  
  [1X38 [33X[0;0YSome functions for accessing basic data[133X[101X
  
  
  [1X38.1 [33X[0;0Y [133X[101X
  
  [1X38.1-1 BoundaryMap[101X
  
  [33X[1;0Y[29X[2XBoundaryMap[102X( [3XC[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  resolution,  chain  complex  or cochain complex [22XC[122X and returns the
  function [22XC!.boundary[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X   1  ([7X../tutorial/chap2.html[107X) ,  2  ([7X../tutorial/chap10.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutTopology.html[107X) [133X
  
  [1X38.1-2 BoundaryMatrix[101X
  
  [33X[1;0Y[29X[2XBoundaryMatrix[102X( [3XC[103X, [3Xn[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  chain  or  cochain complex [22XC[122X and integer [22Xn[122X>[22X0[122X. It returns the [22Xn[122X-th
  boundary map of [22XC[122X as a matrix.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../tutorial/chap11.html[107X) [133X
  
  [1X38.1-3 Dimension[101X
  
  [33X[1;0Y[29X[2XDimension[102X( [3XC[103X ) [32X function[133X
  [33X[1;0Y[29X[2XDimension[102X( [3XM[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  resolution,  chain  complex  or cochain complex [22XC[122X and returns the
  function [22XC!.dimension[122X .[133X
  
  [33X[0;0YAlternatively,  inputs an [22XFpG[122X-module [22XM[122X and returns its dimension as a vector
  space over the field of [22Xp[122X elements.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap3.html[107X) ,  2  ([7X../tutorial/chap5.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                        4
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                         5
  ([7X../www/SideLinks/About/aboutDefinitions.html[107X) ,                           6
  ([7X../www/SideLinks/About/aboutTDA.html[107X) ,                                   7
  ([7X../www/SideLinks/About/aboutTopology.html[107X) ,                              8
  ([7X../www/SideLinks/About/aboutLieCovers.html[107X) [133X
  
  [1X38.1-4 EvaluateProperty[101X
  
  [33X[1;0Y[29X[2XEvaluateProperty[102X( [3XX[103X, [3Xstr[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  component  object  [22XX[122X (such as a [22XZG[122X-resolution or chain map) and a
  string   [22Xstr[122X="name"  (such  as  "characteristic"  or  "type").  It  searches
  [22XX.property[122X for the pair ["name",value] and returns value. If [22XX.property[122X does
  not exist, or if ["name",value] does not exist, it returns fail.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X38.1-5 GroupOfResolution[101X
  
  [33X[1;0Y[29X[2XGroupOfResolution[102X( [3XR[103X ) [32X function[133X
  
  [33X[0;0YInputs a [22XZG[122X-resolution [22XR[122X and returns the group [22XG[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X38.1-6 Length[101X
  
  [33X[1;0Y[29X[2XLength[102X( [3XR[103X ) [32X function[133X
  
  [33X[0;0YInputs  a resolution [22XR[122X and returns its length (i.e. the number of terms of [22XR[122X
  that HAP has computed).[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap3.html[107X) ,  2  ([7X../tutorial/chap4.html[107X) ,  3
  ([7X../tutorial/chap5.html[107X) ,        4       ([7X../tutorial/chap6.html[107X) ,       5
  ([7X../tutorial/chap10.html[107X) ,                                                6
  ([7X../www/SideLinks/About/aboutArithmetic.html[107X) ,                            7
  ([7X../www/SideLinks/About/aboutBogomolov.html[107X) ,                             8
  ([7X../www/SideLinks/About/aboutPerformance.html[107X) ,                           9
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                       10
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                        11
  ([7X../www/SideLinks/About/aboutQuandles.html[107X) ,                             12
  ([7X../www/SideLinks/About/aboutquasi.html[107X) ,                                13
  ([7X../www/SideLinks/About/aboutRandomComplexes.html[107X) ,                      14
  ([7X../www/SideLinks/About/aboutGouter.html[107X) ,                               15
  ([7X../www/SideLinks/About/aboutTensorSquare.html[107X) ,                         16
  ([7X../www/SideLinks/About/aboutTopology.html[107X) [133X
  
  [1X38.1-7 Map[101X
  
  [33X[1;0Y[29X[2XMap[102X( [3Xf[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  chain  map, or cochain map or equivariant chain map [22Xf[122X and returns
  the mapping function (as opposed to the target or the source of [22Xf[122X) .[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap1.html[107X) ,  2  ([7X../tutorial/chap2.html[107X) ,  3
  ([7X../tutorial/chap4.html[107X) ,        4       ([7X../tutorial/chap5.html[107X) ,       5
  ([7X../tutorial/chap6.html[107X) ,        6       ([7X../tutorial/chap7.html[107X) ,       7
  ([7X../tutorial/chap10.html[107X) ,                                                8
  ([7X../www/SideLinks/About/aboutAbelianCategories.html[107X) ,                     9
  ([7X../www/SideLinks/About/aboutCoefficientSequence.html[107X) ,                  10
  ([7X../www/SideLinks/About/aboutCohomologyRings.html[107X) ,                      11
  ([7X../www/SideLinks/About/aboutPoincareSeries.html[107X) ,                       12
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                       13
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                        14
  ([7X../www/SideLinks/About/aboutFunctorial.html[107X) ,                           15
  ([7X../www/SideLinks/About/aboutGouter.html[107X) ,                               16
  ([7X../www/SideLinks/About/aboutTopology.html[107X) [133X
  
  [1X38.1-8 Source[101X
  
  [33X[1;0Y[29X[2XSource[102X( [3Xf[103X ) [32X function[133X
  
  [33X[0;0YInputs  a chain map, or cochain map, or equivariant chain map, or [22XFpG[122X-module
  homomorphism [22Xf[122X and returns it source.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap2.html[107X) ,  2  ([7X../tutorial/chap4.html[107X) ,  3
  ([7X../tutorial/chap7.html[107X) ,        4       ([7X../tutorial/chap8.html[107X) ,       5
  ([7X../www/SideLinks/About/aboutAbelianCategories.html[107X) ,                     6
  ([7X../www/SideLinks/About/aboutNonabelian.html[107X) ,                            7
  ([7X../www/SideLinks/About/aboutCoefficientSequence.html[107X) ,                   8
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                        9
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                        10
  ([7X../www/SideLinks/About/aboutFunctorial.html[107X) ,                           11
  ([7X../www/SideLinks/About/aboutLieCovers.html[107X) [133X
  
  [1X38.1-9 Target[101X
  
  [33X[1;0Y[29X[2XTarget[102X( [3Xf[103X ) [32X function[133X
  
  [33X[0;0YInputs  a chain map, or cochain map, or equivariant chain map, or [22XFpG[122X-module
  homomorphism [22Xf[122X and returns its target.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap1.html[107X) ,  2  ([7X../tutorial/chap2.html[107X) ,  3
  ([7X../tutorial/chap7.html[107X) ,        4       ([7X../tutorial/chap8.html[107X) ,       5
  ([7X../www/SideLinks/About/aboutAbelianCategories.html[107X) ,                     6
  ([7X../www/SideLinks/About/aboutCoefficientSequence.html[107X) ,                   7
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                        8
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) [133X
  
