|
gap>
gap> START_TEST("simpcomp package test");
gap>
gap> SCInfoLevel(0);
true
gap>
gap> complexes:=[
> SCEmpty(),
> SCBdSimplex(4),
> SCBdCrossPolytope(4),
> SC([[1,3,5],[2,3,5],[1,2,4],[1,3,4],[2,3,4]]), #with boundary
> SC([[1,2,3,5], [1,2,3,8], [1,2,4,5], [1,2,4,9], [1,2,7,8], [1,2,7,9], [1,3,4,5],
> [1,3,4,9], [1,3,8,9], [1,6,7,8], [1,6,7,9], [1,6,8,9], [2,3,4,6], [2,3,4,9],
> [2,3,5,6], [2,3,8,9], [2,4,5,6], [2,7,8,9], [3,4,5,7], [3,4,6,7], [3,5,6,7],
> [4,5,6,8], [4,5,7,8], [4,6,7,8], [5,6,7,9], [5,6,8,9], [5,7,8,9]]), #S2~S1
> SC([[1,2,3,8,12], [1,2,3,8,16], [1,2,3,12,16], [1,2,4,7,11], [1,2,4,7,15],
> [1,2,4,11,15], [1,2,5,7,13], [1,2,5,7,15], [1,2,5,8,10], [1,2,5,8,14],
> [1,2,5,10,16], [1,2,5,13,16], [1,2,5,14,15], [1,2,6,7,9], [1,2,6,7,13],
> [1,2,6,8,14], [1,2,6,8,16], [1,2,6,9,15], [1,2,6,13,16], [1,2,6,14,15],
> [1,2,7,9,11], [1,2,8,10,12], [1,2,9,11,15], [1,2,10,12,16], [1,3,4,6,10],
> [1,3,4,6,14], [1,3,4,10,14], [1,3,5,6,9], [1,3,5,6,11], [1,3,5,9,12],
> [1,3,5,11,12], [1,3,6,9,15], [1,3,6,10,11], [1,3,6,14,15], [1,3,7,8,9],
> [1,3,7,8,11], [1,3,7,9,10], [1,3,7,10,11], [1,3,8,9,12], [1,3,8,11,13],
> [1,3,8,13,16], [1,3,9,10,15], [1,3,10,14,15], [1,3,11,12,13], [1,3,12,13,16],
> [1,4,5,6,10], [1,4,5,6,14], [1,4,5,10,16], [1,4,5,14,16], [1,4,7,8,11],
> [1,4,7,8,15], [1,4,8,11,13], [1,4,8,13,15], [1,4,9,11,13], [1,4,9,11,16],
> [1,4,9,13,14], [1,4,9,14,16], [1,4,10,12,13], [1,4,10,12,16], [1,4,10,13,14],
> [1,4,11,15,16], [1,4,12,13,15], [1,4,12,15,16], [1,5,6,9,12], [1,5,6,10,11],
> [1,5,6,12,14], [1,5,7,13,16], [1,5,7,15,16], [1,5,8,10,12], [1,5,8,12,14],
> [1,5,10,11,12], [1,5,14,15,16], [1,6,7,8,9], [1,6,7,8,13], [1,6,8,9,12],
> [1,6,8,12,14], [1,6,8,13,16], [1,7,8,13,15], [1,7,9,10,14], [1,7,9,11,14],
> [1,7,10,11,14], [1,7,12,13,15], [1,7,12,13,16], [1,7,12,15,16], [1,9,10,14,15],
> [1,9,11,13,14], [1,9,11,15,16], [1,9,14,15,16], [1,10,11,12,13],
> [1,10,11,13,14], [2,3,4,5,9], [2,3,4,5,13], [2,3,4,9,13], [2,3,5,6,9],
> [2,3,5,6,13], [2,3,6,9,15], [2,3,6,13,15], [2,3,7,8,12], [2,3,7,8,16],
> [2,3,7,12,14], [2,3,7,14,16], [2,3,9,11,14], [2,3,9,11,15], [2,3,9,13,14],
> [2,3,10,12,14], [2,3,10,12,15], [2,3,10,13,14], [2,3,10,13,15], [2,3,11,14,16],
> [2,3,11,15,16], [2,3,12,15,16], [2,4,5,6,10], [2,4,5,6,12], [2,4,5,9,12],
> [2,4,5,10,16], [2,4,5,13,16], [2,4,6,10,11], [2,4,6,11,12], [2,4,7,8,10],
> [2,4,7,8,12], [2,4,7,10,11], [2,4,7,12,14], [2,4,7,14,15], [2,4,8,9,10],
> [2,4,8,9,12], [2,4,9,10,16], [2,4,9,13,16], [2,4,11,12,14], [2,4,11,14,15],
> [2,5,6,9,12], [2,5,6,10,11], [2,5,6,11,13], [2,5,7,8,10], [2,5,7,8,14],
> [2,5,7,10,11], [2,5,7,11,13], [2,5,7,14,15], [2,6,7,9,11], [2,6,7,11,13],
> [2,6,8,14,15], [2,6,8,15,16], [2,6,9,11,12], [2,6,13,15,16], [2,7,8,14,16],
> [2,8,9,10,13], [2,8,9,12,13], [2,8,10,12,13], [2,8,11,14,15], [2,8,11,14,16],
> [2,8,11,15,16], [2,9,10,13,16], [2,9,11,12,14], [2,9,12,13,14], [2,10,12,13,14],
> [2,10,12,15,16], [2,10,13,15,16], [3,4,5,7,13], [3,4,5,7,15], [3,4,5,8,11],
> [3,4,5,8,15], [3,4,5,9,11], [3,4,6,7,12], [3,4,6,7,16], [3,4,6,8,14],
> [3,4,6,8,16], [3,4,6,10,12], [3,4,7,12,14], [3,4,7,13,16], [3,4,7,14,15],
> [3,4,8,11,13], [3,4,8,13,16], [3,4,8,14,15], [3,4,9,11,13], [3,4,10,12,14],
> [3,5,6,8,11], [3,5,6,8,15], [3,5,6,13,15], [3,5,7,13,14], [3,5,7,14,15],
> [3,5,9,11,16], [3,5,9,12,16], [3,5,10,13,14], [3,5,10,13,15], [3,5,10,14,15],
> [3,5,11,12,16], [3,6,7,10,12], [3,6,7,10,16], [3,6,8,10,11], [3,6,8,10,16],
> [3,6,8,14,15], [3,7,8,9,12], [3,7,8,10,11], [3,7,8,10,16], [3,7,9,10,12],
> [3,7,13,14,16], [3,9,10,12,15], [3,9,11,13,14], [3,9,11,15,16], [3,9,12,15,16],
> [3,11,12,13,16], [3,11,13,14,16], [4,5,6,7,12], [4,5,6,7,16], [4,5,6,14,16],
> [4,5,7,9,12], [4,5,7,9,15], [4,5,7,13,16], [4,5,8,9,11], [4,5,8,9,15],
> [4,6,8,13,14], [4,6,8,13,16], [4,6,9,13,14], [4,6,9,13,16], [4,6,9,14,16],
> [4,6,10,11,15], [4,6,10,12,15], [4,6,11,12,15], [4,7,8,9,12], [4,7,8,9,15],
> [4,7,8,10,11], [4,8,9,10,11], [4,8,13,14,15], [4,9,10,11,16], [4,10,11,15,16],
