  
  [1X35 [33X[0;0YArrays and Pseudo lists[133X[101X
  
  
  [1X35.1 [33X[0;0Y [133X[101X
  
  [1X35.1-1 Array[101X
  
  [33X[1;0Y[29X[2XArray[102X( [3XA[103X, [3Xf[103X ) [32X function[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[12XExamples:[112X   1  ([7X../tutorial/chap2.html[107X) ,  2  ([7X../tutorial/chap10.html[107X) ,  3
  ([7X../www/SideLinks/About/aboutPeripheral.html[107X) ,                            4
  ([7X../www/SideLinks/About/aboutCubical.html[107X) [133X
  
  [1X35.1-2 PermuteArray[101X
  
  [33X[1;0Y[29X[2XPermuteArray[102X( [3XA[103X, [3Xf[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-3 ArrayDimension[101X
  
  [33X[1;0Y[29X[2XArrayDimension[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns its dimension.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X35.1-4 ArrayDimensions[101X
  
  [33X[1;0Y[29X[2XArrayDimensions[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns its dimensions.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X35.1-5 ArraySum[101X
  
  [33X[1;0Y[29X[2XArraySum[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YInputs an array [22XA[122X and returns the sum of its entries.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X35.1-6 ArrayValue[101X
  
  [33X[1;0Y[29X[2XArrayValue[102X( [3XA[103X, [3Xx[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-7 ArrayValueFunctions[101X
  
  [33X[1;0Y[29X[2XArrayValueFunctions[102X( [3Xd[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-8 ArrayAssign[101X
  
  [33X[1;0Y[29X[2XArrayAssign[102X( [3XA[103X, [3Xx[103X, [3Xn[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-9 ArrayAssignFunctions[101X
  
  [33X[1;0Y[29X[2XArrayAssignFunctions[102X( [3Xd[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-10 ArrayIterate[101X
  
  [33X[1;0Y[29X[2XArrayIterate[102X( [3Xd[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-11 BinaryArrayToTextFile[101X
  
  [33X[1;0Y[29X[2XBinaryArrayToTextFile[102X( [3Xfile[103X, [3XA[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-12 FrameArray[101X
  
  [33X[1;0Y[29X[2XFrameArray[102X( [3XA[103X ) [32X function[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[12XExamples:[112X 1 ([7X../www/SideLinks/About/aboutPeripheral.html[107X) [133X
  
  [1X35.1-13 UnframeArray[101X
  
  [33X[1;0Y[29X[2XUnframeArray[102X( [3XA[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X35.1-14 Add[101X
  
  [33X[1;0Y[29X[2XAdd[102X( [3XL[103X, [3Xx[103X ) [32X function[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[12XExamples:[112X   1   ([7X../tutorial/chap4.html[107X) ,  2  ([7X../tutorial/chap5.html[107X) ,  3
  ([7X../tutorial/chap10.html[107X) , 4 ([7X../www/SideLinks/About/aboutBogomolov.html[107X) ,
  5              ([7X../www/SideLinks/About/aboutQuandles2.html[107X) ,              6
  ([7X../www/SideLinks/About/aboutQuandles.html[107X) ,                              7
  ([7X../www/SideLinks/About/aboutquasi.html[107X) ,                                 8
  ([7X../www/SideLinks/About/aboutRandomComplexes.html[107X) [133X
  
  [1X35.1-15 Append[101X
  
  [33X[1;0Y[29X[2XAppend[102X( [3XL[103X, [3XK[103X ) [32X function[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[12XExamples:[112X       1      ([7X../www/SideLinks/About/aboutBogomolov.html[107X) ,      2
  ([7X../www/SideLinks/About/aboutParallel.html[107X) ,                              3
  ([7X../www/SideLinks/About/aboutTensorSquare.html[107X) [133X
  
  [1X35.1-16 ListToPseudoList[101X
  
  [33X[1;0Y[29X[2XListToPseudoList[102X( [3XL[103X ) [32X function[133X
  
  [33X[0;0YInputs a list [22XL[122X and returns the pseudo list representation of [22XL[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
