  
  [1X1 [33X[0;0YCellular complexes[133X[101X
  
  [33X[0;0YData [22X⟶[122X Cellular Complexes[133X
  
      │                                                                                    [10XRegularCWPolytope(L):: List --> RegCWComplex[110X [10XRegularCWPolytope(G,v):: PermGroup, List --> RegCWComplex[110X                                                                                    
      │                                                                                                                  [10XCubicalComplex(A):: List --> CubicalComplex[110X                                                                                                                 
      │                                                                                                              [10XPureCubicalComplex(A):: List --> PureCubicalComplex[110X                                                                                                             
      │                                                                                    [10XPureCubicalKnot(n,k):: Int, Int --> PureCubicalComplex[110X [10XPureCubicalKnot(L):: List --> PureCubicalComplex[110X                                                                                   
      │                                                                        [10XPurePermutahedralKnot(n,k):: Int, Int --> PurePermutahedralComplex[110X [10XPurePermutahedralKnot(L):: List --> PurePermutahedralComplex[110X                                                                       
      │                                                                                                            [10XPurePermutahedralComplex(A):: List --> PurePermComplex[110X                                                                                                            
      │                                                                                                                [10XCayleyGraphOfGroup(G,L):: Group, List --> Graph[110X                                                                                                               
      │                                                                                                [10XEquivariantEuclideanSpace(G,v):: MatrixGroup, List --> EquivariantRegCWComplex[110X                                                                                                
      │                                                                                                  [10XEquivariantOrbitPolytope(G,v):: PermGroup, List --> EquivariantRegCWComplex[110X                                                                                                 
      │                                                                                                         [10XEquivariantTwoComplex(G):: Group --> EquivariantRegCWComplex[110X                                                                                                         
      │                                                                                                            [10XQuillenComplex(G,p):: Group, Int --> SimplicialComplex[110X                                                                                                            
      │                                                                                             [10XRestrictedEquivariantCWComplex(Y,H):: RegCWComplex, Group --> EquivariantRegCWComplex[110X                                                                                            
      │                                                                                                          [10XRandomSimplicialGraph(n,p):: Int, Int --> SimplicialComplex[110X                                                                                                         
      │                                                                                                       [10XRandomSimplicialTwoComplex(n,p):: Int, Int --> SimplicialComplex[110X                                                                                                       
      │ [10XReadCSVfileAsPureCubicalKnot(str):: String --> PureCubicalComplex[110X [10XReadCSVfileAsPureCubicalKnot(str,r):: String, Int --> PureCubicalComplex[110X [10XReadCSVfileAsPureCubicalKnot(L):: List --> PureCubicalComplex[110X [10XReadCSVfileAsPureCubicalKnot(L,R):: List,List --> PureCubicalComplex[110X
      │                                                                                                   [10XReadImageAsPureCubicalComplex(str,t):: String, Int --> PureCubicalComplex[110X                                                                                                  
      │                                                                                           [10XReadImageAsFilteredPureCubicalComplex(str,n):: String, Int --> FilteredPureCubicalComplex[110X                                                                                          
      │                                                                                                   [10XReadImageAsWeightFunction(str,t):: String, Int --> RegCWComplex, Function[110X                                                                                                  
      │                                                               [10XReadPDBfileAsPureCubicalComplex(str):: String --> PureCubicalComplex[110X [10XReadPDBfileAsPureCubicalComplex(str,r):: String, Int --> PureCubicalComplex[110X                                                               
      │                                                            [10XReadPDBfileAsPurepermutahedralComplex(str):: String --> PurePermComplex[110X [10XReadPDBfileAsPurePermutahedralComplex(str,r):: String, Int --> PurePermComplex[110X                                                            
      │                                                                                    [10XRegularCWPolytope(L):: List --> RegCWComplex[110X [10XRegularCWPolytope(G,v):: PermGroup, List --> RegCWComplex[110X                                                                                    
      │                                                                                                               [10XSimplicialComplex(L):: List --> SimplicialComplex[110X                                                                                                              
      │                                                                   [10XSymmetricMatrixToFilteredGraph(A,m,s):: Mat, Int, Rat --> FilteredGraph[110X [10XSymmetricMatrixToFilteredGraph(A,m):: Mat, Int --> FilteredGraph[110X                                                                   
      │                                                                                                               [10XSymmetricMatrixToGraph(A,t):: Mat, Rat --> Graph[110X                                                                                                               
  
