleh@uni-siegen.de">kamal.saleh@uni-siegen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://github.com/kamalsaleh">https://github.com/kamalsaleh</a></span>
<br />Address: <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57068 Siegen<br /> Germany<br />
</p><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>
<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 /> 57068 Siegen<br /> Germany<br />
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<div class="contents">
<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#X8360C04082558A12">1.1 <span class="Heading">Installation</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X85A08CF187A6D986">1.2 <span class="Heading">Requirements</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X87F1120883F5B4D0">2 <span class="Heading">Functionality</span></a>
</div>
<div class="ContChap"><a href="chap3_mj.html#X8359268B7FDA6AEC">3 <span class="Heading">Convex objects</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7C701DBF7BAE649A">3.1 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D87C111848F25C5">3.1-1 AmbientSpaceDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79D9BB0F7BB3B411">3.1-2 Dimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E660B6A7B6D0A9D">3.1-3 IsFullDimensional</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8401C12C7937C521">3.1-4 InteriorPoint</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X8524A7567BA4FFA6">4 <span class="Heading">Cones</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X837F56037886A1EF">4.1 <span class="Heading">Creating cones</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E6FB9EC7DFF5403">4.1-1 ConeByInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8711F345805C5FBD">4.1-2 ConeByEqualitiesAndInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F0634207B3A4EC6">4.1-3 Cone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CD248238093A748">4.1-4 Cone</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X85EE90A37DE1E3AC">4.2 <span class="Heading">Attributes of Cones</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80468DD7834C2EFD">4.2-1 DefiningInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X782F9A6E82AC6EA4">4.2-2 EqualitiesOfCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80DB81B58590FC36">4.2-3 DualCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X825F3C9380C4E2EE">4.2-4 FacesOfCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X82C77B2A8235567E">4.2-5 Facets</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X817CAD1E84C0757A">4.2-6 FVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81488179780BE42F">4.2-7 RelativeInteriorRay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7EB6BB087BE2FFD6">4.2-8 HilbertBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8445477A83A137CB">4.2-9 HilbertBasisOfDualCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X815F2FC4821A961D">4.2-10 LinealitySpaceGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CFFCB5C7F4C183D">4.2-11 ExternalCddCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X79B4436C8051BA08">4.2-12 ExternalNmzCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83709F0380B097BD">4.2-13 AmbientSpaceDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7DC52F6B8490C5C4">4.2-14 LatticePointsGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B0DA052877CE7BC">4.2-15 GridGeneratedByCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8267BFA47CD282E1">4.2-16 FactorGrid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A807C828273D4ED">4.2-17 FactorGridMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X849EFCA77CE04DF9">4.2-18 GridGeneratedByOrthogonalCone</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7DD2805F7DF61F97">4.3 <span class="Heading">Properties of Cones</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8490C19A78ED287A">4.3-1 IsRegularCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X831EBE117FC07C40">4.3-2 IsRay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X810956D0823BDA51">4.3-3 IsZero</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X843CBBD37FC2827B">4.4 <span class="Heading">Operations on cones</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X782E6C6684E1514D">4.4-1 FourierProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80715AC378616F14">4.4-2 IntersectionOfCones</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7946B20D834F31D2">4.4-3 IntersectionOfCones</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X825A7CBD79653961">4.4-4 Contains</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81FBC83B87053C56">4.4-5 IsRelativeInteriorRay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7C52373C83B9282D">4.4-6 NonReducedInequalities</a></span>
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</div>
<div class="ContChap"><a href="chap5_mj.html#X7EB0337A86DDD2F1">5 <span class="Heading">Fans</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X86EC0F0A78ECBC10">5.1 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F5B09727CD79D17">5.1-1 Fan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7FB87B4983087091">5.1-2 Fan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A1FD0BD845E3588">5.1-3 Fan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7D5DE7F08555C8E8">5.1-4 FansFromTriangulation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X853CC6BB854AA139">5.1-5 FanFromTriangulation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7C701DBF7BAE649A">5.2 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X789156E3828930D2">5.2-1 RayGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X86CB98CC80E9C36E">5.2-2 GivenRayGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B0FAF0A8246F5AE">5.2-3 RaysInMaximalCones</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7D586B547A8DB803">5.2-4 MaximalCones</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E5274F987E8FFC5">5.2-5 FVector</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X871597447BB998A1">5.3 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81189D5287FFBEDF">5.3-1 IsWellDefinedFan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X87963F4C84C9EA21">5.3-2 IsComplete</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BE6F87D7BB9A6CD">5.3-3 IsPointed</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C694ECC81F4DECF">5.3-4 IsSmooth</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78A031D8848E0FF8">5.3-5 IsSimplicial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X85C533997DC6B46A">5.3-6 