> [4,10,12,13,14], [4,10,12,15,16], [4,11,12,14,15], [4,12,13,14,15],
> [5,6,7,12,16], [5,6,8,11,15], [5,6,11,13,15], [5,6,12,14,16], [5,7,8,10,14],
> [5,7,9,12,16], [5,7,9,15,16], [5,7,10,11,14], [5,7,11,13,14], [5,8,9,10,13],
> [5,8,9,10,14], [5,8,9,11,16], [5,8,9,13,15], [5,8,9,14,16], [5,8,10,12,13],
> [5,8,11,12,15], [5,8,11,12,16], [5,8,12,13,15], [5,8,12,14,16], [5,9,10,13,15],
> [5,9,10,14,15], [5,9,14,15,16], [5,10,11,12,13], [5,10,11,13,14],
> [5,11,12,13,15], [6,7,8,9,13], [6,7,9,10,13], [6,7,9,10,14], [6,7,9,11,14],
> [6,7,10,12,15], [6,7,10,13,15], [6,7,10,14,16], [6,7,11,12,15], [6,7,11,12,16],
> [6,7,11,13,15], [6,7,11,14,16], [6,8,9,12,13], [6,8,10,11,15], [6,8,10,15,16],
> [6,8,12,13,14], [6,9,10,13,16], [6,9,10,14,16], [6,9,11,12,14], [6,9,12,13,14],
> [6,10,13,15,16], [6,11,12,14,16], [7,8,9,13,15], [7,8,10,14,16], [7,9,10,12,15],
> [7,9,10,13,15], [7,9,12,15,16], [7,11,12,13,15], [7,11,12,13,16],
> [7,11,13,14,16], [8,9,10,11,16], [8,9,10,14,16], [8,10,11,15,16],
> [8,11,12,14,15], [8,11,12,14,16], [8,12,13,14,15]]), #K3
> SC([[1,2],[2,3],[4,5],[5,6]]), #unconnected
> SC([[1,2,3],[1,2,6],[1,3,5],[1,4,5],[1,4,6],
> [2,3,4],[2,4,5],[2,5,6],[3,4,6],[3,5,6]]) #rp2
> ];;
gap>
gap>
gap> #general tests
gap> c:=complexes[1];;
gap> SCDim(c);
-1
gap> SCName(c);
"empty complex"
gap> c.Name;
"empty complex"
gap> c.IsEmpty;
true
gap> c.F;
[ 0 ]
gap> Size(c.Facets);
0
gap> c.Homology;
[ ]
gap> c.Cohomology;
[ ]
gap> c.HasBoundary;
false
gap> c.Orientation;
[ ]
gap> Size(c.ConnectedComponents);
1
gap> Size(c.StronglyConnectedComponents);
1
gap> c.MinimalNonFaces;
[ ]
gap>
gap> c:=complexes[2];;
gap> SCDim(c);
3
gap> c.IsEmpty;
false
gap> c.F;
[ 5, 10, 10, 5 ]
gap> Size(c.Facets);
5
gap> c.Homology;
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> c.Cohomology;
[ [ 1, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> c.HasBoundary;
false
gap> c.Orientation;
[ 1, -1, 1, -1, 1 ]
gap> c.AutomorphismGroup;
Sym( [ 1 .. 5 ] )
gap> c.GeneratorsEx;
[ [ [ 1 .. 4 ], [ 5 ] ] ]
gap> Size(c.ConnectedComponents);
1
gap> Size(c.StronglyConnectedComponents);
1
gap> c.MinimalNonFaces;
[ [ ], [ ], [ ] ]
gap> hd:=SCHasseDiagram(c);
[ [ [ [ 1, 2, 3, 4 ], [ 1, 5, 6, 7 ], [ 2, 5, 8, 9 ], [ 3, 6, 8, 10 ],
[ 4, 7, 9, 10 ] ],
[ [ 1, 2, 3 ], [ 1, 4, 5 ], [ 2, 4, 6 ], [ 3, 5, 6 ], [ 1, 7, 8 ],
[ 2, 7, 9 ], [ 3, 8, 9 ], [ 4, 7, 10 ], [ 5, 8, 10 ], [ 6, 9, 10 ] ]
,
[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 1, 4 ], [ 2, 4 ], [ 3, 4 ], [ 1, 5 ],
[ 2, 5 ], [ 3, 5 ], [ 4, 5 ] ] ],
[ [ [ 2, 1 ], [ 3, 1 ], [ 4, 1 ], [ 5, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 2 ],
[ 4, 3 ], [ 5, 3 ], [ 5, 4 ] ],
[ [ 5, 2, 1 ], [ 6, 3, 1 ], [ 7, 4, 1 ], [ 8, 3, 2 ], [ 9, 4, 2 ],
[ 10, 4, 3 ], [ 8, 6, 5 ], [ 9, 7, 5 ], [ 10, 7, 6 ], [ 10, 9, 8 ] ]
, [ [ 7, 4, 2, 1 ], [ 8, 5, 3, 1 ], [ 9, 6, 3, 2 ], [ 10, 6, 5, 4 ],
[ 10, 9, 8, 7 ] ] ] ]
gap> is:=SCIsSphere(c);
true
gap> isc:=SCIsSimplyConnected(c);
true
gap> hc:=SCHomologyClassic(c);
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> ism:=SCBistellarIsManifold(c);
true
gap>
gap> c:=complexes[3];;
gap> SCAlexanderDual(c);
<SimplicialComplex: Alexander dual of Bd(\beta^4) | dim = 5 | n = 8>
gap> SCAltshulerSteinberg(c);
0
gap> SCAntiStar(c,1);
<SimplicialComplex: ast([ 1 ]) in Bd(\beta^4) | dim = 3 | n = 7>
gap> SCAutomorphismGroup(c) = Group([ (7,8), (5,7)(6,8), (3,5)(4,6), (1,3)(2,4) ]);
true
gap> SCAutomorphismGroupInternal(c) = Group([ (7,8), (5,7)(6,8), (3,5)(4,6), (1,3)(2,4) ]);
true
gap> SCAutomorphismGroupSize(c);
384
gap> SCAutomorphismGroupStructure(c);
"TransitiveGroup(8,44) = [2^4]S(4)"
gap> SCAutomorphismGroupTransitivity(c);
1
gap> SCBoundary(c);
<SimplicialComplex: Bd(Bd(\beta^4)) | dim = -1 | n = 0>
gap> SCCentrallySymmetricElement(c);
(1,2)(3,4)(5,6)(7,8)
gap> SCCohomology(c);
[ [ 1, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> SCCohomologyBasis(c,0);
[ [ 1,
[ [ 1, 8 ], [ 1, 7 ], [ 1, 6 ], [ 1, 5 ], [ 1, 4 ], [ 1, 3 ], [ 1, 2 ],
