  
  [1X31 [33X[0;0YKnots and Links[133X[101X
  
  
  [1X31.1 [33X[0;0Y [133X[101X
  
  [1X31.1-1 PureCubicalKnot[101X
  
  [33X[1;0Y[29X[2XPureCubicalKnot[102X( [3XL[103X ) [32X function[133X
  [33X[1;0Y[29X[2XPureCubicalKnot[102X( [3Xn[103X, [3Xi[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  list  [22XL=[[m1,n1],  [m2,n2],  ...,  [mk,nk]][122X  of pairs of integers
  describing  a  cubical arc presentation of a link with all vertical lines at
  the  front  and all horizontal lines at the back. The bottom horizontal line
  extends  from  the  m1-th  column  to the n1-th column. The second to bottom
  horizontal  line  extends  from the m2-th column to the n2-th column. And so
  on. The link is returned as a 3-dimensional pure cubical complex.[133X
  
  [33X[0;0YAlternatively  the  function  inputs  two integers [22Xn[122X, [22Xi[122X and returns the [22Xi[122X-th
  prime knot on [22Xn[122X crossings.[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/chap6.html[107X) ,                                                 6
  ([7X../www/SideLinks/About/aboutCoveringSpaces.html[107X) ,                        7
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                         8
  ([7X../www/SideLinks/About/aboutQuandles2.html[107X) ,                             9
  ([7X../www/SideLinks/About/aboutQuandles.html[107X) ,                             10
  ([7X../www/SideLinks/About/aboutKnots.html[107X) ,                                11
  ([7X../www/SideLinks/About/aboutKnotsQuandles.html[107X) [133X
  
  [1X31.1-2 ViewPureCubicalKnot[101X
  
  [33X[1;0Y[29X[2XViewPureCubicalKnot[102X( [3XL[103X ) [32X function[133X
  
  [33X[0;0YInputs a pure cubical link [22XL[122X and displays it.[133X
  
  [33X[0;0Y[12XExamples:[112X             1             ([7X../tutorial/chap1.html[107X) ,             2
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X31.1-3 KnotSum[101X
  
  [33X[1;0Y[29X[2XKnotSum[102X( [3XK[103X, [3XL[103X ) [32X function[133X
  
  [33X[0;0YInputs  two  pure cubical knots [22XK[122X, [22XL[122X and returns their sum as a pure cubical
  knot. This function is not defined for links with more than one component.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap2.html[107X) ,  2  ([7X../tutorial/chap3.html[107X) ,  3
  ([7X../tutorial/chap6.html[107X) ,                                                 4
  ([7X../www/SideLinks/About/aboutCoverinSpaces.html[107X) ,                         5
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X31.1-4 KnotGroup[101X
  
  [33X[1;0Y[29X[2XKnotGroup[102X( [3XK[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  pure  cubical  link  [22XK[122X  and  returns the fundamental group of its
  complement. The group is returned as a finitely presented group.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X31.1-5 AlexanderMatrix[101X
  
  [33X[1;0Y[29X[2XAlexanderMatrix[102X( [3XG[103X ) [32X function[133X
  
  [33X[0;0YInputs a finitely presented group [22XG[122X whose abelianization is infinite cyclic.
  It returns the Alexander matrix of the presentation.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X31.1-6 AlexanderPolynomial[101X
  
  [33X[1;0Y[29X[2XAlexanderPolynomial[102X( [3XK[103X ) [32X function[133X
  [33X[1;0Y[29X[2XAlexanderPolynomial[102X( [3XG[103X ) [32X function[133X
  
  [33X[0;0YInputs  either  a  pure cubical knot [22XK[122X or a finitely presented group [22XG[122X whose
  abelianization is infinite cyclic. The Alexander Polynomial is returned.[133X
  
  [33X[0;0Y[12XExamples:[112X   1   ([7X../tutorial/chap1.html[107X) ,  2  ([7X../tutorial/chap2.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
  [1X31.1-7 ProjectionOfPureCubicalComplex[101X
  
  [33X[1;0Y[29X[2XProjectionOfPureCubicalComplex[102X( [3XK[103X ) [32X function[133X
  
  [33X[0;0YInputs   an   $n$-dimensional   pure   cubical  complex  [22XK[122X  and  returns  an
  n-1-dimensional pure cubical complex K'. The returned complex is obtained by
  projecting Euclidean n-space onto Euclidean n-1-space.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X31.1-8 ReadPDBfileAsPureCubicalComplex[101X
  
  [33X[1;0Y[29X[2XReadPDBfileAsPureCubicalComplex[102X( [3Xfile[103X ) [32X function[133X
  [33X[1;0Y[29X[2XReadPDBfileAsPureCubicalComplex[102X( [3Xfile[103X, [3Xm[103X, [3Xc[103X ) [32X function[133X
  
  [33X[0;0YInputs a protein database file describing a protein, and optionally inputs a
  positive  integer  m  and  character  string  c.  The default values for the
  optional  inputs  are  m=5  and  c="A".  It  loads  the chain of amino acids
  labelled  by  c  in  the file as a 3-dimensional pure cubical complex of the
  homotopy type of a circle.[133X
  
  [33X[0;0YIt  might happen that the function fails to construct a pure cubical complex
  of  the  homotopy type of a circle. In this case retry with a larger integer
  m.[133X
  
  [33X[0;0Y[12XExamples:[112X      1      ([7X../www/SideLinks/About/aboutPersistent.html[107X) ,      2
  ([7X../www/SideLinks/About/aboutKnots.html[107X) [133X
  