  [33X[0;0YMetric Spaces[133X
  
      │                          [10XCayleyMetric(g,h):: Permutation, Permutation --> Int[110X                          
      │                                [10XEuclideanMetric(g,h):: List, List --> Rat[110X                               
      │                            [10XEuclideanSquaredMetric(g,h):: List, List --> Rat[110X                            
      │                          [10XHammingMetric(g,h):: Permutation, Permutation --> Int[110X                         
      │                          [10XKendallMetric(g,h):: Permutation, Permutation --> Int[110X                         
      │                                [10XManhattanMetric(g,h):: List, List --> Rat[110X                               
      │ [10XVectorsToSymmetricMatrix(V):: List --> Matrix[110X [10XVectorsToSymmetricMatrix(V,d):: List, Function --> Matrix[110X
  
  [33X[0;0YCellular Complexes [22X⟶[122X Cellular Complexes[133X
  
      │                                                                                                                                           [10XBoundaryMap(K):: RegCWComplex --> RegCWMap[110X                                                                                                                                          
      │                                                                 [10XCliqueComplex(G,n):: Graph, Int --> SimplicialComplex[110X [10XCliqueComplex(F,n):: FilteredGraph, Int --> FilteredSimplicialComplex[110X [10XCliqueComplex(K,n):: SimplicialComplex, Int --> SimplicialComplex[110X                                                                 
      │                                                                                                                       [10XConcentricFiltration(K,n):: PureCubicalComplex, Int --> FilteredPureCubicalComplex[110X                                                                                                                      
      │                                                                                      [10XDirectProduct(M,N):: RegCWComplex, RegCWComplex --> RegCWComplex[110X [10XDirectProduct(M,N):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X                                                                                      
      │                                                                                         [10XFiltrationTerm(K,t):: FilteredPureCubicalComplex, Int --> PureCubicalComplex[110X [10XFiltrationTerm(K,t):: FilteredRegCWComplex, Int --> RegCWComplex[110X                                                                                         
      │                                                                                                                            [10XGraph(K):: RegCWComplex --> Graph[110X [10XGraph(K):: SimplicialComplex --> Graph[110X                                                                                                                           
      │                                                                                                                                           [10XHomotopyGraph(Y):: RegCWComplex --> Graph[110X                                                                                                                                           
      │                                                    [10XNerve(M):: PureCubicalComplex --> SimplicialComplex[110X [10XNerve(M):: PurePermComplex --> SimplicialComplex[110X [10XNerve(M,n):: PureCubicalComplex, Int --> SimplicialComplex[110X [10XNerve(M,n):: PurePermComplex, Int --> SimplicialComplex[110X                                                    
      │ [10XRegularCWComplex(K):: SimplicialComplex --> RegCWComplex[110X [10XRegularCWComplex(K):: PureCubicalComplex --> RegCWComplex[110X [10XRegularCWComplex(K):: CubicalComplex --> RegCWComplex[110X [10XRegularCWComplex(K):: PurePermComplex --> RegCWComplex[110X [10XRegularCWComplex(L):: List --> RegCWComplex[110X [10XRegularCWComplex(L,M):: List,List --> RegCWComplex[110X
      │                                                                                                                            [10XRegularCWMap(M,A):: PureCubicalComplex, PureCubicalComplex --> RegCWMap[110X                                                                                                                            
      │                                                                          [10XThickeningFiltration(K,n):: PureCubicalComplex, Int --> FilteredPureCubicalComplex[110X [10XThickeningFiltration(K,n,s):: PureCubicalComplex, Int, Int --> FilteredPureCubicalComplex[110X                                                                         
  
  [33X[0;0YCellular Complexes [22X⟶[122X Cellular Complexes (Preserving Data Types)[133X
  
