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Quelle class3mflds.gi Sprache: Shell |
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################################################################################ ##<#GAPDoc Label="SCNrCyclic3Mflds"> ## <ManSection> ## <Func Name="SCNrCyclic3Mflds" Arg="i"/> ## <Returns> integer upon success, <K>fail</K> otherwise.</Returns> ## <Description> ## Returns the number of combinatorial 3-manifolds with transitive cyclic ## symmetry with <Arg>i</Arg> vertices. ## ## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification ## of combinatorial 3-manifolds with transitive cyclic symmetry up to ## <M>22</M> vertices. ## <Example><![CDATA[ ## gap> SCNrCyclic3Mflds(22); ## 3090 ## ]]></Example> ## </Description> ## </ManSection> ##<#/GAPDoc> ################################################################################ ################################################################################ ##<#GAPDoc Label="SCCyclic3MfldTopTypes"> ## <ManSection> ## <Func Name="SCCyclic3MfldTopTypes" Arg="i"/> ## <Returns> a list of strings upon success, <K>fail</K> otherwise.</Returns> ## <Description> ## Returns a list of all topological types that occur in the classification ## combinatorial 3-manifolds with transitive cyclic symmetry with <Arg>i</Arg> ## vertices. ## ## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification ## of combinatorial 3-manifolds with transitive cyclic symmetry up to ## <M>22</M> vertices. ## <Example><![CDATA[ ## gap> SCCyclic3MfldTopTypes(19); ## [ "B2", "RP^2xS^1", "SFS[RP^2:(2,1)(3,1)]", "S^2~S^1", "S^3", "Sigma(2,3,7)", ## "T^3" ] ## ]]></Example> ## </Description> ## </ManSection> ##<#/GAPDoc> ################################################################################ ################################################################################ ##<#GAPDoc Label="SCCyclic3Mfld"> ## <ManSection> ## <Func Name="SCCyclic3Mfld" Arg="i,j"/> ## <Returns> simplicial complex of type <C>SCSimplicialComplex</C> upon ## success, <K>fail</K> otherwise.</Returns> ## <Description> ## Returns the <Arg>j</Arg>th combinatorial 3-manifold with <Arg>i</Arg> ## vertices in the classification of combinatorial 3-manifolds with transitive ## cyclic symmetry. ## ## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification ## of combinatorial 3-manifolds with transitive cyclic symmetry up to ## <M>22</M> vertices. ## <Example><![CDATA[ ## gap> SCCyclic3Mfld(15,34); ## <SimplicialComplex: Cyclic 3-mfld (15,34): T^3 | dim = 3 | n = 15> ## ]]></Example> ## </Description> ## </ManSection> ##<#/GAPDoc> ################################################################################ ################################################################################ ##<#GAPDoc Label="SCCyclic3MfldByType"> ## <ManSection> ## <Func Name="SCCyclic3MfldByType" Arg="type"/> ## <Returns> simplicial complex of type <C>SCSimplicialComplex</C> upon ## success, <K>fail</K> otherwise.</Returns> ## <Description> ## Returns the smallest combinatorial 3-manifolds in the classification of ## combinatorial 3-manifolds with transitive cyclic symmetry of topological ## type <Arg>type</Arg>. ## ## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the classification ## of combinatorial 3-manifolds with transitive cyclic symmetry up to ## <M>22</M> vertices. ## <Example><![CDATA[ ## gap> SCCyclic3MfldByType("T^3"); ## <SimplicialComplex: Cyclic 3-mfld (15,34): T^3 | dim = 3 | n = 15> ## ]]></Example> ## </Description> ## </ManSection> ##<#/GAPDoc> ################################################################################ ################################################################################ ##<#GAPDoc Label="SCCyclic3MfldListOfGivenType"> ## <ManSection> ## <Func Name="SCCyclic3MfldListOfGivenType" Arg="type"/> ## <Returns> simplicial complex of type <C>SCSimplicialComplex</C> upon ## success, <K>fail</K> otherwise.</Returns> ## <Description> ## Returns a list of indices ## <M>\{ (i_1, j_1) , (i_1, j_1) , \ldots (i_n, j_n) \}</M> of all ## combinatorial 3-manifolds in the classification of combinatorial ## 3-manifolds with transitive cyclic symmetry of topological type ## <Arg>type</Arg>. Complexes can be obtained by calling ## <Ref Func="SCCyclic3Mfld" /> using these indices. ## ## See <Cite Key="Spreer11CyclicCombMflds"/> for more about the ## classification of combinatorial 3-manifolds with transitive cyclic ## symmetry up to <M>22</M> vertices. ## <Example><![CDATA[ ## gap> SCCyclic3MfldListOfGivenType("Sigma(2,3,7)"); ## [ [ 19, 100 ], [ 19, 118 ], [ 19, 120 ], [ 19, 130 ] ] ## ]]></Example> ## </Description> ## </ManSection> ##<#/GAPDoc> ################################################################################
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2026-11-04