  
  [1X13 [33X[0;0YLibrary and I/O[133X[101X
  
  
  [1X13.1 [33X[0;0YSimplicial complex library[133X[101X
  
  [33X[0;0Y[5Xsimpcomp[105X contains a library of simplicial complexes on few vertices, most of
  them  (combinatorial)  triangulations  of manifolds and pseudomanifolds. The
  user  can load these known triangulations from the library in order to study
  their  properties  or to construct new triangulations out of the known ones.
  For  example,  a  user  could  determine  the  topological  type  of a given
  triangulation  --  which  can  be  quite  tedious  if  done  by  hand  -- by
  establishing a PL equivalence to a complex in the library.[133X
  
  [33X[0;0YAmong  other  known  triangulations,  the library contains all of the vertex
  transitive  triangulations of combinatorial manifolds with up to [22X15[122X vertices
  (for  [22Xd  ∈  { 2,3,9,10,11,12}[122X) and up to [22X13[122X vertices (for [22Xd ∈ { 4,5,6,7,8 }[122X)
  and all of the vertex transitive combinatorial pseudomanifolds with up to [22X15[122X
  vertices (for [22Xd=3[122X) and up to [22X13[122X vertices (for [22Xd ∈ { 4,5,6,7 }[122X) classified by
  Frank    Lutz    that    can    be    found   on   his   ``Manifold   Page''
  [7Xhttp://www.math.tu-berlin.de/diskregeom/stellar/[107X,     along     with    some
  triangulations of sphere bundles and some bounded triangulated PL-manifolds.[133X
  
  [33X[0;0YSee  [2XSCLib[102X  ([14X13.1-2[114X)  for a naming convention used for the global library of
  [5Xsimpcomp[105X.  Note: Another way of storing and loading complexes is provided by
  the   functions   [2XSCExportIsoSig[102X   ([14X6.2-2[114X),   [2XSCExportToString[102X  ([14X6.2-1[114X)  and
  [2XSCFromIsoSig[102X ([14X6.2-3[114X), see Section [14X6.2[114X for details.[133X
  
  [1X13.1-1 SCIsLibRepository[101X
  
  [33X[1;0Y[29X[2XSCIsLibRepository[102X( [3Xobject[103X ) [32X filter[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X or [9Xfalse[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YFilter  for  the  category of a library repository [10XSCIsLibRepository[110X used by
  the  [5Xsimpcomp[105X  library.  The  category  [10XSCLibRepository[110X  is derived from the
  category [10XSCPropertyObject[110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCIsLibRepository(SCLib); #the global library is stored in SCLib[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-2 SCLib[101X
  
  [33X[1;0Y[29X[2XSCLib[102X [32X global variable[133X
  
  [33X[0;0YThe  global variable [10XSCLib[110X contains the library object of the global library
  of  [5Xsimpcomp[105X  through which the user can access the library. The path to the
  global library is [10XGAPROOT/pkg/simpcomp/complexes[110X.[133X
  
  [33X[0;0YThe  naming convention in the global library is the following: complexes are
  usually named by their topological type. As usual, `S^d' denotes a [22Xd[122X-sphere,
  `T'  a torus, `x' the cartesian product, `~' the twisted product and `#' the
  connected sum. The Klein Bottle is denoted by `K' or `K^2'.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLib;[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=648[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/home/jonathan/bin/gap-4.11.1/pkg/simpcomp/complexes/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X gap> SCLib.Size;[128X[104X
    [4X[28X 648[128X[104X
    [4X[28X gap> SCLib.SearchByName("S^4~");[128X[104X
    [4X[28X [ [ 203, "S^4~S^1 (VT)" ], [ 330, "S^4~S^1 (VT)" ], [ 332, "S^4~S^1 (VT)" ], [128X[104X
    [4X[28X   [ 395, "S^4~S^1 (VT)" ], [ 451, "S^4~S^1 (VT)" ], [ 452, "S^4~S^1 (VT)" ], [128X[104X
    [4X[28X   [ 453, "S^4~S^1 (VT)" ], [ 454, "S^4~S^1 (VT)" ], [ 455, "S^4~S^1 (VT)" ], [128X[104X
    [4X[28X   [ 458, "S^4~S^1 (VT)" ], [ 459, "S^4~S^1 (VT)" ], [ 460, "S^4~S^1 (VT)" ] ][128X[104X
    [4X[28X gap> SCLib.Load(last[1][1]);          [128X[104X
    [4X[28X <SimplicialComplex: S^4~S^1 (VT) | dim = 5 | n = 13>[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-3 SCLibAdd[101X
  