      │ [10XContractedComplex(K):: RegularCWComplex --> RegularCWComplex[110X [10XContractedComplex(K):: FilteredRegularCWComplex --> FilteredRegularCWComplex[110X [10XContractedComplex(K):: CubicalComplex --> CubicalComplex[110X [10XContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex[110X [10XContractedComplex(K,S):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X [10XContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex[110X [10XContractedComplex(K):: PurePermComplex --> PurePermComplex[110X [10XContractedComplex(K,S):: PurePermComplex, PurePermComplex --> PurePermComplex[110X [10XContractedComplex(K):: SimplicialComplex --> SimplicialComplex[110X [10XContractedComplex(G):: Graph --> Graph[110X
      │                                                                                                                                                                                                                                         [10XContractibleSubcomplex(K):: PureCubicalComplex --> PureCubicalComplex[110X [10XContractibleSubcomplex(K):: PurePermComplex --> PurePermComplex[110X [10XContractibleSubcomplex(K):: SimplicialComplex --> SimplicialComplex[110X                                                                                                                                                                                                                                         
      │                                                                                                                                                                                                                                                                                                               [10XKnotReflection(K):: PureCubicalComplex --> PureCubicalComplex[110X                                                                                                                                                                                                                                                                                                               
      │                                                                                                                                                                                                                                                                                                        [10XKnotSum(K,L):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X                                                                                                                                                                                                                                                                                                       
      │                                                                                                                                                                                                                                                                                                                     [10XOrientRegularCWComplex(Y):: RegCWComplex --> Void[110X                                                                                                                                                                                                                                                                                                                     
      │                                                                                                                                                                                                                                            [10XPathComponent(K,n):: SimplicialComplex, Int --> SimplicialComplex[110X [10XPathComponent(K,n):: PureCubicalComplex, Int --> PureCubicalComplex[110X [10XPathComponent(K,n):: PurePermComplex, Int --> PurePermComplex[110X                                                                                                                                                                                                                                            
      │                                                                                                                                                                                                                                                                              [10XPureComplexBoundary(M):: PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexBoundary(M):: PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                                              
      │                                                                                                                                                                                                                                                                            [10XPureComplexComplement(M):: PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexComplement(M):: PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                                            
      │                                                                                                                                                                                                                                                        [10XPureComplexDifference(M,N):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexDifference(M,N):: PurePermComplex, PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                       
      │                                                                                                                                                                                                                                                     [10XPureComplexInterstection(M,N):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexIntersection(M,N):: PurePermComplex, PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                     
      │                                                                                                                                                                                                                                                                             [10XPureComplexThickened(M):: PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexThickened(M):: PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                                             
      │                                                                                                                                                                                                                                                             [10XPureComplexUnion(M,N):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex[110X [10XPureComplexUnion(M,N):: PurePermComplex, PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                                                            
      │                                                                                                                                                                                                                           [10XSimplifiedComplex(K):: RegularCWComplex --> RegularCWComplex[110X [10XSimplifiedComplex(K):: PurePermComplex --> PurePermComplex[110X [10XSimplifiedComplex(R):: FreeResolution --> FreeResolution[110X [10XSimplifiedComplex(C):: ChainComplex --> ChainComplex[110X                                                                                                                                                                                                                           
      │                                                                                                                                                                                                                               [10XZigZagContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex[110X [10XZigZagContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex[110X [10XZigZagContractedComplex(K):: PurePermComplex --> PurePermComplex[110X                                                                                                                                                                                                                              
  
