  
  [1X30 [33X[0;0YRegular CW-Complexes[133X[101X
  
  
  [1X30.1 [33X[0;0Y [133X[101X
  
  [1X30.1-1 SimplicialComplexToRegularCWComplex[101X
  
  [33X[1;0Y[29X[2XSimplicialComplexToRegularCWComplex[102X( [3XK[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  simplicial  complex  [22XK[122X  and  returns  the  corresponding  regular
  CW-complex.[133X
  
  [33X[0;0Y[12XExamples:[112X       1       ([7X../www/SideLinks/About/aboutMetrics.html[107X) ,       2
  ([7X../www/SideLinks/About/aboutRandomComplexes.html[107X) [133X
  
  [1X30.1-2 CubicalComplexToRegularCWComplex[101X
  
  [33X[1;0Y[29X[2XCubicalComplexToRegularCWComplex[102X( [3XK[103X ) [32X function[133X
  [33X[1;0Y[29X[2XCubicalComplexToRegularCWComplex[102X( [3XK[103X, [3Xn[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  pure  cubical  complex  (or  cubical  complex)  [22XK[122X and returns the
  corresponding  regular  CW-complex. If a positive integer [22Xn[122X is entered as an
  optional second argument, then just the [22Xn[122X-skeleton of [22XK[122X is returned.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X30.1-3 CriticalCellsOfRegularCWComplex[101X
  
  [33X[1;0Y[29X[2XCriticalCellsOfRegularCWComplex[102X( [3XY[103X ) [32X function[133X
  [33X[1;0Y[29X[2XCriticalCellsOfRegularCWComplex[102X( [3XY[103X, [3Xn[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  regular  CW-complex  [22XY[122X  and  returns the critical cells of [22XY[122X with
  respect  to  some  discrete  vector  field.  If  [22XY[122X does not initially have a
  discrete vector field then one is constructed.[133X
  
  [33X[0;0YIf  a  positive integer [22Xn[122X is given as a second optional input, then just the
  critical cells in dimensions up to and including [22Xn[122X are returned.[133X
  
  [33X[0;0YThe  function  [22XCriticalCellsOfRegularCWComplex(Y)[122X works by homotopy reducing
  cells     starting     at     the     top     dimension.     The    function
  [22XCriticalCellsOfRegularCWComplex(Y,n)[122X  works  by  homotopy  coreducing  cells
  starting  at  dimension 0. The two methods may well return different numbers
  of cells.[133X
  
  [33X[0;0Y[12XExamples:[112X      1      ([7X../www/SideLinks/About/aboutPeripheral.html[107X) ,      2
  ([7X../www/SideLinks/About/aboutRandomComplexes.html[107X) ,                       3
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X30.1-4 ChainComplex[101X
  
  [33X[1;0Y[29X[2XChainComplex[102X( [3XY[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  regular  CW-complex [22XY[122X and returns the cellular chain complex of a
  CW-complex  W whose cells correspond to the critical cells of [22XY[122X with respect
  to  some  discrete  vector  field.  If  [22XY[122X does not initially have a discrete
  vector field then one is constructed.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap1.html[107X) ,  2  ([7X../tutorial/chap3.html[107X) ,  3
  ([7X../tutorial/chap4.html[107X) ,       4       ([7X../tutorial/chap10.html[107X) ,       5
  ([7X../tutorial/chap12.html[107X) , 6 ([7X../www/SideLinks/About/aboutMetrics.html[107X) , 7
  ([7X../www/SideLinks/About/aboutBredon.html[107X) ,                                8
  ([7X../www/SideLinks/About/aboutPersistent.html[107X) ,                            9
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                       10
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                        11
  ([7X../www/SideLinks/About/aboutCubical.html[107X) ,                              12
  ([7X../www/SideLinks/About/aboutSimplicialGroups.html[107X) ,                     13
  ([7X../www/SideLinks/About/aboutIntro.html[107X) [133X
  
  [1X30.1-5 ChainComplexOfRegularCWComplex[101X
  
  [33X[1;0Y[29X[2XChainComplexOfRegularCWComplex[102X( [3XY[103X ) [32X function[133X
  
  [33X[0;0YInputs a regular CW-complex [22XY[122X and returns the cellular chain complex of [22XY[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../tutorial/chap1.html[107X) , 2 ([7X../tutorial/chap10.html[107X) [133X
  
  [1X30.1-6 FundamentalGroup[101X
  
  [33X[1;0Y[29X[2XFundamentalGroup[102X( [3XY[103X ) [32X function[133X
  [33X[1;0Y[29X[2XFundamentalGroup[102X( [3XY[103X, [3Xn[103X ) [32X function[133X
  
  [33X[0;0YInputs a regular CW-complex [22XY[122X and, optionally, the number of some 0-cell. It
  returns  the  fundamental  group  of  [22XY[122X  based at the 0-cell [22Xn[122X. The group is
  returned as a finitely presented group. If [22Xn[122X is not specified then it is set
  [22Xn=1[122X.  The  algorithm  requires  a  discrete vector field on [22XY[122X. If [22XY[122X does not
  initially have a discrete vector field then one is constructed.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap1.html[107X) ,  2  ([7X../tutorial/chap2.html[107X) ,  3
  ([7X../tutorial/chap3.html[107X) ,        4       ([7X../tutorial/chap4.html[107X) ,       5
  ([7X../tutorial/chap5.html[107X) ,       6       ([7X../tutorial/chap11.html[107X) ,       7
  ([7X../www/SideLinks/About/aboutLinks.html[107X) ,                                 8
  ([7X../www/SideLinks/About/aboutPeripheral.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/aboutRandomComplexes.html[107X) ,                      13
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
