  
  [1X33 [33X[0;0YArrays and Pseudo lists[133X[101X
  
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArray(A,f)[110X[133X
  
  [33X[0;0YInputs  an  array  [22XA[122X  and a function [22Xf[122X. It returns the the array obtained by
  applying [22Xf[122X to each entry of [22XA[122X (and leaves [22XA[122X unchanged).[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XPermuteArray(A,f)[110X[133X
  
  [33X[0;0YInputs an array [22XA[122X of dimension [22Xd[122X and a permutation [22Xf[122X of degree at most [22Xd[122X. It
  returns the array [22XB[122X defined by [22XB[i1][i2]...[id] = A[f(i1)][f(i2)]...A[f(id)][122X
  (and leaves [22XA[122X unchanged).[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayDimension(A)[110X[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns its dimension.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayDimensions(A)[110X[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns its dimensions.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArraySum(A)[110X[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns the sum of its entries.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayValue(A,x)[110X[133X
  
  [33X[0;0YInputs  an  array  [22XA[122X  and a coordinate vector [22Xx[122X. It returns the value of the
  entry in [22XA[122X with coordinate [22Xx[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayValueFunctions(d)[110X[133X
  
  [33X[0;0YInputs a positive integer [22Xd[122X and returns an efficient version of the function
  ArrayValue for arrays of dimension [22Xd[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayAssign(A,x,n)[110X[133X
  
  [33X[0;0YInputs  an  array  [22XA[122X and a coordinate vector [22Xx[122X and an integer [22Xn[122X. It sets the
  entry of [22XA[122X with coordinate [22Xx[122X equal to [22Xn[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayAssignFunctions(d)[110X[133X
  
  [33X[0;0YInputs a positive integer [22Xd[122X and returns an efficient version of the function
  ArrayAssign for arrays of dimension [22Xd[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XArrayIterate(d)[110X[133X
  
  [33X[0;0YInputs  a  positive  integer [22Xd[122X and returns a function ArrayIt(Dimensions,f).
  This  function  inputs  a  list Dimensions of [22Xd[122X positive integers and also a
  function [22Xf(x)[122X. It applies the function [22Xf(x)[122X to each integer list [22Xx[122X of length
  [22Xd[122X with entries [22Xx[i][122X in the range [1..Dimension[i]].[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XBinaryArrayToTextFile(file,A)[110X[133X
  
  [33X[0;0YInputs  a  string containing the address of a file, and an array [22XA[122X of 0s and
  1s.  The  array  represents a pure cubical complex. A representation of this
  complex  is  written  to  the  file in a format that can be read by the CAPD
  (Computer  Assisted  Proofs in Dynamics) software developed by Marian Mrozek
  and others.[133X
  
  [33X[0;0YThe second input [22XA[122X can also be a pure cubical complex.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XFrameArray(A)[110X[133X
  
  [33X[0;0YInputs  an  array  [22XA[122X  and returns the array obtained by appending a 0 to the
  beginning and end of each "row" of the array.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XUnframeArray(A)[110X[133X
  
  [33X[0;0YInputs  an  array [22XA[122X and returns the array obtained by removing the first and
  last entry in each "row" of the array.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XAdd(L,x)[110X[133X
  
  [33X[0;0YLet  [22XL[122X  be  a  pseudo  list of length [22Xn[122X, and [22Xx[122X an object compatible with the
  entries  in [22XL[122X. If [22Xx[122X is not in [22XL[122X then this operation converts [22XL[122X into a pseudo
  list  of  length  n+1  by  adding  [22Xx[122X  as  the  final entry. If [22Xx[122X is in [22XL[122X the
  operation has no effect on [22XL[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XAppend(L,K)[110X[133X
  
  [33X[0;0YLet  [22XL[122X be a pseudo list and [22XK[122X a list whose objects are compatible with those
  in [22XL[122X. This operation applies Add(L,x) for each x in [22XK[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XListToPseudoList(L)[110X[133X
  
  [33X[0;0YInputs a list [22XL[122X and returns the pseudo list representation of [22XL[122X.[133X
  
