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\GAPDocLabFile{fining}
\makelabel{fining:Title page}{}{X7D2C85EC87DD46E5}
\makelabel{fining:Copyright}{}{X81488B807F2A1CF1}
\makelabel{fining:Acknowledgements}{}{X82A988D47DFAFCFA}
\makelabel{fining:Table of Contents}{}{X8537FEB07AF2BEC8}
\makelabel{fining:Introduction}{1}{X7DFB63A97E67C0A1}
\makelabel{fining:Philosophy}{1.1}{X873C99678745ABAF}
\makelabel{fining:How to cite FinInG}{1.2}{X837E428E80B6049C}
\makelabel{fining:Overview of this manual}{1.3}{X87B5A1377BCABBD6}
\makelabel{fining:Getting and installing FinInG}{1.4}{X7EEBA9577BA68BA6}
\makelabel{fining:Installation procedure under UNIX like systems}{1.4.1}{X7F499E8A79509971}
\makelabel{fining:Compiling packages}{1.4.2}{X83A6C48E806EC0E9}
\makelabel{fining:Updating FinInG}{1.4.3}{X78F15DAE873084A5}
\makelabel{fining:The Development Team}{1.5}{X83BC24CC831A2542}
\makelabel{fining:Examples}{2}{X7A489A5D79DA9E5C}
\makelabel{fining:Elementary examples}{2.1}{X81660CB279889CB6}
\makelabel{fining:subspaces of projective spaces}{2.1.1}{X8016E6857D53F2ED}
\makelabel{fining:Subspaces of classical polar spaces}{2.1.2}{X7B99511887D41A95}
\makelabel{fining:Underlying objects}{2.1.3}{X8555398C83677C27}
\makelabel{fining:Constructing polar spaces}{2.1.4}{X8771ACB879E479C6}
\makelabel{fining:Some collineation groups}{2.1.5}{X85D3BB2A8274DDCB}
\makelabel{fining:Some objects with interesting combinatorial properties}{2.2}{X825F78F57E309197}
\makelabel{fining:The Tits ovoid}{2.2.1}{X815BB30986E84DB1}
\makelabel{fining:Lines meeting a hermitian curve}{2.2.2}{X7E79F18B8170B4B3}
\makelabel{fining:The Patterson ovoid}{2.2.3}{X85C255FD78C50992}
\makelabel{fining:A hyperoval}{2.2.4}{X80B93785876EF3E0}
\makelabel{fining:Geometry morphisms}{2.3}{X876240A479A5717C}
\makelabel{fining:Isomorphic polar spaces}{2.3.1}{X79CE092B7E17DF24}
\makelabel{fining:Intertwiners}{2.3.2}{X83ADB5AE8624C74C}
\makelabel{fining:Klein correspondence}{2.3.3}{X7C7438AB86A493FE}
\makelabel{fining:Embedding in a subspace}{2.3.4}{X869EB94D841AE028}
\makelabel{fining:Subgeometries}{2.3.5}{X7FE8E4BF7E700E65}
\makelabel{fining:Embedding by field reduction}{2.3.6}{X838BBDD97FA03FD0}
\makelabel{fining:Some geometrical objects}{2.4}{X855C8E6D819EB975}
\makelabel{fining:Spreads of W(5,3)}{2.4.1}{X8475841778D3BEEC}
\makelabel{fining:Distance-6 spread of the split Cayley hexagon}{2.4.2}{X81F516D07E8165B9}
\makelabel{fining:Some particular incidence geometries}{2.5}{X7F13364A7EEA2AD1}
\makelabel{fining:The split Cayley hexagon}{2.5.1}{X79623B9E7D5816B3}
\makelabel{fining:An (apartment of) a building of type E6}{2.5.2}{X8528558E87DE72C5}
\makelabel{fining:A rank 4 geometry for PSL(2,11)}{2.5.3}{X7B783473852C7899}
\makelabel{fining:The Ree-Tits octagon of order [2,4] as coset geometry}{2.5.4}{X80128FF17BB62C83}
\makelabel{fining:Elation generalised quadrangles}{2.6}{X7BA462527B2777BC}
\makelabel{fining:The classical q-clan}{2.6.1}{X7E3707857A74AB5E}
\makelabel{fining:Two ways to construct a flock generalised quadrangle from a Kantor-Knuth semifield q-clan}{2.6.2}{X83357ED78789111E}
\makelabel{fining:Algebraic varieties}{2.7}{X87EC44BF7F24486E}
\makelabel{fining:A projective variety}{2.7.1}{X7ABCF9637B60FF37}
\makelabel{fining:Incidence Geometry}{3}{X838ACF8A7F100A2B}
\makelabel{fining:Incidence structures}{3.1}{X7FB175337C4F8B76}