[ 1, 1 ] ] ] ]
gap> SCCohomologyBasisAsSimplices(c,0);
[ [ 1,
[ [ 1, [ 8 ] ], [ 1, [ 7 ] ], [ 1, [ 6 ] ], [ 1, [ 5 ] ], [ 1, [ 4 ] ],
[ 1, [ 3 ] ], [ 1, [ 2 ] ], [ 1, [ 1 ] ] ] ] ]
gap> SCCollapseGreedy(c);
<SimplicialComplex: collapsed version of Bd(\beta^4) | dim = 3 | n = 8>
gap> SCCone(c);
<SimplicialComplex: cone over Bd(\beta^4) | dim = 4 | n = 9>
gap> SCConnectedComponents(c);
[ <SimplicialComplex: Connected component #1 of Bd(\beta^4) | dim = 3 | n = 8> ]
gap> SCConnectedProduct(c,2);
<SimplicialComplex: Bd(\beta^4)#+-Bd(\beta^4) | dim = 3 | n = 12>
gap> SCConnectedSum(c,c);
<SimplicialComplex: Bd(\beta^4)#+-Bd(\beta^4) | dim = 3 | n = 12>
gap> SCConnectedSumMinus(c,c);
<SimplicialComplex: Bd(\beta^4)#+-Bd(\beta^4) | dim = 3 | n = 12>
gap> IsIdenticalObj(c,SCCopy(c));
false
gap> SCDifference(c,c);
<SimplicialComplex: Bd(\beta^4) \ Bd(\beta^4) | dim = -1 | n = 0>
gap> SCDim(c);
3
gap> SCFVector(SCDualGraph(c));
[ 16, 32 ]
gap> SCEquivalent(c,c);
true
gap> SCEulerCharacteristic(c);
0
gap> SCExamineComplexBistellar(c)<>fail;
true
gap> SCFVector(c);
[ 8, 24, 32, 16 ]
gap> SCFaceLattice(c);
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ] ],
[ [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 1, 8 ], [ 2, 3 ],
[ 2, 4 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 2, 8 ], [ 3, 5 ], [ 3, 6 ],
[ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ], [ 4, 8 ], [ 5, 7 ],
[ 5, 8 ], [ 6, 7 ], [ 6, 8 ] ],
[ [ 1, 3, 5 ], [ 1, 3, 6 ], [ 1, 3, 7 ], [ 1, 3, 8 ], [ 1, 4, 5 ],
[ 1, 4, 6 ], [ 1, 4, 7 ], [ 1, 4, 8 ], [ 1, 5, 7 ], [ 1, 5, 8 ],
[ 1, 6, 7 ], [ 1, 6, 8 ], [ 2, 3, 5 ], [ 2, 3, 6 ], [ 2, 3, 7 ],
[ 2, 3, 8 ], [ 2, 4, 5 ], [ 2, 4, 6 ], [ 2, 4, 7 ], [ 2, 4, 8 ],
[ 2, 5, 7 ], [ 2, 5, 8 ], [ 2, 6, 7 ], [ 2, 6, 8 ], [ 3, 5, 7 ],
[ 3, 5, 8 ], [ 3, 6, 7 ], [ 3, 6, 8 ], [ 4, 5, 7 ], [ 4, 5, 8 ],
[ 4, 6, 7 ], [ 4, 6, 8 ] ],
[ [ 1, 3, 5, 7 ], [ 1, 3, 5, 8 ], [ 1, 3, 6, 7 ], [ 1, 3, 6, 8 ],
[ 1, 4, 5, 7 ], [ 1, 4, 5, 8 ], [ 1, 4, 6, 7 ], [ 1, 4, 6, 8 ],
[ 2, 3, 5, 7 ], [ 2, 3, 5, 8 ], [ 2, 3, 6, 7 ], [ 2, 3, 6, 8 ],
[ 2, 4, 5, 7 ], [ 2, 4, 5, 8 ], [ 2, 4, 6, 7 ], [ 2, 4, 6, 8 ] ] ]
gap> SCFaces(c,1);
[ [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 1, 8 ], [ 2, 3 ],
[ 2, 4 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 2, 8 ], [ 3, 5 ], [ 3, 6 ],
[ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ], [ 4, 8 ], [ 5, 7 ],
[ 5, 8 ], [ 6, 7 ], [ 6, 8 ] ]
gap> SCFacets(c);
[ [ 1, 3, 5, 7 ], [ 1, 3, 5, 8 ], [ 1, 3, 6, 7 ], [ 1, 3, 6, 8 ],
[ 1, 4, 5, 7 ], [ 1, 4, 5, 8 ], [ 1, 4, 6, 7 ], [ 1, 4, 6, 8 ],
[ 2, 3, 5, 7 ], [ 2, 3, 5, 8 ], [ 2, 3, 6, 7 ], [ 2, 3, 6, 8 ],
[ 2, 4, 5, 7 ], [ 2, 4, 5, 8 ], [ 2, 4, 6, 7 ], [ 2, 4, 6, 8 ] ]
gap> SCFillSphere(c);
<SimplicialComplex: FilledSphere(Bd(\beta^4)) at vertex [ 1 ] | dim = 4 | n = 8>
gap> SCFpBettiNumbers(c,2);
[ 1, 0, 0, 1 ]
gap> Size(SCFundamentalGroup(c));
1
gap> SCGVector(c);
[ 3, 2 ]
gap> SCGenerators(c);
[ [ [ 1, 3, 5, 7 ], 16 ] ]
gap> SCHVector(c);
[ 4, 6, 4, 1 ]
gap> SCHasBoundary(c);
false
gap> SCHasInterior(c);
true
gap> SCHomology(c);
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> SCHomologyBasis(c,0);
[ [ 1, [ [ 1, 1 ] ] ] ]
gap> SCHomologyBasisAsSimplices(c,0);
[ [ 1, [ [ 1, [ 1 ] ] ] ] ]
gap> SCHomologyInternal(c);
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> SCInterior(c);
<SimplicialComplex: Int(Bd(\beta^4)) | dim = 2 | n = 8>
gap> SCIntersection(c,c);
<SimplicialComplex: Bd(\beta^4) cap Bd(\beta^4) | dim = 3 | n = 8>
gap> SCIsCentrallySymmetric(c);
true
gap> SCIsConnected(c);
true
gap> SCIsEmpty(c);
false
gap> SCIsEulerianManifold(c);
true
gap> SCIsFlag(c);
true
gap> SCIsHomologySphere(c);
true
gap> SCIsInKd(c,1);
false
gap> SCIsIsomorphic(c,c);
true
gap> SCIsKNeighborly(c,2);
false
gap> SCIsKStackedSphere(c,1);
[ false, <SimplicialComplex: empty complex | dim = -1 | n = 0> ]
gap> SCIsManifold(c);
true
gap> SCIsMovableComplex(c);
true
gap> SCIsOrientable(c);
true
gap> SCIsPolyhedralComplex(c);
true