  [33X[1;0Y[29X[2XSCLibAdd[102X( [3Xrepository[103X, [3Xcomplex[103X[, [3Xname[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YAdds  a given simplicial complex [3Xcomplex[103X to a given repository [3Xrepository[103X of
  type  [10XSCIsLibRepository[110X.  [3Xcomplex[103X  is saved to a file with suffix [10X.sc[110X in the
  repositories  base  path,  where  the  file  name  is either formed from the
  optional  argument  [3Xname[103X  and the current time or taken from the name of the
  complex, if it is named.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> info:=InfoLevel(InfoSimpcomp);;[128X[104X
    [4X[28X gap> SCInfoLevel(0);;[128X[104X
    [4X[28X gap> myRepository:=SCLibInit("/tmp/repository");[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=0[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/tmp/repository/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X gap> complex1:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> SCLibAdd(myRepository,complex1);[128X[104X
    [4X[28X true[128X[104X
    [4X[28X gap> complex2:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> myRepository.Add(complex2);; # alternative syntax[128X[104X
    [4X[28X gap> SCInfoLevel(info);;[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-4 SCLibAllComplexes[101X
  
  [33X[1;0Y[29X[2XSCLibAllComplexes[102X( [3Xrepository[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylist of entries of the form [10X[ integer, string ][110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YReturns a list with entries of the form [10X[ ID, NAME ][110X of all the complexes in
  the given repository [3Xrepository[103X of type [10XSCIsLibRepository[110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> all:=SCLibAllComplexes(SCLib);;[128X[104X
    [4X[28X gap> all[1];[128X[104X
    [4X[28X [ 1, "Moebius Strip" ][128X[104X
    [4X[28X gap> Length(all);[128X[104X
    [4X[28X 648[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-5 SCLibDelete[101X
  
  [33X[1;0Y[29X[2XSCLibDelete[102X( [3Xrepository[103X, [3Xid[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YDeletes  the  simplicial  complex  with  the  given  id  [3Xid[103X  from  the given
  repository  [3Xrepository[103X.  Apart from deleting the complexes' index entry, the
  associated [10X.sc[110X file is also deleted.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> myRepository:=SCLibInit("/tmp/repository");[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=2[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/tmp/repository/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X gap> SCLibAdd(myRepository,SCSimplex(2));;[128X[104X
    [4X[28X gap> SCLibDelete(myRepository,1);[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-6 SCLibDetermineTopologicalType[101X
  
  [33X[1;0Y[29X[2XSCLibDetermineTopologicalType[102X( [[3Xrepository[103X, ][3Xcomplex[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ysimplicial  complex  of  type  [10XSCSimplicialComplex[110X  or  a  list of
            integers upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YTries  to determine the topological type of a given complex [3Xcomplex[103X by first
  looking  for  complexes  with  matching  homology  in the library repository
  [3Xrepository[103X (if no repository is passed, the global repository [10XSCLib[110X is used)
  and  either  returns  a  simplicial  complex object (that is combinatorially
  isomorphic  to  the  complex given) or a list of library ids of complexes in
  the library with the same homology as the complex provided.[133X
  
  [33X[0;0YThe  ids  obtained in this way can then be used to compare the corresponding
  complexes with [3Xcomplex[103X via the function [2XSCEquivalent[102X ([14X9.2-2[114X).[133X
  
  [33X[0;0YIf  [3Xcomplex[103X  is a combinatorial manifold of dimension [22X1[122X or [22X2[122X its topological
  type  is  computed,  stored  to  the property [10XTopologicalType[110X and [3Xcomplex[103X is
  returned.[133X
  
  [33X[0;0YIf  no  complexes  with  matching  homology  can  be found, the empty set is
  returned.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCFromFacets([[1,2,3],[1,2,6],[1,3,5],[1,4,5],[1,4,6],[128X[104X
    [4X[28X                       [2,3,4],[2,4,5],[2,5,6],[3,4,6],[3,5,6]]);;[128X[104X
    [4X[28X gap> SCLibDetermineTopologicalType(c);[128X[104X
    [4X[28X <SimplicialComplex: unnamed complex 250 | dim = 2 | n = 6>[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-7 SCLibFlush[101X
  