\makelabel{fining:Main categories in IsIncidenceGeometry}{3.1.4}{X7B0347E2863C1E8C}
\makelabel{fining:Examples of categories of incidence geometries}{3.1.5}{X87FFB1648575FFF2}
\makelabel{fining:Elements of incidence structures}{3.2}{X7BBDB0AE7E29F3FB}
\makelabel{fining:Main categories for individual elements of incidence structures}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:Main categories for collections of all the elements of a given type of an incidence structure}{3.2.5}{X7DE974E687A2ABFB}
\makelabel{fining:Short names for ElementsOfIncidenceStructure}{3.2.8}{X87E64DA67C3D6661}
\makelabel{fining:Flags of incidence structures}{3.3}{X7DACFB6785029BF0}
\makelabel{fining:Shadow of elements}{3.4}{X7AA14EDF7B0B1569}
\makelabel{fining:Short names for ElementsIncidentWithElementOfIncidenceStructure}{3.4.5}{X7E29C31D7CB5DB23}
\makelabel{fining:Enumerating elements of an incidence structure}{3.5}{X8133F88478BAFCB7}
\makelabel{fining:Lie geometries}{3.6}{X84D77D437B5F3716}
\makelabel{fining:Main categories in IsLieGeometry}{3.6.1}{X7D012B9F86E63702}
\makelabel{fining:Elements of Lie geometries}{3.7}{X7FBCF60385E8C1D8}
\makelabel{fining:More short names for ElementsIncidentWithElementOfIncidenceStructure}{3.7.4}{X814C3AC27E49AD5B}
\makelabel{fining:Changing the ambient geometry of elements of a Lie geometry}{3.8}{X7A9EBF9782671634}
\makelabel{fining:Projective Spaces}{4}{X83BBAA668672A76D}
\makelabel{fining:Projective Spaces and basic operations}{4.1}{X7862BC887D20B37A}
\makelabel{fining:Subspaces of projective spaces}{4.2}{X8016E6857D53F2ED}
\makelabel{fining:Short names for ElementsOfIncidenceStructure}{4.2.5}{X87E64DA67C3D6661}
\makelabel{fining:Incidence and containment}{4.2.6}{X7904128479BDFCC9}
\makelabel{fining:Shadows of Projective Subspaces}{4.3}{X7BD8312C85784503}
\makelabel{fining:Short names for ElementsIncidentWithElementOfIncidenceStructure}{4.3.4}{X7E29C31D7CB5DB23}
\makelabel{fining:Enumerating subspaces of a projective space}{4.4}{X799F3A2A86F82E5B}
\makelabel{fining:Projective Groups}{5}{X816FCFB683915E8A}
\makelabel{fining:Projectivities, collineations and correlations of projective spaces.}{5.1}{X7A9762F8861B0772}
\makelabel{fining:Categories for group elements}{5.1.1}{X851186297A91C1C6}
\makelabel{fining:Representations for group elements}{5.1.2}{X7BBF688083857760}
\makelabel{fining:Projectivities}{5.1.3}{X8160615081358132}
\makelabel{fining:Collineations of projective spaces}{5.1.4}{X7E881C237D117C6C}
\makelabel{fining:Projective strictly semilinear maps}{5.1.5}{X7B89B51F86AE2BCC}
\makelabel{fining:Correlations and collineations}{5.1.6}{X815B68277D0500C3}
\makelabel{fining:Construction of projectivities, collineations and correlations.}{5.2}{X78EDF0357B58FC0E}
\makelabel{fining:Basic operations for projectivities, collineations and correlations of projective spaces}{5.3}{X83A5F86F82598AA6}
\makelabel{fining:The groups PΓL, PGL, and PSL in FinInG}{5.4}{X78E99D9086D64FD9}
\makelabel{fining:Basic operations for projective groups}{5.5}{X7C4C7ADE8746C1B1}
\makelabel{fining:Basic action of projective group elements}{5.7}{X7AAD7DDD7E19595E}
\makelabel{fining:Projective group actions}{5.8}{X7EBA895D7A501CE0}
\makelabel{fining:Special subgroups of the projectivity group}{5.9}{X809F0F2B857FA178}
\makelabel{fining:Nice Monomorphisms}{5.10}{X7FFD731684606BC6}
\makelabel{fining:Polarities of Projective Spaces}{6}{X87BA55CB86B110EC}