IsNormalFan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A2AE62C86CE72B8">5.3-7 IsRegularFan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81D74C107DBB7C21">5.3-8 IsFanoFan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X86BC038782EFD451">5.4 <span class="Heading">Operations on fans</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X85633D87813F12B0">6 <span class="Heading">Polyhedrons</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7C1A095983C57A83">6.1 <span class="Heading">Creating polyhedron</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X83EF304B85ED4C5B">6.1-1 PolyhedronByInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X842F90887840D3B9">6.1-2 Polyhedron</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X861DE99B8007A4C4">6.1-3 Polyhedron</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X78BCB2888114F56F">6.1-4 Polyhedron</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A8ECB9B8542EDFF">6.1-5 Polyhedron</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7C701DBF7BAE649A">6.2 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7ECCE0E480D88952">6.2-1 ExternalCddPolyhedron</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7C7CC5497FC52B67">6.2-2 ExternalNmzPolyhedron</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X842632AB7A09A820">6.2-3 DefiningInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87375C8586090666">6.2-4 MainRatPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A16114A7FFB3309">6.2-5 MainPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A3FB56D7E895535">6.2-6 VerticesOfMainRatPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8697AC27862160FE">6.2-7 VerticesOfMainPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7C248476851AEB4A">6.2-8 TailCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7DB9524D7C1A5361">6.2-9 RayGeneratorsOfTailCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X79351A698787C5CA">6.2-10 LatticePointsGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B57BEAF78559D12">6.2-11 BasisOfLinealitySpace</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X81435DD28524EEE8">6.2-12 FVector</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X871597447BB998A1">6.3 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B25E29378AF4489">6.3-1 IsBounded</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B8DDCE685798D9C">6.3-2 IsPointed</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X819F85537D5D9D15">6.4 <span class="Heading">Solving Linear programs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X879BD74A7F6327B2">6.4-1 SolveLinearProgram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7F4FE0C883B8AA50">6.4-2 SolveLinearProgram</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X84237872798DB501">6.5 <span class="Heading">ZSolve</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X81CA403280755A9B">6.5-1 SolveEqualitiesAndInequalitiesOverIntergers</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X7B933C4686727183">7 <span class="Heading">Polytopes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X801887DC7E5F6AB7">7.1 <span class="Heading">Creating polytopes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X83FB00B383A19F03">7.1-1 PolytopeByInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X81DC4EE8849B08DA">7.1-2 Polytope</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7C701DBF7BAE649A">7.2 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7D8727917B72396A">7.2-1 ExternalCddPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X83B1CBC67B34BE04">7.2-2 LatticePoints</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7FB9E36C7B6C616F">7.2-3 RelativeInteriorLatticePoints</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X816ACBEF786C23F2">7.2-4 VerticesOfPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X805FCCD583DACF8F">7.2-5 Vertices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B39989A7F321147">7.2-6 DefiningInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7DAF68C08043105D">7.2-7 EqualitiesOfPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7FDABF3D84E67F2C">7.2-8 FacetInequalities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7EC0B0818106EA50">7.2-9 VerticesInFacets</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7DE7E52D800A7258">7.2-10 NormalFan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8453091478A4C0F1">7.2-11 FaceFan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85EC550B7FCAECB5">7.2-12 AffineCone</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7ACC98FD78ACDC57">7.2-13 PolarPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8349F8DA81418C35">7.2-14 DualPolytope</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X871597447BB998A1">7.3 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X863F64947BDFC654">7.3-1 IsEmpty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85181A5986107254">7.3-2 IsLatticePolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7918DAE87B159619">7.3-3 IsVeryAmple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X851AD9E684CA7434">7.3-4 IsNormalPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F39F2BF835AA337">7.3-5 IsSimplicial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X797F6A0778C70DD0">7.3-6 IsSimplexPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X815A80E785E52474">7.3-7 IsSimplePolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85BE2236780D0957">7.3-8 IsReflexive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85DEC39081FD04E9">7.3-9 IsFanoPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X780D5BDE7C177166">7.3-10 IsCanonicalFanoPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X78B2B9747E9A6FEA">7.3-11 IsTerminalFanoPolytope</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7946CEA886A48F96">7.3-12 IsSmoothFanoPolytope</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7B71F2A2834E84CE">7.4 <span class="Heading">Operations on polytopes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F9303847F938C87"><code>7.4-1 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7AEF19987E29612E"><code>7.4-2 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8079AF527BA681D1">7.4-3 IntersectionOfPolytopes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F2AE1197AAFF273">7.4-4 RandomInteriorPoint</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7E36517B808D2E44">7.4-5 IsInteriorPoint</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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