  [33X[1;0Y[29X[2XSCLibFlush[102X( [3Xrepository[103X, [3Xconfirm[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YCompletely  empties  a  given  repository  [3Xrepository[103X.  The  index  and  all
  simplicial  complexes  in  this repository are deleted. The second argument,
  [3Xconfirm[103X, must be the string [10X"yes"[110X in order to confirm the deletion.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> myRepository:=SCLibInit("/tmp/repository");;[128X[104X
    [4X[28X gap> SCLibFlush(myRepository,"yes");[128X[104X
    [4X[28X #I  SCLibInit: invalid parameters.[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-8 SCLibInit[101X
  
  [33X[1;0Y[29X[2XSCLibInit[102X( [3Xdir[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylibrary  repository  of  type  [10XSCLibRepository[110X  upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YThis  function  initializes  a  library  repository  object  for  the  given
  directory  [3Xdir[103X  (which  has  to  be provided in form of a [5XGAP[105X object of type
  [10XString[110X  or  [10XDirectory[110X) and returns that library repository object in case of
  success.  The  returned  object  then  provides a mean to access the library
  repository via the [10XSCLib[110X-functions of [5Xsimpcomp[105X.[133X
  
  [33X[0;0YThe global library repository of [5Xsimpcomp[105X is loaded automatically at startup
  and  is  stored  in  the variable [10XSCLib[110X. User repositories can be created by
  calling  [10XSCLibInit[110X  with  a  desired  destination  directory. Note that each
  repository  must  reside  in  a  different path since otherwise data may get
  lost.[133X
  
  [33X[0;0YThe  function  first  tries  to  load  the  repository  index  for the given
  directory to rebuild it (by calling [10XSCLibUpdate[110X) if loading the index fails.
  The  library index of a library repository is stored in its base path in the
  XML  file  [10Xcomplexes.idx[110X, the complexes are stored in files with suffix [10X.sc[110X,
  also in XML format.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> myRepository:=SCLibInit("/tmp/repository");[128X[104X
    [4X[28X #I  SCLibInit: made directory "/tmp/repository/" for user library.[128X[104X
    [4X[28X #I  SCIntFunc.SCLibInit: index not found -- trying to reconstruct it.[128X[104X
    [4X[28X #I  SCLibUpdate: rebuilding index for /tmp/repository/.[128X[104X
    [4X[28X #I  SCLibUpdate: rebuilding index done.[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=0[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/tmp/repository/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-9 SCLibIsLoaded[101X
  
  [33X[1;0Y[29X[2XSCLibIsLoaded[102X( [3Xrepository[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X or [9Xfalse[109X upon succes, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YReturns  [9Xtrue[109X when a given library repository [3Xrepository[103X is in loaded state.
  This  means  that  the  directory  of  this  repository  is accessible and a
  repository  index file for this repository exists in the repositories' path.
  If this is not the case [9Xfalse[109X is returned.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLibIsLoaded(SCLib);[128X[104X
    [4X[28X true[128X[104X
    [4X[28X gap> SCLib.IsLoaded;[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-10 SCLibSearchByAttribute[101X
  
  [33X[1;0Y[29X[2XSCLibSearchByAttribute[102X( [3Xrepository[103X, [3Xexpr[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10YA list of items of the form [10X[ integer, string ][110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YSearches  a  given repository [3Xrepository[103X for complexes for which the boolean
  expression  [3Xexpr[103X,  passed as string, evaluates to [9Xtrue[109X and returns a list of
  complexes  with  entries  of  the  form  [10X[ID,  NAME][110X or [9Xfail[109X upon error. The
  expression  may  use  all  [5XGAP[105X  functions  and  can  access  all the indexed
  attributes  of  the  complexes  in  the  given repository for the query. The
  standard  attributes  are:  Dim  (Dimension),  F (f-vector), G (g-vector), H
  (h-vector),  Chi  (Euler  characteristic), Homology, Name, IsPM, IsManifold.
  See  [10XSCLib[110X  for  the  set  of  indexed  attributes  of the global library of
  [5Xsimpcomp[105X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLibSearchByAttribute(SCLib,"Dim=4 and F[3]=Binomial(F[1],3)");[128X[104X
    [4X[28X [ [ 16, "CP^2 (VT)" ], [ 520, "K3_16" ] ][128X[104X
    [4X[28X gap> SCLib.SearchByAttribute("Dim=4 and F[3]=Binomial(F[1],3)");[128X[104X
    [4X[28X [ [ 16, "CP^2 (VT)" ], [ 520, "K3_16" ] ][128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-11 SCLibSearchByName[101X
  