gap> SCIsPropertyObject(c);
true
gap> SCIsPseudoManifold(c);
true
gap> SCIsPure(c);
true
gap> SCIsSimplicialComplex(c);
true
gap> SCIsStronglyConnected(c);
true
gap> SCIsTight(c);
false
gap> SCLabelMax(c);
8
gap> SCLabelMin(c);
1
gap> SCLabels(c) = [ 1 .. 8] ;
true
gap> SCSpanningTree(c);
<SimplicialComplex: spanning tree of Bd(\beta^4) | dim = 1 | n = 8>
gap> SCLink(c,1);
<SimplicialComplex: lk([ 1 ]) in Bd(\beta^4) | dim = 2 | n = 6>
gap> SCLinks(c,0);
[ <SimplicialComplex: lk([ 1 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 2 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 3 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 4 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 5 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 6 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 7 ]) in Bd(\beta^4) | dim = 2 | n = 6>,
<SimplicialComplex: lk([ 8 ]) in Bd(\beta^4) | dim = 2 | n = 6> ]
gap> SCMinimalNonFaces(c);
[ [ ], [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 7, 8 ] ], [ ] ]
gap> SCMorseIsPerfect(c,SCVertices(c));
false
gap> SCMorseMultiplicityVector(c,SCVertices(c));
[ [ 1, 0, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 1, 0, 0 ],
[ 0, 0, 1, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 0, 1 ] ]
gap> SCMorseNumberOfCriticalPoints(c,SCVertices(c));
[ 8, [ 2, 2, 2, 2 ] ]
gap> SCNeighborliness(c);
1
gap> SCNumFaces(c,1);
24
gap> SCOrientation(c);
[ 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1 ]
gap> SCRMoves(c,1);
[ [ [ 1, 3, 5 ], [ 7, 8 ] ], [ [ 1, 3, 6 ], [ 7, 8 ] ],
[ [ 1, 3, 7 ], [ 5, 6 ] ], [ [ 1, 3, 8 ], [ 5, 6 ] ],
[ [ 1, 4, 5 ], [ 7, 8 ] ], [ [ 1, 4, 6 ], [ 7, 8 ] ],
[ [ 1, 4, 7 ], [ 5, 6 ] ], [ [ 1, 4, 8 ], [ 5, 6 ] ],
[ [ 1, 5, 7 ], [ 3, 4 ] ], [ [ 1, 5, 8 ], [ 3, 4 ] ],
[ [ 1, 6, 7 ], [ 3, 4 ] ], [ [ 1, 6, 8 ], [ 3, 4 ] ],
[ [ 2, 3, 5 ], [ 7, 8 ] ], [ [ 2, 3, 6 ], [ 7, 8 ] ],
[ [ 2, 3, 7 ], [ 5, 6 ] ], [ [ 2, 3, 8 ], [ 5, 6 ] ],
[ [ 2, 4, 5 ], [ 7, 8 ] ], [ [ 2, 4, 6 ], [ 7, 8 ] ],
[ [ 2, 4, 7 ], [ 5, 6 ] ], [ [ 2, 4, 8 ], [ 5, 6 ] ],
[ [ 2, 5, 7 ], [ 3, 4 ] ], [ [ 2, 5, 8 ], [ 3, 4 ] ],
[ [ 2, 6, 7 ], [ 3, 4 ] ], [ [ 2, 6, 8 ], [ 3, 4 ] ],
[ [ 3, 5, 7 ], [ 1, 2 ] ], [ [ 3, 5, 8 ], [ 1, 2 ] ],
[ [ 3, 6, 7 ], [ 1, 2 ] ], [ [ 3, 6, 8 ], [ 1, 2 ] ],
[ [ 4, 5, 7 ], [ 1, 2 ] ], [ [ 4, 5, 8 ], [ 1, 2 ] ],
[ [ 4, 6, 7 ], [ 1, 2 ] ], [ [ 4, 6, 8 ], [ 1, 2 ] ] ]
gap> SCRelabel(c,[11..18]);
true
gap> SCRelabelTransposition(c,[11,12]);
true
gap> SCRelabelStandard(c);
true
gap> SCRename(c,"test");
true
gap> SCName(c);
"test"
gap> SCSkel(c,0);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ] ]
gap> SCSpan(c,[ 1, 2, 3, 4 ]);
<SimplicialComplex: span([ 1, 2, 3, 4 ]) in test | dim = 1 | n = 4>
gap> SCStar(c,1);
<SimplicialComplex: star([ 1 ]) in test | dim = 3 | n = 7>
gap> SCStars(c,0);
[ <SimplicialComplex: star([ 1 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 2 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 3 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 4 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 5 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 6 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 7 ]) in test | dim = 3 | n = 7>,
<SimplicialComplex: star([ 8 ]) in test | dim = 3 | n = 7> ]
gap> SCStronglyConnectedComponents(c);
[ <SimplicialComplex: Strongly connected component #1 of test | dim = 3 | n = 8> ]
gap> SCSuspension(c);
<SimplicialComplex: susp of test | dim = 4 | n = 10>
gap> SCTopologicalType(c);
"S^3"
gap> SCVertexIdentification(c,[1],[2]);
<SimplicialComplex: test vertex identified ([ 1 ]=[ 2 ]) | dim = 3 | n = 7>
gap> SCVertices(c) = [ 1 .. 8 ];
true
gap> SCVerticesEx(c);
[ 1 .. 8 ]
gap> SCIsSimplicialComplex(SCWedge(c,c));
true
gap> hd:=SCHasseDiagram(c);
[ [ [ [ 1, 2, 3, 4, 5, 6 ], [ 7, 8, 9, 10, 11, 12 ], [ 1, 7, 13, 14, 15, 16 ],
[ 2, 8, 17, 18, 19, 20 ], [ 3, 9, 13, 17, 21, 22 ],
[ 4, 10, 14, 18, 23, 24 ], [ 5, 11, 15, 19, 21, 23 ],
[ 6, 12, 16, 20, 22, 24 ] ],