  [33X[0;0YCellular Complexes [22X⟶[122X Homotopy Invariants[133X
  
      │                                                                                                                                                                                                                                                                                       [10XAlexanderPolynomial(K):: PureCubicalComplex --> Polynomial[110X [10XAlexanderPolynomial(K):: PurePermComplex --> Polynomial[110X [10XAlexanderPolynomial(G):: FpGroup --> Polynomial[110X                                                                                                                                                                                                                                                                                      
      │                                                      [10XBettiNumber(K,n):: SimplicialComplex, Int --> Int[110X [10XBettiNumber(K,n):: PureCubicalComplex, Int --> Int[110X [10XBettiNumber(K,n):: CubicalComplex, Int --> Int[110X [10XBettiNumber(K,n):: PurePermComplex, Int --> Int[110X [10XBettiNumber(K,n):: RegCWComplex, Int --> Int[110X [10XBettiNumber(K,n):: ChainComplex, Int --> Int[110X [10XBettiNumber(K,n):: SparseChainComplex, Int --> Int[110X [10XBettiNumber(K,n,p):: SimplicialComplex, Int, Int --> Int[110X [10XBettiNumber(K,n,p):: PureCubicalComplex, Int, Int --> Int[110X [10XBettiNumber(K,n,p):: CubicalComplex, Int, Int --> Int[110X [10XBettiNumber(K,n,p):: PurePermComplex, Int, Int --> Int[110X [10XBettiNumber(K,n,p):: RegCWComplex, Int, Int --> Int[110X                                                     
      │                                                                                                                                                                                                                      [10XEulerCharacteristic(C):: ChainComplex --> Int[110X [10XEulerCharacteristic(K):: CubicalComplex --> Int[110X [10XEulerCharacteristic(K):: PureCubicalComplex --> Int[110X [10XEulerCharacteristic(K):: PurePermComplex --> Int[110X [10XEulerCharacteristic(K):: RegCWComplex --> Int[110X [10XEulerCharacteristic(K):: SimplicialComplex --> Int[110X                                                                                                                                                                                                                      
      │                                                                                                                                                                                                                                                                                                                                                 [10XEulerIntegral(Y,w):: RegCWComplex, Int --> Int[110X                                                                                                                                                                                                                                                                                                                                                
      │                                                                                                                                                                                                                                        [10XFundamentalGroup(K):: RegCWComplex --> FpGroup[110X [10XFundamentalGroup(K,n):: RegCWComplex, Int --> FpGroup[110X [10XFundamentalGroup(K):: SimplicialComplex --> FpGroup[110X [10XFundamentalGroup(K):: PureCubicalComplex --> FpGroup[110X [10XFundamentalGroup(K):: PurePermComplex --> FpGroup[110X                                                                                                                                                                                                                                        
      │                                                                                                                                                                                                                                                                                                                                       [10XFundamentalGroupOfQuotient(Y):: EquivariantRegCWComplex --> Group[110X                                                                                                                                                                                                                                                                                                                                       
      │                                                                                                                                                                                                                                                                                                                                                [10XIsAspherical(F,R):: FreeGroup, List --> Boolean[110X                                                                                                                                                                                                                                                                                                                                                
      │                                                                                                                                                                                                                                                                                                                          [10XKnotGroup(K):: PureCubicalComplex --> FpGroup[110X [10XKnotGroup(K):: PureCubicalComplex --> FpGroup[110X                                                                                                                                                                                                                                                                                                                          
      │                                                                                                                                                                                                                                                                                                                      [10XPiZero(Y):: RegCWComplex --> List[110X [10XPiZero(Y):: Graph --> List[110X [10XPiZero(Y):: SimplicialComplex --> List[110X                                                                                                                                                                                                                                                                                                                      
      │ [10XPersistentBettiNumbers(K,n):: FilteredSimplicialComplex, Int --> List[110X [10XPersistentBettiNumbers(K,n):: FilteredPureCubicalComplex, Int --> List[110X [10XPersistentBettiNumbers(K,n):: FilteredRegCWComplex, Int --> List[110X [10XPersistentBettiNumbers(K,n):: FilteredChainComplex, Int --> List[110X [10XPersistentBettiNumbers(K,n):: FilteredSparseChainComplex, Int --> List[110X [10XPersistentBettiNumbers(K,n,p):: FilteredSimplicialComplex, Int, Int --> List[110X [10XPersistentBettiNumbers(K,n,p):: FilteredPureCubicalComplex, Int, Int --> List[110X [10XPersistentBettiNumbers(K,n,p):: FilteredRegCWComplex, Int, Int --> List[110X [10XPersistentBettiNumbers(K,n,p):: FilteredChainComplex, Int, Int --> List[110X [10XPersistentBettiNumbers(K,n,p):: FilteredSparseChainComplex, Int, Int --> List[110X
  
  [33X[0;0YData [22X⟶[122X Homotopy Invariants[133X
  
      │ [10XDendrogramMat(A,t,s):: Mat, Rat, Int --> List[110X
  
  [33X[0;0YCellular Complexes [22X⟶[122X Non Homotopy Invariants[133X
  
      │          [10XChainComplex(K):: CubicalComplex --> ChainComplex[110X [10XChainComplex(K):: PureCubicalComplex --> ChainComplex[110X [10XChainComplex(K):: PurePermComplex --> ChainComplex[110X [10XChainComplex(Y):: RegCWComplex --> ChainComplex[110X [10XChainComplex(K):: SimplicialComplex --> ChainComplex[110X          
      │                                                                                                                 [10XChainComplexEquivalence(X):: RegCWComplex --> List[110X                                                                                                                
      │                                                                                                        [10XChainComplexOfQuotient(Y):: EquivariantRegCWComplex --> ChainComplex[110X                                                                                                       
      │                                          [10XChainMap(X,A,Y,B):: PureCubicalComplex, PureCubicalComplex, PureCubicalComplex, PureCubicalComplex --> ChainMap[110X [10XChainMap(f):: RegCWMap --> ChainMap[110X [10XChainMap(f):: SimplicialMap --> ChainComplex[110X                                         
      │ [10XCochainComplex(K):: CubicalComplex --> CochainComplex[110X [10XCochainComplex(K):: PureCubicalComplex --> CochainComplex[110X [10XCochainComplex(K):: PurePermComplex --> CochainComplex[110X [10XCochainComplex(Y):: RegCWComplex --> CochainComplex[110X [10XCochainComplex(K):: SimplicialComplex --> CohainComplex[110X
      │                                                                                                                      [10XCriticalCells(K):: RegCWComplex --> List[110X                                                                                                                     
      │                                                                                                           [10XDiagonalApproximation(X):: RegCWComplex --> RegCWMap, RegCWMap[110X                                                                                                          
      │                                                                     [10XSize(Y):: RegCWComplex --> Int[110X [10XSize(Y):: SimplicialComplex --> Int[110X [10XSize(K):: PureCubicalComplex --> Int[110X [10XSize(K):: PurePermComplex --> Int[110X                                                                     
  