\makelabel{fining:Creating polarities of projective spaces}{6.1}{X86D948C3875A5005}
\makelabel{fining:Operations, attributes and properties for polarities of projective spaces}{6.2}{X81CC3CBE7879FD7B}
\makelabel{fining:Polarities, absolute points, totally isotropic elements and finite classical polar spaces}{6.3}{X83F8149B7D23301E}
\makelabel{fining:Commuting polarities}{6.4}{X7ADFEAC07CE25530}
\makelabel{fining:Finite Classical Polar Spaces}{7}{X7F96B1327C022A28}
\makelabel{fining:Finite Classical Polar Spaces}{7.1}{X7F96B1327C022A28}
\makelabel{fining:Canonical and standard Polar Spaces}{7.2}{X850CD32686B0656B}
\makelabel{fining:Basic operations for finite classical polar spaces}{7.3}{X7A04340A7EC9215B}
\makelabel{fining:Subspaces of finite classical polar spaces}{7.4}{X787E0AEA8284B34B}
\makelabel{fining:Basic operations for polar spaces and subspaces of projective spaces}{7.5}{X8472E78A79F44828}
\makelabel{fining:Incidence and containment}{7.5.1}{X7904128479BDFCC9}
\makelabel{fining:Shadow of elements}{7.6}{X7AA14EDF7B0B1569}
\makelabel{fining:Enumerating subspaces of polar spaces}{7.8}{X855D48A07E0BBCDB}
\makelabel{fining:Enumerators for polar spaces}{7.8.1}{X7AB1BA95825BDE71}
\makelabel{fining:Iterators for polar spaces}{7.8.3}{X861463147B738DF1}
\makelabel{fining:Orbits, stabilisers and actions}{8}{X87A0A15D8588D62F}
\makelabel{fining:Orbits}{8.1}{X81E0FF0587C54543}
\makelabel{fining:Stabilisers}{8.2}{X7EAB52F67B3A0003}
\makelabel{fining:Actions and nice monomorphisms revisited}{8.3}{X7B449F3B7F23A30A}
\makelabel{fining:Action functions}{8.3.1}{X86A646FF8668D82E}
\makelabel{fining:Generic GAP functions}{8.3.2}{X8474367181BB501E}
\makelabel{fining:Different behaviour for different collineation groups}{8.3.5}{X86AC831981D89DF1}
\makelabel{fining:Affine Spaces}{9}{X7A63E8817A819046}
\makelabel{fining:Affine spaces and basic operations}{9.1}{X7ADF809E85917970}
\makelabel{fining:Subspaces of affine spaces}{9.2}{X7AC346337E23D34F}
\makelabel{fining:Short names for ElementsOfIncidenceStructure}{9.2.3}{X87E64DA67C3D6661}
\makelabel{fining:Incidence and containment}{9.2.4}{X7904128479BDFCC9}
\makelabel{fining:Shadows of Affine Subspaces}{9.3}{X835B9A1F7EFE4640}
\makelabel{fining:Iterators and enumerators}{9.4}{X7836304580E12428}
\makelabel{fining:Affine groups}{9.5}{X78B78D517B22FB7E}
\makelabel{fining:Low level operations}{9.6}{X8769AA7080854675}
\makelabel{fining:Geometry Morphisms}{10}{X876240A479A5717C}
\makelabel{fining:Geometry morphisms in FinInG}{10.1}{X850559BF7886E0D2}
\makelabel{fining:Type preserving bijective geometry morphisms}{10.2}{X7926E5367D0C80B7}
\makelabel{fining:Klein correspondence and derived dualities}{10.3}{X79C677CD7B7EC451}
\makelabel{fining:Embeddings of projective spaces}{10.4}{X86D21DCB7C0029F9}
\makelabel{fining:Embedding of projective spaces by field reduction}{10.4.3}{X7BC7FCDC7D9E1A09}
\makelabel{fining:Embeddings of polar spaces}{10.5}{X7C00DD48787B1EEE}
\makelabel{fining:Embedding of polar spaces by field reduction}{10.5.3}{X7823BA95797898CE}
\makelabel{fining:Projections}{10.6}{X81FAC1DE7C4B1972}
\makelabel{fining:Projective completion}{10.7}{X7952EE1A80D53825}
\makelabel{fining:Algebraic Varieties}{11}{X87EC44BF7F24486E}
\makelabel{fining:Algebraic Varieties}{11.1}{X87EC44BF7F24486E}
\makelabel{fining:Projective Varieties}{11.2}{X79EC6F8381337C08}