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 1, 5, 9, 10 ], [ 2, 6, 11, 12 ],
[ 3, 7, 9, 11 ], [ 4, 8, 10, 12 ], [ 13, 14, 15, 16 ],
[ 17, 18, 19, 20 ], [ 13, 17, 21, 22 ], [ 14, 18, 23, 24 ],
[ 15, 19, 21, 23 ], [ 16, 20, 22, 24 ], [ 1, 13, 25, 26 ],
[ 2, 14, 27, 28 ], [ 3, 15, 25, 27 ], [ 4, 16, 26, 28 ],
[ 5, 17, 29, 30 ], [ 6, 18, 31, 32 ], [ 7, 19, 29, 31 ],
[ 8, 20, 30, 32 ], [ 9, 21, 25, 29 ], [ 10, 22, 26, 30 ],
[ 11, 23, 27, 31 ], [ 12, 24, 28, 32 ] ],
[ [ 1, 2 ], [ 3, 4 ], [ 1, 3 ], [ 2, 4 ], [ 5, 6 ], [ 7, 8 ], [ 5, 7 ],
[ 6, 8 ], [ 1, 5 ], [ 2, 6 ], [ 3, 7 ], [ 4, 8 ], [ 9, 10 ],
[ 11, 12 ], [ 9, 11 ], [ 10, 12 ], [ 13, 14 ], [ 15, 16 ],
[ 13, 15 ], [ 14, 16 ], [ 9, 13 ], [ 10, 14 ], [ 11, 15 ],
[ 12, 16 ], [ 1, 9 ], [ 2, 10 ], [ 3, 11 ], [ 4, 12 ], [ 5, 13 ],
[ 6, 14 ], [ 7, 15 ], [ 8, 16 ] ] ],
[ [ [ 3, 1 ], [ 4, 1 ], [ 5, 1 ], [ 6, 1 ], [ 7, 1 ], [ 8, 1 ], [ 3, 2 ],
[ 4, 2 ], [ 5, 2 ], [ 6, 2 ], [ 7, 2 ], [ 8, 2 ], [ 5, 3 ],
[ 6, 3 ], [ 7, 3 ], [ 8, 3 ], [ 5, 4 ], [ 6, 4 ], [ 7, 4 ],
[ 8, 4 ], [ 7, 5 ], [ 8, 5 ], [ 7, 6 ], [ 8, 6 ] ],
[ [ 13, 3, 1 ], [ 14, 4, 1 ], [ 15, 5, 1 ], [ 16, 6, 1 ], [ 17, 3, 2 ],
[ 18, 4, 2 ], [ 19, 5, 2 ], [ 20, 6, 2 ], [ 21, 5, 3 ],
[ 22, 6, 3 ], [ 23, 5, 4 ], [ 24, 6, 4 ], [ 13, 9, 7 ],
[ 14, 10, 7 ], [ 15, 11, 7 ], [ 16, 12, 7 ], [ 17, 9, 8 ],
[ 18, 10, 8 ], [ 19, 11, 8 ], [ 20, 12, 8 ], [ 21, 11, 9 ],
[ 22, 12, 9 ], [ 23, 11, 10 ], [ 24, 12, 10 ], [ 21, 15, 13 ],
[ 22, 16, 13 ], [ 23, 15, 14 ], [ 24, 16, 14 ], [ 21, 19, 17 ],
[ 22, 20, 17 ], [ 23, 19, 18 ], [ 24, 20, 18 ] ],
[ [ 25, 9, 3, 1 ], [ 26, 10, 4, 1 ], [ 27, 11, 3, 2 ], [ 28, 12, 4, 2 ],
[ 29, 9, 7, 5 ], [ 30, 10, 8, 5 ], [ 31, 11, 7, 6 ],
[ 32, 12, 8, 6 ], [ 25, 21, 15, 13 ], [ 26, 22, 16, 13 ],
[ 27, 23, 15, 14 ], [ 28, 24, 16, 14 ], [ 29, 21, 19, 17 ],
[ 30, 22, 20, 17 ], [ 31, 23, 19, 18 ], [ 32, 24, 20, 18 ] ] ] ]
gap> is:=SCIsSphere(c);
true
gap> isc:=SCIsSimplyConnected(c);
true
gap> hc:=SCHomologyClassic(c);
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> ism:=SCBistellarIsManifold(c);
true
gap>
gap> c:=complexes[4];;
gap> SCDim(c);
2
gap> c.IsEmpty;
false
gap> c.F;
[ 5, 9, 5 ]
gap> Size(c.Facets);
5
gap> c.Homology;
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ] ]
gap> c.Cohomology;
[ [ 1, [ ] ], [ 0, [ ] ], [ 0, [ ] ] ]
gap> c.HasBoundary;
true
gap> c.Orientation;
[ 1, -1, 1, 1, -1 ]
gap> Size(c.ConnectedComponents);
1
gap> Size(c.StronglyConnectedComponents);
1
gap> c.MinimalNonFaces;
[ [ ], [ [ 4, 5 ] ] ]
gap> hd:=SCHasseDiagram(c);
[ [ [ [ 1, 2, 3, 4 ], [ 1, 5, 6, 7 ], [ 2, 5, 8, 9 ], [ 3, 6, 8 ],
[ 4, 7, 9 ] ],
[ [ 1 ], [ 2, 3 ], [ 1, 2 ], [ 3 ], [ 4, 5 ], [ 1, 4 ], [ 5 ],
[ 2, 4 ], [ 3, 5 ] ] ],
[ [ [ 2, 1 ], [ 3, 1 ], [ 4, 1 ], [ 5, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 2 ],
[ 4, 3 ], [ 5, 3 ] ],
[ [ 6, 3, 1 ], [ 8, 3, 2 ], [ 9, 4, 2 ], [ 8, 6, 5 ], [ 9, 7, 5 ] ] ] ]
gap> is:=SCIsSphere(c);
false
gap> isc:=SCIsSimplyConnected(c);
true
gap> hc:=SCHomologyClassic(c);
[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ] ]
gap>
gap> c:=complexes[5];;
gap> SCDim(c);
3
gap> c.IsEmpty;
false
gap> c.F;
[ 9, 36, 54, 27 ]
gap> Size(c.Facets);
27
gap> c.Homology;
[ [ 0, [ ] ], [ 1, [ ] ], [ 0, [ 2 ] ], [ 0, [ ] ] ]
gap> c.Cohomology;
[ [ 1, [ ] ], [ 1, [ ] ], [ 0, [ ] ], [ 0, [ 2 ] ] ]
gap> c.HasBoundary;
false
gap> c.Orientation;
[ ]
gap> c.AutomorphismGroup = Group([ (1,2,3,4,5,6,7,8,9), (1,3)(4,9)(5,8)(6,7) ]);
true
gap> c.GeneratorsEx;
[ [ [ 1, 2, 3, 5 ], 18 ], [ [ 1, 2, 4, 5 ], 9 ] ]
gap> Size(c.ConnectedComponents);
1
gap> Size(c.StronglyConnectedComponents);
1
gap> c.MinimalNonFaces;
[ [ ], [ ],
[ [ 1, 2, 6 ], [ 1, 3, 6 ], [ 1, 3, 7 ], [ 1, 4, 6 ], [ 1, 4, 7 ],
[ 1, 4, 8 ], [ 1, 5, 6 ], [ 1, 5, 7 ], [ 1, 5, 8 ], [ 1, 5, 9 ],
[ 2, 3, 7 ], [ 2, 4, 7 ], [ 2, 4, 8 ], [ 2, 5, 7 ], [ 2, 5, 8 ],
[ 2, 5, 9 ], [ 2, 6, 7 ], [ 2, 6, 8 ], [ 2, 6, 9 ], [ 3, 4, 8 ],
[ 3, 5, 8 ], [ 3, 5, 9 ], [ 3, 6, 8 ], [ 3, 6, 9 ], [ 3, 7, 8 ],