  [33X[1;0Y[29X[2XSCLibSearchByName[102X( [3Xrepository[103X, [3Xname[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10YA list of items of the form [10X[ integer, string ][110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YSearches a given repository [3Xrepository[103X for complexes that contain the string
  [3Xname[103X  as  a  substring  of  their  name  attribute and returns a list of the
  complexes  found with entries of the form [10X[ID, NAME][110X. See [2XSCLib[102X ([14X13.1-2[114X) for
  a naming convention used for the global library of [5Xsimpcomp[105X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLibSearchByName(SCLib,"K3");[128X[104X
    [4X[28X [ [ 520, "K3_16" ], [ 539, "K3_17" ] ][128X[104X
    [4X[28X gap> SCLib.SearchByName("K3"); #alternative syntax[128X[104X
    [4X[28X [ [ 520, "K3_16" ], [ 539, "K3_17" ] ][128X[104X
    [4X[28X gap> SCLib.SearchByName("S^4x"); #search for products with S^4[128X[104X
    [4X[28X [ [ 282, "S^4xS^1 (VT)" ], [ 329, "S^4xS^1 (VT)" ], [ 331, "S^4xS^1 (VT)" ] ][128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-12 SCLibSize[101X
  
  [33X[1;0Y[29X[2XSCLibSize[102X( [3Xrepository[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yinteger upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YReturns   the   number  of  complexes  contained  in  the  given  repository
  [3Xrepository[103X.  Fails  if the library repository was not previously loaded with
  [10XSCLibInit[110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLibSize(SCLib); #SCLib is the repository of the global library[128X[104X
    [4X[28X 648[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-13 SCLibUpdate[101X
  
  [33X[1;0Y[29X[2XSCLibUpdate[102X( [3Xrepository[103X[, [3Xrecalc[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylibrary  repository  of  type  [10XSCLibRepository[110X  upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YRecreates the index of a given repository (either via a repository object or
  a  base  path  of a repository [3Xrepository[103X) by scanning the base path for all
  [10X.sc[110X  files  containing  simplicial  complexes  of  the repository. Returns a
  repository object with the newly created index on success or [9Xfail[109X in case of
  an  error. The optional boolean argument [3Xrecalc[103X forces [5Xsimpcomp[105X to recompute
  all  the  indexed  properties  (such  as  f-vector,  homology,  etc.) of the
  simplicial complexes in the repository if set to [9Xtrue[109X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> myRepository:=SCLibInit("/tmp/repository");;[128X[104X
    [4X[28X gap> SCLibUpdate(myRepository);[128X[104X
    [4X[28X #I  SCLibUpdate: rebuilding index for /tmp/repository/.[128X[104X
    [4X[28X #I  SCLibUpdate: rebuilding index done.[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=0[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/tmp/repository/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.1-14 SCLibStatus[101X
  
  [33X[1;0Y[29X[2XSCLibStatus[102X( [3Xrepository[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylibrary  repository  of  type  [10XSCLibRepository[110X  upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YLets  [5XGAP[105X  print  the  status  of  a  given  library  repository [3Xrepository[103X.
  [10XIndexAttributes[110X  is  the  list of attributes indexed for this repository. If
  [10XCalculateIndexAttributes[110X  is  true, the index attributes for a complex added
  to  the  library  are calculated automatically upon addition of the complex,
  otherwise  this  is  left to the user and only pre-calculated attributes are
  indexed.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLibStatus(SCLib);[128X[104X
    [4X[28X [Simplicial complex library. Properties:[128X[104X
    [4X[28X CalculateIndexAttributes=true[128X[104X
    [4X[28X Number of complexes in library=648[128X[104X
    [4X[28X IndexAttributes=[ "Name", "Dim", "F", "G", "H", "Chi", "Homology", "IsPM", [128X[104X
    [4X[28X   "IsManifold" ][128X[104X
    [4X[28X Loaded=true[128X[104X
    [4X[28X Path="/home/jonathan/bin/gap-4.11.1/pkg/simpcomp/complexes/"[128X[104X
    [4X[28X ][128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  
  [1X13.2 [33X[0;0Y[5Xsimpcomp[105X[101X[1X input / output functions[133X[101X
  
  [33X[0;0YThis  section  contains  a  description  of  the  input/output-functionality
  provided  by  [5Xsimpcomp[105X.  The  package provides the functionality to save and
  load simplicial complexes (and their known properties) to, respectively from
  files  in  XML  format.  Furthermore, it provides the user with functions to
  export simplicial complexes into polymake format (for this format there also
  exists rudimentary import functionality), as JavaView geometry or in form of
  a  LaTeX  table.  For  importing  more  complex  polymake  data  the package
  polymaking [R\t13] can be used.[133X
  
