<?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 (HAPcryst) - 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="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="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 >HAPcryst</h1 >div >br />Email: <span class="URL" ><a href="mailto:roeder.marc@gmail.com" >roeder.marc@gmail.com</a></span >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>r (at your convenience). See the file <code class="file" >LICENSE</code > or <span class="URL" ><a href="https://www.gnu.org/copyleft/gpl.html " >https://www.gnu.org/copyleft/gpl.html </a></span ></p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>"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#X813275957BA5B5E0" >1.1 <span class="Heading" >Abstract and Notation</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F4A00F481A1FB39" >1.1-1 <span class="Heading" >The natural action of crystallographic groups</span ></a>span >div ></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 class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7990986A8114E0DB" >1.2-1 <span class="Heading" >Recommendation concerning polymake</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7D9044767BEB1523" >1.3 <span class="Heading" >Global Variables</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X78B0A21E7FD0F3BB" >1.3-1 InfoHAPcryst</a></span >div ></div >div >div class="ContChap" ><a href="chap2.html#X86FBE5B77C2F9442" >2 <span class="Heading" >Bits and Pieces</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X8019925B8294F5B4" >2.1 <span class="Heading" >Matrices and Vectors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7D58A1848182EC26" >2.1-1 SignRat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7C0552BA873515B9" >2.1-2 VectorModOne</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7BB083A57C474F45" >2.1-3 IsSquareMat</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X78C932A48515EF10" >2.1-4 DimensionSquareMat</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X86BD4FE4871379AD" >2.2 <span class="Heading" >Affine Matrices OnRight</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X838946957FC75C17" >2.2-1 LinearPartOfAffineMatOnRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X80DD4F2286D49F8D" >2.2-2 BasisChangeAffineMatOnRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X81F3C49580958FB6" >2.2-3 TranslationOnRightFromVector</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X84A0B0637F269E37" >2.3 <span class="Heading" >Geometry</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7A94DAE679AD73E3" >2.3-1 GramianOfAverageScalarProductFromFiniteMatrixGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X866942167802E036" >2.3-2 <span class="Heading" >Inequalities</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X80C365AA87BDDAFA" >2.3-3 BisectorInequalityFromPointPair</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8790464D86D189F4" >2.3-4 WhichSideOfHyperplane</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X83392C417B311B6B" >2.3-5 RelativePositionPointAndPolygon</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7B14774981F80108" >2.4 <span class="Heading" >Space Groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7E2F20607F278B70" >2.4-1 PointGroupRepresentatives</a></span >div ></div >div >div class="ContChap" ><a href="chap3.html#X7F6789767FB36E74" >3 <span class="Heading" >Algorithms of Orbit-Stabilizer Type</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X85CAB2EB85A6E17A" >3.1 <span class="Heading" >Orbit Stabilizer for Crystallographic Groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7BED233684B2F811" >3.1-1 OrbitStabilizerInUnitCubeOnRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X82BD20307A67C119" >3.1-2 OrbitStabilizerInUnitCubeOnRightOnSets</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X82CCCD597C86A08A" >3.1-3 OrbitPartInVertexSetsStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8022CD75819DE536" >3.1-4 OrbitPartInFacesStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X86A80FA17A4D6664" >3.1-5 OrbitPartAndRepresentativesInFacesStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X81DE08687F0DBCC6" >3.1-6 StabilizerOnSetsStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83C6448679A54F9D" >3.1-7 RepresentativeActionOnRightOnSets</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8002407080DB3EA2" >3.1-8 <span class="Heading" >Getting other orbit parts</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8751429287034F4A" >3.1-9 ShiftedOrbitPart</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X82656DE584E8DC5D" >3.1-10 TranslationsToOneCubeAroundCenter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X858C787E83A902AB" >3.1-11 TranslationsToBox</a></span >div ></div >div >div class="ContChap" ><a href="chap4.html#X852C41A77C759D82" >4 <span class="Heading" >Resolutions of Crystallographic Groups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7F48638F817A14B0" >4.1 <span class="Heading" >Fundamental Domains</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79F4F7938116201E" >4.1-1 FundamentalDomainStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A07AB55831F212F" >4.1-2 FundamentalDomainBieberbachGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X86A09AC4842827C9" >4.1-3 FundamentalDomainFromGeneralPointAndOrbitPartGeometric</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X824BC99584F5F865" >4.1-4 IsFundamentalDomainStandardSpaceGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D79DD6E87BCC1DC" >4.1-5 IsFundamentalDomainBieberbachGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X78D68F6087238F97" >4.2 <span class="Heading" >Face Lattice and Resolution</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CA87AA478007468" >4.2-1 ResolutionBieberbachGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E854FC47F9E479E" >4.2-2 FaceLatticeAndBoundaryBieberbachGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79A0B28A7FAE31B9" >4.2-3 ResolutionFromFLandBoundary</a></span >div ></div >div >div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></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="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " 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