  [33X[0;0Y(Co)chain Complexes [22X⟶[122X (Co)chain Complexes[133X
  
      │                                                           [10XFilteredTensorWithIntegers(R):: FreeResolution, Int --> FilteredChainComplex[110X                                                          
      │                                                        [10XFilteredTensorWithIntegersModP(R,p):: FreeResolution, Int --> FilteredChainComplex[110X                                                       
      │                      [10XHomToIntegers(C):: ChainComplex --> CochainComplex[110X [10XHomToIntegers(R):: FreeResolution --> CochainComplex[110X [10XHomToIntegers(F):: EquiChainMap --> CochainMap[110X                     
      │ [10XTensorWithIntegersModP(C,p):: ChainComplex, Int --> ChainComplex[110X [10XTensorWithIntegersModP(R,p):: FreeResolution, Int --> ChainComplex[110X [10XTensorWithIntegersModP(F,p):: EquiChainMap, Int --> ChainMap[110X
  
  [33X[0;0Y(Co)chain Complexes [22X⟶[122X Homotopy Invariants[133X
  
      │ [10XCohomology(C,n):: CochainComplex, Int --> List[110X [10XCohomology(F,n):: CochainMap, Int --> GroupHomomorphism[110X [10XCohomology(K,n):: CubicalComplex, Int --> List[110X [10XCohomology(K,n):: PureCubicalComplex, Int --> List[110X [10XCohomology(K,n):: PurePermComplex, Int --> List[110X [10XCohomology(K,n):: RegCWComplex, Int --> List[110X [10XCohomology(K,n):: SimplicialComplex, Int --> List[110X
      │                                                                                                                        [10XCupProduct(Y):: RegCWComplex --> Function[110X [10XCupProduct(R,p,q,P,Q):: FreeRes, Int, Int, List, List --> List[110X                                                                                                                        
      │          [10XHomology(C,n):: ChainComplex, Int --> List[110X [10XHomology(F,n):: ChainMap, Int --> GroupHomomorphism[110X [10XHomology(K,n):: CubicalComplex, Int --> List[110X [10XHomology(K,n):: PureCubicalComplex, Int --> List[110X [10XHomology(K,n):: PurePermComplex, Int --> List[110X [10XHomology(K,n):: RegCWComplex, Int --> List[110X [10XHomology(K,n):: SimplicialComplex, Int --> List[110X         
  
  [33X[0;0YVisualization[133X
  
      │                                           [10XBarCodeDisplay(L) :: List --> void[110X                                          
      │                                       [10XBarCodeCompactDisplay(L) :: List --> void[110X                                       
      │                                     [10XCayleyGraphOfGroup(G,L):: Group, List --> Void[110X                                    
      │ [10XDisplay(G) :: Graph --> void[110X [10XDisplay(M) :: PureCubicalComplex --> void[110X [10XDisplay(M) :: PurePermutahedralComplex --> void[110X
      │                                [10XDisplayArcPresentation(K) :: PureCubicalComplex --> void[110X                               
      │                                       [10XDisplayCSVKnotFile(str) :: String --> void[110X                                      
      │                                          [10XDisplayDendrogram(L):: List --> Void[110X                                         
      │                                  [10XDisplayDendrogramMat(A,t,s):: Mat, Rat, Int --> Void[110X                                 
      │                                         [10XDisplayPDBfile(str):: String --> Void[110X                                         
      │                                 [10XOrbitPolytope(G,v,L) :: PermGroup, List, List --> void[110X                                
      │                                             [10XScatterPlot(L):: List --> Void[110X                                            
  