  [1X13.2-1 SCLoad[101X
  
  [33X[1;0Y[29X[2XSCLoad[102X( [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ysimplicial  complex of type [10XSCSimplicialComplex[110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YLoads  a simplicial complex stored in a binary format (using [10XIO_Pickle[110X) from
  a  file specified in [3Xfilename[103X (as string). If [3Xfilename[103X does not end in [10X.scb[110X,
  this suffix is appended to the file name.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdSimplex(3);;[128X[104X
    [4X[28X gap> SCSave(c,"/tmp/bddelta3");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X gap> d:=SCLoad("/tmp/bddelta3");[128X[104X
    [4X[28X <SimplicialComplex: S^2_4 | dim = 2 | n = 4>[128X[104X
    [4X[28X gap> c=d;[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-2 SCLoadXML[101X
  
  [33X[1;0Y[29X[2XSCLoadXML[102X( [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ysimplicial  complex of type [10XSCSimplicialComplex[110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YLoads  a  simplicial  complex  stored in XML format from a file specified in
  [3Xfilename[103X  (as  string).  If  [3Xfilename[103X  does  not  end in [10X.sc[110X, this suffix is
  appended to the file name.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdSimplex(3);;[128X[104X
    [4X[28X gap> SCSaveXML(c,"/tmp/bddelta3");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X gap> d:=SCLoadXML("/tmp/bddelta3");[128X[104X
    [4X[28X <SimplicialComplex: S^2_4 | dim = 2 | n = 4>[128X[104X
    [4X[28X gap> c=d;[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-3 SCSave[101X
  
  [33X[1;0Y[29X[2XSCSave[102X( [3Xcomplex[103X, [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YSaves  a  simplicial  complex in a binary format (using [10XIO_Pickle[110X) to a file
  specified  in  [3Xfilename[103X  (as string). If [3Xfilename[103X does not end in [10X.scb[110X, this
  suffix is appended to the file name.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdSimplex(3);;[128X[104X
    [4X[28X gap> SCSave(c,"/tmp/bddelta3");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-4 SCSaveXML[101X
  
  [33X[1;0Y[29X[2XSCSaveXML[102X( [3Xcomplex[103X, [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YSaves  a  simplicial  complex  [3Xcomplex[103X  to  a file specified by [3Xfilename[103X (as
  string)  in  XML  format.  If  [3Xfilename[103X  does not end in [10X.sc[110X, this suffix is
  appended to the file name.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdSimplex(3);;[128X[104X
    [4X[28X gap> SCSaveXML(c,"/tmp/bddelta3");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-5 SCExportMacaulay2[101X
  
  [33X[1;0Y[29X[2XSCExportMacaulay2[102X( [3Xcomplex[103X, [3Xring[103X, [3Xfilename[103X[, [3Xalphalabels[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports  the  facet  list of a given simplicial complex [3Xcomplex[103X in [10XMacaulay2[110X
  format  to a file specified by [3Xfilename[103X. The argument [3Xring[103X can either be the
  ring of integers (specified by [10XIntegers[110X) or the ring of rationals (sepcified
  by  [10XRationals[110X). The optional boolean argument [3Xalphalabels[103X labels the complex
  with  characters  from [22Xa, dots ,z[122X in the exported file if a value of [9Xtrue[109X is
  supplied,  while  the  standard  labeling  of the vertices is [22Xv_1, dots ,v_n[122X
  where  [22Xn[122X  is  the number of vertices of [3Xcomplex[103X. If [3Xcomplex[103X has more than [22X26[122X
  vertices, the argument [3Xalphalabels[103X is ignored.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> SCExportMacaulay2(c,Integers,"/tmp/bdbeta4.m2");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-6 SCExportPolymake[101X
  
  [33X[1;0Y[29X[2XSCExportPolymake[102X( [3Xcomplex[103X, [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports  the  facet  list  with  vertex labels of a given simplicial complex
  [3Xcomplex[103X  in [10Xpolymake[110X format to a file specified by [3Xfilename[103X. Currently, only
  the export in the format of [10Xpolymake[110X version 2.3 is supported.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> SCExportPolymake(c,"/tmp/bdbeta4.poly");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-7 SCImportPolymake[101X
  
