<?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 >title >GAP (NConvex) - 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.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="chap7.html" >7</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="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >NConvex</h1 >div >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 />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 />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X85A08CF187A6D986" >1.2 <span class="Heading" >Requirements</span ></a>span >div >div >div class="ContChap" ><a href="chap2.html#X87F1120883F5B4D0" >2 <span class="Heading" >Functionality</span ></a>div >div class="ContChap" ><a href="chap3.html#X8359268B7FDA6AEC" >3 <span class="Heading" >Convex objects</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.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.html#X7D87C111848F25C5" >3.1-1 AmbientSpaceDimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X79D9BB0F7BB3B411" >3.1-2 Dimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7E660B6A7B6D0A9D" >3.1-3 IsFullDimensional</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8401C12C7937C521" >3.1-4 InteriorPoint</a></span >div ></div >div >div class="ContChap" ><a href="chap4.html#X8524A7567BA4FFA6" >4 <span class="Heading" >Cones</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X7E6FB9EC7DFF5403" >4.1-1 ConeByInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8711F345805C5FBD" >4.1-2 ConeByEqualitiesAndInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F0634207B3A4EC6" >4.1-3 Cone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CD248238093A748" >4.1-4 Cone</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X80468DD7834C2EFD" >4.2-1 DefiningInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X782F9A6E82AC6EA4" >4.2-2 EqualitiesOfCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80DB81B58590FC36" >4.2-3 DualCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X825F3C9380C4E2EE" >4.2-4 FacesOfCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X82C77B2A8235567E" >4.2-5 Facets</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X817CAD1E84C0757A" >4.2-6 FVector</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81488179780BE42F" >4.2-7 RelativeInteriorRay</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EB6BB087BE2FFD6" >4.2-8 HilbertBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8445477A83A137CB" >4.2-9 HilbertBasisOfDualCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X815F2FC4821A961D" >4.2-10 LinealitySpaceGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CFFCB5C7F4C183D" >4.2-11 ExternalCddCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79B4436C8051BA08" >4.2-12 ExternalNmzCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83709F0380B097BD" >4.2-13 AmbientSpaceDimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7DC52F6B8490C5C4" >4.2-14 LatticePointsGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7B0DA052877CE7BC" >4.2-15 GridGeneratedByCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8267BFA47CD282E1" >4.2-16 FactorGrid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A807C828273D4ED" >4.2-17 FactorGridMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X849EFCA77CE04DF9" >4.2-18 GridGeneratedByOrthogonalCone</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X8490C19A78ED287A" >4.3-1 IsRegularCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X831EBE117FC07C40" >4.3-2 IsRay</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X810956D0823BDA51" >4.3-3 IsZero</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X782E6C6684E1514D" >4.4-1 FourierProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80715AC378616F14" >4.4-2 IntersectionOfCones</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7946B20D834F31D2" >4.4-3 IntersectionOfCones</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X825A7CBD79653961" >4.4-4 Contains</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81FBC83B87053C56" >4.4-5 IsRelativeInteriorRay</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C52373C83B9282D" >4.4-6 NonReducedInequalities</a></span >div ></div >div >div class="ContChap" ><a href="chap5.html#X7EB0337A86DDD2F1" >5 <span class="Heading" >Fans</span div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.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.html#X7F5B09727CD79D17" >5.1-1 Fan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7FB87B4983087091" >5.1-2 Fan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7A1FD0BD845E3588" >5.1-3 Fan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7D5DE7F08555C8E8" >5.1-4 FansFromTriangulation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X853CC6BB854AA139" >5.1-5 FanFromTriangulation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.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.html#X789156E3828930D2" >5.2-1 RayGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X86CB98CC80E9C36E" >5.2-2 GivenRayGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7B0FAF0A8246F5AE" >5.2-3 RaysInMaximalCones</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7D586B547A8DB803" >5.2-4 MaximalCones</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7E5274F987E8FFC5" >5.2-5 FVector</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.