\makelabel{fining:Quadrics and Hermitian varieties}{11.3}{X8030D25C79C50847}
\makelabel{fining:Affine Varieties}{11.4}{X82BE5DEE843F5490}
\makelabel{fining:Geometry maps}{11.5}{X862822D57D48DD8E}
\makelabel{fining:Segre Varieties}{11.6}{X81374CC57CA01150}
\makelabel{fining:Veronese Varieties}{11.7}{X8759309A83991AB7}
\makelabel{fining:Grassmann Varieties}{11.8}{X7B4A786B7EA1388C}
\makelabel{fining:Generalised Polygons}{12}{X7E1F10767D2A4D6A}
\makelabel{fining:Categories}{12.1}{X7CC6903E78F24167}
\makelabel{fining:Subcategories in IsGeneralisedPolygon}{12.1.2}{X832E75AE7CCC5BB2}
\makelabel{fining:Subcategories in IsProjectivePlaneCategory}{12.1.4}{X8540C04887CF8824}
\makelabel{fining:Subcategories in IsGeneralisedQuadrangle}{12.1.5}{X7CF10DAE7847939D}
\makelabel{fining:Generic functions to create generalised polygons}{12.2}{X8614D6A779F9B1AA}
\makelabel{fining:Attributes and operations for generalised polygons}{12.3}{X864C966D8184A9C0}
\makelabel{fining:Elements of generalised polygons}{12.4}{X7A13D5EB82E01576}
\makelabel{fining:Collections of elements of generalised polygons}{12.4.1}{X7E7607CA7D59D086}
\makelabel{fining:Creating elements from objects and retrieving objects from elements}{12.4.3}{X7E9B2A217DBF2849}
\makelabel{fining:Incidence}{12.4.4}{X83B0FA9E7AE3DF01}
\makelabel{fining:Shadow elements}{12.4.7}{X8154BB13844AA0FD}
\makelabel{fining:The classical generalised hexagons}{12.5}{X7934EB788049B533}
\makelabel{fining:Trialities of the hyperbolic quadric and generalised hexagons}{12.5.1}{X7BF1D2E57B7630CB}
\makelabel{fining:Span and meet of elements}{12.5.9}{X7B1380878358938C}
\makelabel{fining:Elation generalised quadrangles}{12.6}{X7BA462527B2777BC}
\makelabel{fining:Elation generalised quadrangles and Kantor families}{12.6.1}{X86BD86C77BAAF887}
\makelabel{fining:Categories}{12.6.2}{X7CC6903E78F24167}
\makelabel{fining:Kantor families}{12.6.3}{X820A2D6A84A259FC}
\makelabel{fining:Representation of elements and underlying objects}{12.6.5}{X80C93974807A342B}
\makelabel{fining:Elation group and natural action on elements}{12.6.6}{X7DCD7EAB839BD97F}
\makelabel{fining:Kantor families, q-clans, and elation generalised quadrangles}{12.6.7}{X8462F11584736E32}
\makelabel{fining:Particular q-clans}{12.6.9}{X858A1EA8843BEC13}
\makelabel{fining:BLT-sets, flocks, q-clans, and elation generalised quadrangles}{12.6.12}{X7FAE48497B2F658A}
\makelabel{fining:Representation of elements and underlying objects}{12.6.17}{X80C93974807A342B}
\makelabel{fining:Coset Geometries and Diagrams}{13}{X8328AFAC7CF1EB1B}
\makelabel{fining:Coset Geometries}{13.1}{X781B20AC8097AC9F}
\makelabel{fining:Automorphisms, Correlations and Isomorphisms}{13.2}{X7967CA67876214A6}
\makelabel{fining:Diagrams}{13.3}{X78932FB48237B18F}
\makelabel{fining:Subgeometries of projective spaces}{14}{X79A3CC6E85E72EC1}
\makelabel{fining:Particular Categories}{14.1}{X7D237EAD8797C140}
\makelabel{fining:Categories for elements and collections of elements}{14.1.2}{X7D908542820D2FBE}
\makelabel{fining:Subgeometries of projective spaces}{14.2}{X79A3CC6E85E72EC1}
\makelabel{fining:Basic operations}{14.3}{X82EB5BE77F9F686A}
\makelabel{fining:Underlying vector space and ambient projective space}{14.3.1}{X8058FF3479158445}
\makelabel{fining:Projective dimension and rank}{14.3.3}{X79CC2F0483575105}
\makelabel{fining:Underlying algebraic structures}{14.3.4}{X85437D577DE97AEF}