  [33X[1;0Y[29X[2XSCImportPolymake[102X( [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ysimplicial  complex of type [10XSCSimplicialComplex[110X upon success, [9Xfail[109X
            otherwise.[133X
  
  [33X[0;0YImports  the  facet  list  of  a  [10Xtopaz[110X  [10Xpolymake[110X file specified by [3Xfilename[103X
  (discarding  any vertex labels) and creates a simplicial complex object from
  these facets.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> SCExportPolymake(c,"/tmp/bdbeta4.poly");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X gap> d:=SCImportPolymake("/tmp/bdbeta4.poly");[128X[104X
    [4X[28X <SimplicialComplex: polymake import '/tmp/bdbeta4.poly' | dim = 3 | n = 8>[128X[104X
    [4X[28X gap> c=d;[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-8 SCExportLatexTable[101X
  
  [33X[1;0Y[29X[2XSCExportLatexTable[102X( [3Xcomplex[103X, [3Xfilename[103X, [3Xitemsperline[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X on success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports  the  facet  list of a given simplicial complex [3Xcomplex[103X (or any list
  given  as  first  argument)  in form of a LaTeX table to a file specified by
  [3Xfilename[103X.  The argument [3Xitemsperline[103X specifies how many columns the exported
  table should have. The faces are exported in the format [22X⟨ v_1,dots,v_k ⟩[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdSimplex(5);;[128X[104X
    [4X[28X gap> SCExportLatexTable(c,"/tmp/bd5simplex.tex",5);[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-9 SCExportJavaView[101X
  
  [33X[1;0Y[29X[2XSCExportJavaView[102X( [3Xcomplex[103X, [3Xfile[103X, [3Xcoords[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X on success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports  the  2-skeleton  of  the  given  simplicial complex [3Xcomplex[103X (or the
  facets  if  the  complex is of dimension 2 or less) in [10XJavaView[110X format (file
  name  suffix  [10X.jvx[110X)  to  a  file specified by [3Xfilename[103X (as string). The list
  [3Xcoords[103X  must  contain  a  [22X3[122X-tuple  of  real  coordinates  for each vertex of
  [3Xcomplex[103X,  either  as  tuple  of  length  three  containing  the  coordinates
  (Warning:  as  [5XGAP[105X  only  has rudimentary support for floating point values,
  currently  only  integer  numbers  can be used as coordinates when providing
  [3Xcoords[103X  as  list  of  [22X3[122X-tuples)  or as string of the form [10X"x.x y.y z.z"[110X with
  decimal  numbers  [10Xx.x[110X,  [10Xy.y[110X,  [10Xz.z[110X  for  the three coordinates (i.e. [10X"1.0 0.0
  0.0"[110X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> coords:=[[1,0,0],[0,1,0],[0,0,1]];;[128X[104X
    [4X[28X gap> SCExportJavaView(SCBdSimplex(2),"/tmp/triangle.jvx",coords);[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-10 SCExportRecognizer[101X
  
  [33X[1;0Y[29X[2XSCExportRecognizer[102X( [3Xcomplex[103X, [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports  the  gluings  of the tetrahedra of a given combinatorial [22X3[122X-manifold
  [3Xcomplex[103X   in   a   format  compatible  with  Matveev's  [22X3[122X-manifold  software
  [10XRecognizer[110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> c:=SCBdCrossPolytope(4);;[128X[104X
    [4X[28X gap> SCExportRecognizer(c,"/tmp/bdbeta4.mv");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
  [1X13.2-11 SCExportSnapPy[101X
  
  [33X[1;0Y[29X[2XSCExportSnapPy[102X( [3Xcomplex[103X, [3Xfilename[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Y[9Xtrue[109X upon success, [9Xfail[109X otherwise.[133X
  
  [33X[0;0YExports   the   facet  list  and  orientability  of  a  given  combinatorial
  [22X3[122X-pseudomanifold [3Xcomplex[103X in [10XSnapPy[110X format to a file specified by [3Xfilename[103X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X gap> SCLib.SearchByAttribute("Dim=3 and F=[8,28,56,28]");[128X[104X
    [4X[28X [ [ 8, "PM^3 - TransitiveGroup(8,43), No. 1" ] ][128X[104X
    [4X[28X gap> c:=SCLib.Load(last[1][1]);;[128X[104X
    [4X[28X gap> SCExportSnapPy(c,"/tmp/M38.tri");[128X[104X
    [4X[28X true[128X[104X
    [4X[28X [128X[104X
  [4X[32X[104X
  
