  
  [1X2 [33X[0;0Y[22XZG[122X[101X[1X-Resolutions and Group Cohomology[133X[101X
  
  [33X[0;0YResolutions[133X
  
      │                                [10XEquivariantChainMap(R,S,f):: FreeResolution, FreeResolution, GroupHomomorphisms --> EquiChainMap[110X                                
      │                                                [10XFreeGResolution(P,n):: NonFreeResolution, Int --> FreeResolution[110X                                                
      │               [10XResolutionBieberbachGroup(G):: MatrixGroup --> FreeResolution[110X [10XResolutionBieberbachGroup(G,v):: MatrixGroup, List --> FreeResolution[110X              
      │                                             [10XResolutionCubicalCrustGroup(G,k):: MatrixGroup, Int --> FreeResolution[110X                                             
      │                                                   [10XResolutionFiniteGroup(G,k):: Group, Int --> FreeResolution[110X                                                   
      │                                                  [10XResolutionNilpotentGroup(G,k):: Group, Int --> FreeResolution[110X                                                 
      │                                                   [10XResolutionNormalSeries(L,k):: List, Int --> FreeResolution[110X                                                   
      │                                                 [10XResolutionPrimePowerGroup(G,k):: Group, Int --> FreeResolution[110X                                                 
      │ [10XResolutionSL2Z(m,k):: Int, Int --> FreeResolution[110X Inputs positive integers [22Xm, n[122X and returns [22Xn[122X terms of a free [22XZG[122X-resolution of [22XZ[122X for the group [22XG=SL_2( Z[1/m])[122X.
      │                      [10XResolutionSmallGroup(G,k):: Group, Int --> FreeResolution[110X [10XResolutionSmallGroup(G,k):: FpGroup, Int --> FreeResolution[110X                     
      │                                               [10XResolutionSubgroup(R,H):: FreeResolution, Group --> FreeResolution[110X                                               
  
  [33X[0;0YAlgebras [22X⟶[122X (Co)chain Complexes[133X
  
      │ [10XLeibnizComplex(g,n):: LeibnizAlgebra, Int --> ChainComplex[110X
  
  [33X[0;0YResolutions [22X⟶[122X (Co)chain Complexes[133X
  
      │                      [10XHomToIntegers(C):: ChainComplex --> CochainComplex[110X [10XHomToIntegers(R):: FreeResolution --> CochainComplex[110X [10XHomToIntegers(F):: EquiChainMap --> CochainMap[110X                     
      │                                                         [10XHomToIntegralModule(R,A):: FreeResolution, GroupHomomorphism --> CochainComplex[110X                                                         
      │                                            [10XTensorWithIntegers(R):: FreeResolution --> ChainComplex[110X [10XTensorWithIntegers(F):: EquiChainMap --> ChainMap[110X                                            
      │ [10XTensorWithIntegersModP(C,p):: ChainComplex, Int --> ChainComplex[110X [10XTensorWithIntegersModP(R,p):: FreeResolution, Int --> ChainComplex[110X [10XTensorWithIntegersModP(F,p):: EquiChainMap, Int --> ChainMap[110X
  
  [33X[0;0YCohomology rings[133X
  
      │                                                                                                                       [10XAreIsomorphicGradedAlgebras(A,B):: PresentedGradedAlgebra, PresentedGradedAlgebra --> Boolean[110X                                                                                                                       
      │                                                                                                                                      [10XHAPDerivation(R,I,L):: PolynomialRing, List, List --> Derivation[110X                                                                                                                                     
      │ [10XHilbertPoincareSeries::PresentedGradedAlgebra --> RationalFunction[110X Inputs a presentation [22XE= F[x_1,...,x_m]/I[122X of a graded algebra and returns its Hilbert-Poincar\'e series. This function was written by Paul Smith and uses the Singular commutative algebra package. It is essentially a wrapper for Singular's Hilbert-Poincare series.
      │                                                                                                                                               [10XHomologyOfDerivation(d):: Derivation --> List[110X                                                                                                                                               
      │                                                                                                                                      [10XIntegralCohomologyGenerators(R,n):: FreeResolution, Int --> List[110X                                                                                                                                     
      │                                                                                                                                           [10XLHSSpectralSequence(G,N,r):: Group, Int, Int --> List[110X                                                                                                                                           
      │                                                                                                                                          [10XLHSSpectralSequenceLastSheet(G,N):: Group, Int --> List[110X                                                                                                                                          
      │                                                                                                                 [10XModPCohomologyGenerators(G,n):: Group, Int --> List[110X [10XModPCohomologyGenerators(R):: FreeResolution --> List[110X                                                                                                                 
      │                                                [10XModPCohomologyRing(R):: FreeResolution --> SCAlgebra[110X [10XModPCohomologyRing(R,level):: FreeResolution, String --> SCAlgebra[110X [10XModPCohomologyRing(G,n):: Group, Int --> SCAlgebra[110X [10XModPCohomologyRing(G,n,level):: Group, Int, String --> SCAlgebra[110X                                                
      │                           [10XMod2CohomologyRingPresentation(G):: Group --> PresentedGradedAlgebra[110X [10XMod2CohomologyRingPresentation(G,n):: Group --> PresentedGradedAlgebra[110X [10XMod2CohomologyRingPresentation(A):: Group --> PresentedGradedAlgebra[110X [10XMod2CohomologyRingPresentation(R):: Group --> PresentedGradedAlgebra[110X                           
  
  [33X[0;0YGroup Invariants[133X
  
      │                                                           [10XGroupCohomology(G,k):: Group, Int --> List[110X [10XGroupCohomology(G,k,p):: Group, Int, Int --> List[110X                                                          
      │                                                             [10XGroupHomology(G,k):: Group, Int --> List[110X [10XGroupHomology(G,k,p):: Group, Int, Int --> List[110X                                                            
      │                                                                 [10XPrimePartDerivedFunctor(G,R,A,k):: Group, FreeResolution, Function, Int --> List[110X                                                                
      │ [10XPoincareSeries(G,n):: Group, Int --> RationalFunction[110X [10XPoincareSeries(G):: Group --> RationalFunction[110X [10XPoincareSeries(R,n):: Group, Int --> RationalFunction[110X [10XPoincareSeries(L,n):: Group, Int --> RationalFunction[110X
      │ [10XPoincareSeries(G,n):: Group, Int --> RationalFunction[110X [10XPoincareSeries(G):: Group --> RationalFunction[110X [10XPoincareSeries(R,n):: Group, Int --> RationalFunction[110X [10XPoincareSeries(L,n):: Group, Int --> RationalFunction[110X
      │                                                                         [10XRankHomologyPGroup(G,P,n):: Group, RationalFunction, Int --> Int[110X                                                                        
  
  [33X[0;0Y[22XF_p[122X-modules[133X
  
      │                           [10XGroupAlgebraAsFpGModule:: Group --> FpGModule[110X                           
      │                                 [10XRadical:: FpGModule --> FpGModule[110X                                 
      │ [10XRadicalSeries(M):: FpGModule --> List[110X [10XRadicalSeries(R):: Resolution --> FilteredSparseChainComplex[110X
  