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.html#X81189D5287FFBEDF" >5.3-1 IsWellDefinedFan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X87963F4C84C9EA21" >5.3-2 IsComplete</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7BE6F87D7BB9A6CD" >5.3-3 IsPointed</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7C694ECC81F4DECF" >5.3-4 IsSmooth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X78A031D8848E0FF8" >5.3-5 IsSimplicial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X85C533997DC6B46A" >5.3-6 IsNormalFan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7A2AE62C86CE72B8" >5.3-7 IsRegularFan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X81D74C107DBB7C21" >5.3-8 IsFanoFan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X86BC038782EFD451" >5.4 <span class="Heading" >Operations on fans</span ></a>span >div >div >div class="ContChap" ><a href="chap6.html#X85633D87813F12B0" >6 <span class="Heading" >Polyhedrons</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X83EF304B85ED4C5B" >6.1-1 PolyhedronByInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X842F90887840D3B9" >6.1-2 Polyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X861DE99B8007A4C4" >6.1-3 Polyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X78BCB2888114F56F" >6.1-4 Polyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7A8ECB9B8542EDFF" >6.1-5 Polyhedron</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X7ECCE0E480D88952" >6.2-1 ExternalCddPolyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7C7CC5497FC52B67" >6.2-2 ExternalNmzPolyhedron</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X842632AB7A09A820" >6.2-3 DefiningInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X87375C8586090666" >6.2-4 MainRatPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7A16114A7FFB3309" >6.2-5 MainPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7A3FB56D7E895535" >6.2-6 VerticesOfMainRatPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X8697AC27862160FE" >6.2-7 VerticesOfMainPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7C248476851AEB4A" >6.2-8 TailCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7DB9524D7C1A5361" >6.2-9 RayGeneratorsOfTailCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X79351A698787C5CA" >6.2-10 LatticePointsGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7B57BEAF78559D12" >6.2-11 BasisOfLinealitySpace</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X81435DD28524EEE8" >6.2-12 FVector</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X7B25E29378AF4489" >6.3-1 IsBounded</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7B8DDCE685798D9C" >6.3-2 IsPointed</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X879BD74A7F6327B2" >6.4-1 SolveLinearProgram</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7F4FE0C883B8AA50" >6.4-2 SolveLinearProgram</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X81CA403280755A9B" >6.5-1 SolveEqualitiesAndInequalitiesOverIntergers</a></span >div ></div >div >div class="ContChap" ><a href="chap7.html#X7B933C4686727183" >7 <span class="Heading" >Polytopes</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X83FB00B383A19F03" >7.1-1 PolytopeByInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X81DC4EE8849B08DA" >7.1-2 Polytope</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X7D8727917B72396A" >7.2-1 ExternalCddPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X83B1CBC67B34BE04" >7.2-2 LatticePoints</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7FB9E36C7B6C616F" >7.2-3 RelativeInteriorLatticePoints</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X816ACBEF786C23F2" >7.2-4 VerticesOfPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X805FCCD583DACF8F" >7.2-5 Vertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7B39989A7F321147" >7.2-6 DefiningInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7DAF68C08043105D" >7.2-7 EqualitiesOfPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7FDABF3D84E67F2C" >7.2-8 FacetInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7EC0B0818106EA50" >7.2-9 VerticesInFacets</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7DE7E52D800A7258" >7.2-10 NormalFan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8453091478A4C0F1" >7.2-11 FaceFan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X85EC550B7FCAECB5" >7.2-12 AffineCone</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7ACC98FD78ACDC57" >7.2-13 PolarPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8349F8DA81418C35" >7.2-14 DualPolytope</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X863F64947BDFC654" >7.3-1 IsEmpty</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X85181A5986107254" >7.3-2 IsLatticePolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7918DAE87B159619" >7.3-3 IsVeryAmple</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X851AD9E684CA7434" >7.3-4 IsNormalPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7F39F2BF835AA337" >7.3-5 IsSimplicial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X797F6A0778C70DD0" >7.3-6 IsSimplexPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X815A80E785E52474" >7.3-7 IsSimplePolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X85BE2236780D0957" >7.3-8 IsReflexive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X85DEC39081FD04E9" >7.3-9 IsFanoPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X780D5BDE7C177166" >7.3-10 IsCanonicalFanoPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X78B2B9747E9A6FEA" >7.3-11 IsTerminalFanoPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7946CEA886A48F96" >7.3-12 IsSmoothFanoPolytope</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X7F9303847F938C87" ><code >7.4-1 \+</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7AEF19987E29612E" ><code >7.4-2 \*</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8079AF527BA681D1" >7.4-3 IntersectionOfPolytopes</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7F2AE1197AAFF273" >7.4-4 RandomInteriorPoint</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7E36517B808D2E44" >7.4-5 IsInteriorPoint</a></span >div ></div >div >div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next 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="chap7.html" >7</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a 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