[ 3, 7, 9 ], [ 4, 5, 9 ], [ 4, 6, 9 ], [ 4, 7, 9 ], [ 4, 8, 9 ] ] ]
gap> hd:=SCHasseDiagram(c);
[ [ [ [ 1, 2, 3, 4, 5, 6, 7, 8 ], [ 1, 9, 10, 11, 12, 13, 14, 15 ],
[ 2, 9, 16, 17, 18, 19, 20, 21 ], [ 3, 10, 16, 22, 23, 24, 25, 26 ],
[ 4, 11, 17, 22, 27, 28, 29, 30 ], [ 5, 12, 18, 23, 27, 31, 32, 33 ]
, [ 6, 13, 19, 24, 28, 31, 34, 35 ],
[ 7, 14, 20, 25, 29, 32, 34, 36 ],
[ 8, 15, 21, 26, 30, 33, 35, 36 ] ],
[ [ 1, 2, 3, 4, 5, 6 ], [ 1, 7, 8, 9, 10 ], [ 2, 7, 11, 12 ],
[ 3, 8, 11 ], [ 13, 14, 15 ], [ 4, 13, 16, 17 ],
[ 5, 9, 14, 16, 18 ], [ 6, 10, 12, 15, 17, 18 ],
[ 1, 19, 20, 21, 22, 23 ], [ 2, 19, 24, 25, 26 ], [ 3, 20, 24, 27 ],
[ 21, 25, 27 ], [ 4, 28, 29 ], [ 5, 22, 28, 30 ],
[ 6, 23, 26, 29, 30 ], [ 7, 19, 31, 32, 33, 34 ],
[ 8, 20, 31, 35, 36 ], [ 21, 32, 35, 37 ], [ 33, 36, 37 ],
[ 9, 22, 38 ], [ 10, 23, 34, 38 ], [ 11, 24, 31, 39, 40, 41 ],
[ 25, 32, 39, 42, 43 ], [ 33, 40, 42, 44 ], [ 41, 43, 44 ],
[ 12, 26, 34 ], [ 27, 35, 39, 45, 46, 47 ], [ 36, 40, 45, 48, 49 ],
[ 41, 46, 48, 50 ], [ 47, 49, 50 ], [ 13, 37, 42, 45, 51, 52 ],
[ 14, 43, 46, 51, 53 ], [ 15, 47, 52, 53 ],
[ 16, 28, 44, 48, 51, 54 ], [ 17, 29, 49, 52, 54 ],
[ 18, 30, 38, 50, 53, 54 ] ],
[ [ 1, 2 ], [ 3, 4 ], [ 1, 3 ], [ 5, 6 ], [ 2, 5 ], [ 4, 6 ], [ 7, 8 ],
[ 1, 7 ], [ 2, 9 ], [ 8, 9 ], [ 3, 7 ], [ 4, 8 ], [ 10, 11 ],
[ 10, 12 ], [ 11, 12 ], [ 5, 10 ], [ 6, 11 ], [ 9, 12 ],
[ 13, 14 ], [ 1, 15 ], [ 13, 15 ], [ 2, 16 ], [ 14, 16 ],
[ 3, 17 ], [ 13, 17 ], [ 4, 14 ], [ 15, 17 ], [ 5, 18 ], [ 6, 18 ],
[ 16, 18 ], [ 7, 19 ], [ 13, 20 ], [ 19, 20 ], [ 8, 14 ],
[ 15, 21 ], [ 19, 21 ], [ 20, 21 ], [ 9, 16 ], [ 17, 22 ],
[ 19, 23 ], [ 22, 23 ], [ 20, 24 ], [ 22, 24 ], [ 23, 24 ],
[ 21, 25 ], [ 22, 26 ], [ 25, 26 ], [ 23, 27 ], [ 25, 27 ],
[ 26, 27 ], [ 10, 24 ], [ 11, 25 ], [ 12, 26 ], [ 18, 27 ] ] ],
[ [ [ 2, 1 ], [ 3, 1 ], [ 4, 1 ], [ 5, 1 ], [ 6, 1 ], [ 7, 1 ], [ 8, 1 ],
[ 9, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 2 ], [ 6, 2 ], [ 7, 2 ],
[ 8, 2 ], [ 9, 2 ], [ 4, 3 ], [ 5, 3 ], [ 6, 3 ], [ 7, 3 ],
[ 8, 3 ], [ 9, 3 ], [ 5, 4 ], [ 6, 4 ], [ 7, 4 ], [ 8, 4 ],
[ 9, 4 ], [ 6, 5 ], [ 7, 5 ], [ 8, 5 ], [ 9, 5 ], [ 7, 6 ],
[ 8, 6 ], [ 9, 6 ], [ 8, 7 ], [ 9, 7 ], [ 9, 8 ] ],
[ [ 9, 2, 1 ], [ 10, 3, 1 ], [ 11, 4, 1 ], [ 13, 6, 1 ], [ 14, 7, 1 ],
[ 15, 8, 1 ], [ 16, 3, 2 ], [ 17, 4, 2 ], [ 20, 7, 2 ],
[ 21, 8, 2 ], [ 22, 4, 3 ], [ 26, 8, 3 ], [ 31, 6, 5 ],
[ 32, 7, 5 ], [ 33, 8, 5 ], [ 34, 7, 6 ], [ 35, 8, 6 ],
[ 36, 8, 7 ], [ 16, 10, 9 ], [ 17, 11, 9 ], [ 18, 12, 9 ],
[ 20, 14, 9 ], [ 21, 15, 9 ], [ 22, 11, 10 ], [ 23, 12, 10 ],
[ 26, 15, 10 ], [ 27, 12, 11 ], [ 34, 14, 13 ], [ 35, 15, 13 ],
[ 36, 15, 14 ], [ 22, 17, 16 ], [ 23, 18, 16 ], [ 24, 19, 16 ],
[ 26, 21, 16 ], [ 27, 18, 17 ], [ 28, 19, 17 ], [ 31, 19, 18 ],
[ 36, 21, 20 ], [ 27, 23, 22 ], [ 28, 24, 22 ], [ 29, 25, 22 ],
[ 31, 24, 23 ], [ 32, 25, 23 ], [ 34, 25, 24 ], [ 31, 28, 27 ],
[ 32, 29, 27 ], [ 33, 30, 27 ], [ 34, 29, 28 ], [ 35, 30, 28 ],
[ 36, 30, 29 ], [ 34, 32, 31 ], [ 35, 33, 31 ], [ 36, 33, 32 ],
[ 36, 35, 34 ] ],
[ [ 20, 8, 3, 1 ], [ 22, 9, 5, 1 ], [ 24, 11, 3, 2 ], [ 26, 12, 6, 2 ],
[ 28, 16, 5, 4 ], [ 29, 17, 6, 4 ], [ 31, 11, 8, 7 ],
[ 34, 12, 10, 7 ], [ 38, 18, 10, 9 ], [ 51, 16, 14, 13 ],
[ 52, 17, 15, 13 ], [ 53, 18, 15, 14 ], [ 32, 25, 21, 19 ],
[ 34, 26, 23, 19 ], [ 35, 27, 21, 20 ], [ 38, 30, 23, 22 ],
[ 39, 27, 25, 24 ], [ 54, 30, 29, 28 ], [ 40, 36, 33, 31 ],
[ 42, 37, 33, 32 ], [ 45, 37, 36, 35 ], [ 46, 43, 41, 39 ],
[ 48, 44, 41, 40 ], [ 51, 44, 43, 42 ], [ 52, 49, 47, 45 ],
[ 53, 50, 47, 46 ], [ 54, 50, 49, 48 ] ] ] ]
gap> is:=SCIsSphere(c);
false
gap> isc:=SCIsSimplyConnected(c);
false
gap> hc:=SCHomologyClassic(c);
[ [ 0, [ ] ], [ 1, [ ] ], [ 0, [ 2 ] ], [ 0, [ ] ] ]
gap> ism:=SCBistellarIsManifold(c);
true
gap>
gap> c:=complexes[6];;
gap> SCDim(c);
4
gap> SCRename(c,"K3 surface");
true
gap> SCName(c)=c.Name;
true
gap> c.IsEmpty;
false
gap> c.F;
[ 16, 120, 560, 720, 288 ]
gap> Size(c.Facets);
288
gap> c.Homology;
[ [ 0, [ ] ], [ 0, [ ] ], [ 22, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> c.Cohomology;
