### 35 Arrays and Pseudo lists

#### 35.1

##### 35.1-1 Array
 ‣ Array( A, f ) ( function )

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).

1 , 2

##### 35.1-2 PermuteArray
 ‣ PermuteArray( A, f ) ( function )

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).

##### 35.1-3 ArrayDimension
 ‣ ArrayDimension( A ) ( function )

Inputs an array A and returns its dimension.

##### 35.1-4 ArrayDimensions
 ‣ ArrayDimensions( A ) ( function )

Inputs an array A and returns its dimensions.

##### 35.1-5 ArraySum
 ‣ ArraySum( A ) ( function )

Inputs an array A and returns the sum of its entries.

##### 35.1-6 ArrayValue
 ‣ ArrayValue( A, x ) ( function )

Inputs an array A and a coordinate vector x. It returns the value of the entry in A with coordinate x.

##### 35.1-7 ArrayValueFunctions
 ‣ ArrayValueFunctions( d ) ( function )

Inputs a positive integer d and returns an efficient version of the function ArrayValue for arrays of dimension d.

##### 35.1-8 ArrayAssign
 ‣ ArrayAssign( A, x, n ) ( function )

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.

##### 35.1-9 ArrayAssignFunctions
 ‣ ArrayAssignFunctions( d ) ( function )

Inputs a positive integer d and returns an efficient version of the function ArrayAssign for arrays of dimension d.

##### 35.1-10 ArrayIterate
 ‣ ArrayIterate( d ) ( function )

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]].

##### 35.1-11 BinaryArrayToTextFile
 ‣ BinaryArrayToTextFile( file, A ) ( function )

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.

##### 35.1-12 FrameArray
 ‣ FrameArray( A ) ( function )

Inputs an array A and returns the array obtained by appending a 0 to the beginning and end of each "row" of the array.

1

##### 35.1-13 UnframeArray
 ‣ UnframeArray( A ) ( function )

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 ) ( function )

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.

1 , 2 , 3 , 4 , 5 , 6

##### 35.1-15 Append
 ‣ Append( L, K ) ( function )

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.

1 , 2 , 3 , 4

##### 35.1-16 ListToPseudoList
 ‣ ListToPseudoList( L ) ( function )

Inputs a list L and returns the pseudo list representation of L.

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