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### 25 Arrays and Pseudo lists

 `Array(A,f)` Inputs an array A and a function f. It returns the the array obtained by applying f to each entry of A (and leaves A unchanged). `PermuteArray(A,f)` Inputs an array A of dimension d and a permutation f of degree at most d. It returns the array B defined by B[i1][i2]...[id] = A[f(i1)][f(i2)]...A[f(id)] (and leaves A unchanged). `ArrayDimension(A)` Inputs an array A and returns its dimension. `ArrayDimensions(A)` Inputs an array A and returns its dimensions. `ArraySum(A)` Inputs an array A and returns the sum of its entries. `ArrayValue(A,x)` Inputs an array A and a coordinate vector x. It returns the value of the entry in A with coordinate x. `ArrayValueFunctions(d)` Inputs a positive integer d and returns an efficient version of the function ArrayValue for arrays of dimension d. `ArrayAssign(A,x,n)` Inputs an array A and a coordinate vector x and an integer n. It sets the entry of A with coordinate x equal to n. `ArrayAssignFunctions(d)` Inputs a positive integer d and returns an efficient version of the function ArrayAssign for arrays of dimension d. `ArrayIterate(d)` Inputs a positive integer d and returns a function ArrayIt(Dimensions,f). This function inputs a list Dimensions of d positive integers and also a function f(x). It applies the function f(x) to each integer list x of length d with entries x[i] in the range [1..Dimension[i]]. `BinaryArrayToTextFile(file,A)` Inputs a string containing the address of a file, and an array A 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. The second input A can also be a pure cubical complex. `FrameArray(A)` Inputs an array A and returns the array obtained by appending a 0 to the beginning and end of each "row" of the array. `UnframeArray(A)` Inputs an array A and returns the array obtained by removing the first and last entry in each "row" of the array. `Add(L,x)` Let L be a pseudo list of length n, and x an object compatible with the entries in L. If x is not in L then this operation converts L into a pseudo list of length n+1 by adding x as the final entry. If x is in L the operation has no effect on L. `Append(L,K)` Let L be a pseudo list and K a list whose objects are compatible with those in L. This operation applies Add(L,x) for each x in K. `ListToPseudoList(L)` Inputs a list L and returns the pseudo list representation of L.

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