\makelabel{fining:Constructing elements of a subgeometry}{14.4}{X7836EC02824B9425}
\makelabel{fining:Flags}{14.4.4}{X7B1757048405DD29}
\makelabel{fining:Groups and actions}{14.5}{X80503DDC8270EE69}
\makelabel{fining:Groups of collineations}{14.5.1}{X78F858C8863C7721}
\makelabel{fining:The structure of FinInG}{A}{X7F3345C884CD0268}
\makelabel{fining:The different components}{A.1}{X84D6D0EC7989CF5E}
\makelabel{fining:The complete inventory}{A.2}{X83E153B784E17E05}
\makelabel{fining:Declarations}{A.2.1}{X844A8A1F85E6E038}
\makelabel{fining:The finite classical groups in FinInG}{B}{X866C644987E43DF8}
\makelabel{fining:Standard forms used to produce the finite classical groups.}{B.1}{X7F297E2B7D98DC76}
\makelabel{fining:Direct commands to construct the projective classical groups in FinInG}{B.2}{X7D9E27E986AEB973}
\makelabel{fining:Basis of the collineation groups}{B.3}{X7F1343937C036C7A}
\makelabel{fining:Low level functions for morphisms}{C}{X874D94F47C943D71}
\makelabel{fining:Field reduction and vector spaces}{C.1}{X799BE5108516D030}
\makelabel{fining:Field reduction and forms}{C.2}{X7F06BA41857256B8}
\makelabel{fining:Low level functions}{C.3}{X81CCB1F5789CD7D8}
\makelabel{fining:Bibliography}{Bib}{X7A6F98FD85F02BFE}
\makelabel{fining:References}{Bib}{X7A6F98FD85F02BFE}
\makelabel{fining:Index}{Ind}{X83A0356F839C696F}
\makelabel{fining:FinInG}{1.4}{X7EEBA9577BA68BA6}
\makelabel{fining:IsIncidenceStructure}{3.1.1}{X81F7D8FA82A55561}
\makelabel{fining:IsIncidenceGeometry}{3.1.2}{X78C74BE87E050E84}
\makelabel{fining:IncidenceStructure}{3.1.3}{X7C3258887C8DF5C1}
\makelabel{fining:IsLieGeometry}{3.1.4}{X7B0347E2863C1E8C}
\makelabel{fining:IsAffineSpace}{3.1.4}{X7B0347E2863C1E8C}
\makelabel{fining:IsGeneralisedPolygon}{3.1.4}{X7B0347E2863C1E8C}
\makelabel{fining:IsCosetGeometry}{3.1.4}{X7B0347E2863C1E8C}
\makelabel{fining:TypesOfElementsOfIncidenceStructure}{3.1.6}{X7E574AB27DA97063}
\makelabel{fining:TypesOfElementsOfIncidenceStructurePlural}{3.1.6}{X7E574AB27DA97063}
\makelabel{fining:Rank}{3.1.7}{X827146F37E2AA841}
\makelabel{fining:RankAttr}{3.1.7}{X827146F37E2AA841}
\makelabel{fining:IncidenceGraph}{3.1.8}{X815BE6D57D623452}
\makelabel{fining:IsElementOfIncidenceStructure}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsElementOfIncidenceGeometry}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsElementOfLieGeometry}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsElementOfAffineSpace}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsElementOfCosetGeometry}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsSubspaceOfProjectiveSpace}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsSubspaceOfClassicalPolarSpace}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:IsElementOfGeneralisedPolygon}{3.2.1}{X827CD3C881DC8364}
\makelabel{fining:UnderlyingObject}{3.2.2}{X810D4D6D87069697}
\makelabel{fining:Type}{3.2.3}{X823B3D0F87FB5403}
\makelabel{fining:ObjectToElement}{3.2.4}{X7809B7C183FA7213}
\makelabel{fining:IsElementsOfIncidenceStructure}{3.2.5}{X7DE974E687A2ABFB}
\makelabel{fining:IsElementsOfIncidenceGeometry}{3.2.5}{X7DE974E687A2ABFB}
\makelabel{fining:IsElementsOfLieGeometry}{3.2.5}{X7DE974E687A2ABFB}
\makelabel{fining:IsElementsOfAffineSpace}{3.2.5}{X7DE974E687A2ABFB}
\makelabel{fining:IsElementsOfCosetGeometry}{3.2.5}{X7DE974E687A2ABFB}
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