[ [ 1, [ ] ], [ 0, [ ] ], [ 22, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ]
gap> c.HasBoundary;
false
gap> c.Orientation;
[ 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1,
1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1,
1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1,
1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1,
-1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1,
1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1,
-1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1,
-1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1,
1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1,
1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1,
1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1,
-1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1,
1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1,
-1, -1, 1, 1, -1, 1, 1, -1, 1, -1 ]
gap> c.AutomorphismGroup = Group([ (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),
> (1,2,8,14,5)(3,11,9,4,13)(6,7,12,15,10), (1,3,2)(5,11,14)(6,9,15)(7,10,13)(8,12,16) ]);
true
gap> c.GeneratorsEx;
[ [ [ 1, 2, 3, 8, 12 ], 240 ], [ [ 1, 2, 5, 8, 14 ], 48 ] ]
gap> Size(c.ConnectedComponents);
1
gap> Size(c.StronglyConnectedComponents);
1
gap> Size(c.MinimalNonFaces[4]);
1100
gap> c.IntersectionForm;
[ [ -2, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 2, 1,
0, 1 ],
[ 1, -2, 1, 0, 0, 1, 1, 1, 0, 0, -1, 0, 0, 1, 1, 0, -1, 0, -1, -1, 0, -1 ],
[ -1, 1, -2, -1, 0, -1, -1, 0, -1, 0, 0, 0, 1, -1, -1, -1, 1, -2, 2, 1, 0,
0 ], [ -1, 0, -1, -2, 1, -1, 0, 0, -1, 1, 1, 0, 1, -1, -1, -1, 1, -1,
1, 1, 0, 1 ],
[ 1, 0, 0, 1, -2, 1, 0, 1, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1 ],
[ -1, 1, -1, -1, 1, -2, -1, -1, -1, 1, 1, 0, 1, -1, -1, 0, 1, -1, 1, 1, 0,
1 ], [ -1, 1, -1, 0, 0, -1, -2, -1, -1, 1, 0, -1, 1, -1, -1, 0, 1, -1,
1, 1, 0, 1 ],
[ -1, 1, 0, 0, 1, -1, -1, -2, 0, 1, 1, -1, 0, 0, -1, 0, 1, 1, 1, 1, 0, 1 ],
[ -1, 0, -1, -1, 0, -1, -1, 0, -2, 1, -1, -1, 1, 0, -1, -1, 1, -2, 2, 1, 0,
0 ], [ 1, 0, 0, 1, -1, 1, 1, 1, 1, -2, -1, 1, -1, 0, 1, 0, 0, 1, -1, 0,
0, -1 ],
[ 1, -1, 0, 1, -2, 1, 0, 1, -1, -1, -4, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, -2 ],
[ -1, 0, 0, 0, 0, 0, -1, -1, -1, 1, 0, -2, 1, 0, 0, 0, 0, -1, 1, 0, 0, 1 ],
[ 1, 0, 1, 1, 0, 1, 1, 0, 1, -1, 0, 1, -2, 1, 1, 1, -1, 2, -1, -1, 0, -1 ],
[ -1, 1, -1, -1, 0, -1, -1, 0, 0, 0, 1, 0, 1, -2, -1, -1, 1, -1, 1, 1, 0, 1
], [ -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 0, 1, -1, -2, 0, 1, -1, 2,
1, -1, 1 ],
[ -1, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, -2, 1, -2, 1, 0, 1, 0 ],
[ 1, -1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, -1, 1, 1, 1, -2, 1, -2, -1, 0, 0 ],
[ -1, 0, -2, -1, 0, -1, -1, 1, -2, 1, -1, -1, 2, -1, -1, -2, 1, -4, 2, 1,
0, 0 ],
[ 2, -1, 2, 1, -1, 1, 1, 1, 2, -1, 0, 1, -1, 1, 2, 1, -2, 2, -4, -2, 1, -1 ]
, [ 1, -1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, -1, 1, 1, 0, -1, 1, -2, -2, 1,
-1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 1, -2, 1 ],
[ 1, -1, 0, 1, -1, 1, 1, 1, 0, -1, -2, 1, -1, 1, 1, 0, 0, 0, -1, -1, 1, -2
] ]
gap> d:=c.DualGraph;;
gap> Size(d.Facets);
720
gap> d:=c.SpanningTree;;
gap> Size(d.Facets);
15
gap>
gap> #labels
gap> labels:="abcdefghijklmnopqrstuvwxyz";;
gap> SCRelabel(c,List([1..c.F[1]],x->labels[x]));
true
gap> c.Facets{[1..10]};
[ "abchl", "abchp", "abclp", "abdgk", "abdgo", "abdko", "abegm", "abego",
"abehj", "abehn" ]
gap> c.Generators;
[ [ "abchl", 240 ], [ "abehn", 48 ] ]
gap>
gap> #connected/unconnected complexes
gap> c:=complexes[7];;
gap> SCDim(c);
1
gap> c.F;
[ 6, 4 ]
gap> c.FaceLattice;
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ] ],
[ [ 1, 2 ], [ 2, 3 ], [ 4, 5 ], [ 5, 6 ] ] ]
gap> c.IsStronglyConnected;
false
gap> Size(c.StronglyConnectedComponents);
2
gap> c.IsConnected;
false
gap> Size(c.ConnectedComponents);
2
gap>
gap> #homology and cohomology
gap> c:=complexes[8];;
