GAP (HAP commands) - Chapter 35: Arrays and Pseudo lists

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35 Arrays and Pseudo lists
35.1
35.1-1 Array
35.1-2 PermuteArray
35.1-3 ArrayDimension
35.1-4 ArrayDimensions
35.1-5 ArraySum
35.1-6 ArrayValue
35.1-7 ArrayValueFunctions
35.1-8 ArrayAssign
35.1-9 ArrayAssignFunctions
35.1-10 ArrayIterate
35.1-11 BinaryArrayToTextFile
35.1-12 FrameArray
35.1-13 UnframeArray
35.1-14 Add
35.1-15 Append
35.1-16 ListToPseudoList

### 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).

Examples: 1 , 2 , 3

##### 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).

Examples:

##### 35.1-3 ArrayDimension

`‣ ArrayDimension`( A ) | ( function )

Inputs an array \(A\) and returns its dimension.

Examples:

##### 35.1-4 ArrayDimensions

`‣ ArrayDimensions`( A ) | ( function )

Inputs an array \(A\) and returns its dimensions.

Examples:

##### 35.1-5 ArraySum

`‣ ArraySum`( A ) | ( function )

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

Examples:

##### 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 \(x\).

Examples:

##### 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 \(d\).

Examples:

##### 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 \(n\).

Examples:

##### 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 \(d\).

Examples:

##### 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]].

Examples:

##### 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.

Examples:

##### 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.

Examples: 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.

Examples:

##### 35.1-14 Add

`‣ 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 \(L\).

Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8

##### 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 \(K\).

Examples: 1 , 2 , 3 , 4 , 5 , 6

##### 35.1-16 ListToPseudoList

`‣ ListToPseudoList`( L ) | ( function )

Inputs a list \(L\) and returns the pseudo list representation of \(L\).

Examples:

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