gap> SCCohomology(c);
[ [ 1, [ ] ], [ 0, [ ] ], [ 0, [ 2 ] ] ]
gap> h:=SCHomology(c);
[ [ 0, [ ] ], [ 0, [ 2 ] ], [ 0, [ ] ] ]
gap> c:=complexes[8];;
gap> h=SCHomologyInternal(c);
true
gap>
gap>
gap> #operators
gap> c:=SCCartesianPower(SCBdSimplex(2),2);;
gap> c.F;
[ 9, 27, 18 ]
gap> c.Homology;
[ [ 0, [ ] ], [ 2, [ ] ], [ 1, [ ] ] ]
gap> d:=SCConnectedSum(c,c);;
gap> d=c+c;
true
gap> d.F;
[ 15, 51, 34 ]
gap> d.Homology;
[ [ 0, [ ] ], [ 4, [ ] ], [ 1, [ ] ] ]
gap>
gap> c:=SCCartesianProduct(SCBdSimplex(3),SCBdCrossPolytope(3));;
gap> c=SCBdSimplex(3)*SCBdCrossPolytope(3);
true
gap> SCDim(c);
4
gap> c.F;
[ 24, 156, 424, 480, 192 ]
gap> c.IsCentrallySymmetric;
true
gap> c.CentrallySymmetricElement;
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
gap>
gap> #generating complexes
gap> c:=SCFromDifferenceCycles([[1,1,6],[3,3,2]]);;
gap> SCDim(c);
2
gap> SCRelabel(c,List([1..c.F[1]],x->labels[x]));
true
gap> c.F;
[ 8, 24, 16 ]
gap> c.Homology;
[ [ 0, [ ] ], [ 2, [ ] ], [ 1, [ ] ] ]
gap>
gap> G:=Group([ (2,6)(4,8), (1,4,3,6,5,8,7,2), (1,3)(2,6)(5,7) ]);;
gap> d:=SCFromGenerators(G,[[1,2,3]]);;
gap> SCIsomorphism(c,d);
[ [ 'a', 1 ], [ 'b', 2 ], [ 'c', 3 ], [ 'd', 4 ], [ 'e', 5 ], [ 'f', 6 ],
[ 'g', 7 ], [ 'h', 8 ] ]
gap>
gap> #bistellar moves
gap> c:=SCBdSimplex(3);;
gap> c.F;
[ 4, 6, 4 ]
gap>
gap> c:=SCMove(c,[[1,2,3],[]]);;
gap> c.F;
[ 5, 9, 6 ]
gap>
gap> c:=SCMove(c,[[5],[1,2,3]]);;
gap> c.F;
[ 4, 6, 4 ]
gap>
gap> c:=SCBdCrossPolytope(4);;
gap> SCIsNormalSurface(SCNS([[1,2,3],[2,3,4],[1,3,4],[1,2,4]]));
true
gap> SCNSEmpty();
<NormalSurface: empty normal surface | dim = -1>
gap> sl:=SCNSSlicing(c,[[1,2,3,4],[5,6,7,8]]);;
gap> sl<>fail;
true
gap> SCIsSimplicialComplex(SCNSTriangulation(sl));
true
gap>
gap> SCMappingCylinder(2);
<SimplicialComplex: Mapping cylinder Bd(CP^2) = L(2,1) | dim = 4 | n = 32>
gap>
gap> SCSeriesAGL(17);
[ AGL(1,17), [ [ 1, 2, 4, 8, 16 ] ] ]
gap> SCSeriesBdHandleBody(3,9);
<SimplicialComplex: Sphere bundle S^2 ~ S^1 | dim = 3 | n = 9>
gap> SCSeriesC2n(16);
<SimplicialComplex: C_32 = { (1:1:11:19),(1:1:19:11),(1:11:1:19),(2:11:2:17),(2:13:2:15) } | dim = 3 | n = 32>
gap> SCSeriesCSTSurface(1,2,8);
<SimplicialComplex: cst surface S_{(1,2,8)} = { (1:2:5),(1:5:2) } | dim = 2 | n = 8>
gap> SCSeriesD2n(20);
<SimplicialComplex: D_40 = { (1:1:1:37),(1:2:35:2),(3:16:5:16),(2:3:16:19),(2:19:16:3) } | dim = 3 | n = 40>
gap> SCSeriesHandleBody(3,9);
<SimplicialComplex: Handle body B^2 x S^1 | dim = 3 | n = 9>
gap> SCSeriesK(1,0);
<SimplicialComplex: K^1_0 | dim = 3 | n = 9>
gap> SCSeriesKu(3);
<SimplicialComplex: Sl_12 = G{ [1,2,4,7],[1,2,7,8],[1,4,7,12] } | dim = 3 | n = 12>
gap> SCSeriesL(1,0);
<SimplicialComplex: L^1_0 | dim = 3 | n = 10>
gap> SCSeriesLe(7)<>fail;
true
gap> SCSeriesNSB1(11);
<SimplicialComplex: Neighborly sphere bundle NSB_1 | dim = 3 | n = 23>
gap> SCSeriesNSB2(11);
<SimplicialComplex: Neighborly sphere bundle NSB_2 | dim = 3 | n = 22>
gap> SCSeriesNSB3(11);
<SimplicialComplex: Neighborly sphere bundle NSB_3 | dim = 3 | n = 11>
gap> SCSeriesPrimeTorus(1,2,7);
<SimplicialComplex: prime torus S_{(1,2,7)} = { (1:2:4),(1:4:2) } | dim = 2 | n = 7>
gap>
gap> SCFVectorBdCrossPolytope(4);
[ 8, 24, 32, 16 ]
gap> SCFVectorBdCyclicPolytope(4,7);
[ 7, 21, 28, 14 ]
gap> SCFVectorBdSimplex(4);
[ 5, 10, 10, 5 ]
gap>
gap> G:=Group((1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),
> (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),
> (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),
> (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16),
> (2,13,15,11,14,3,5,8,16,7,4,9,10,6,12));;
gap> K3:=SCFromGenerators(G,[[2,3,4,5,9],[2,5,7,10,11]]);
<SimplicialComplex: complex from generators under unknown group | dim = 4 | n = 16>
gap> ll:=SCsFromGroupExt(G,16,4,0,0,false,false,0,[]);;
gap> Size(ll);
4
gap> SCIsIsomorphic(ll[1],K3);
true
gap>
gap> SCInfoLevel(1);
true
gap>
gap> STOP_TEST("simpcomp.tst", 1000000000 );
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