GAP (HAP commands) - Chapter 38: Some functions for accessing basic data

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38 Some functions for accessing basic data
38.1
38.1-1 BoundaryMap
38.1-2 BoundaryMatrix
38.1-3 Dimension
38.1-4 EvaluateProperty
38.1-5 GroupOfResolution
38.1-6 Length
38.1-7 Map
38.1-8 Source
38.1-9 Target

### 38 Some functions for accessing basic data

#### 38.1

##### 38.1-1 BoundaryMap

`‣ BoundaryMap`( C ) | ( function )

Inputs a resolution, chain complex or cochain complex \(C\) and returns the function \(C!.boundary\).

Examples: 1 , 2 , 3

##### 38.1-2 BoundaryMatrix

`‣ BoundaryMatrix`( C, n ) | ( function )

Inputs a chain or cochain complex \(C\) and integer \(n\)>\(0\). It returns the \(n\)-th boundary map of \(C\) as a matrix.

Examples: 1

##### 38.1-3 Dimension

`‣ Dimension`( C ) | ( function )

`‣ Dimension`( M ) | ( function )

Inputs a resolution, chain complex or cochain complex \(C\) and returns the function \(C!.dimension\) .

Alternatively, inputs an \(FpG\)-module \(M\) and returns its dimension as a vector space over the field of \(p\) elements.

Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

##### 38.1-4 EvaluateProperty

`‣ EvaluateProperty`( X, str ) | ( function )

Inputs a component object \(X\) (such as a \(ZG\)-resolution or chain map) and a string \(str\)="name" (such as "characteristic" or "type"). It searches \(X.property\) for the pair ["name",value] and returns value. If \(X.property\) does not exist, or if ["name",value] does not exist, it returns fail.

Examples:

##### 38.1-5 GroupOfResolution

`‣ GroupOfResolution`( R ) | ( function )

Inputs a \(ZG\)-resolution \(R\) and returns the group \(G\).

Examples:

##### 38.1-6 Length

`‣ Length`( R ) | ( function )

Inputs a resolution \(R\) and returns its length (i.e. the number of terms of \(R\) that HAP has computed).

Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18

##### 38.1-7 Map

`‣ Map`( f ) | ( function )

Inputs a chain map, or cochain map or equivariant chain map \(f\) and returns the mapping function (as opposed to the target or the source of \(f\)) .

Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16

##### 38.1-8 Source

`‣ Source`( f ) | ( function )

Inputs a chain map, or cochain map, or equivariant chain map, or \(FpG\)-module homomorphism \(f\) and returns it source.

Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12

##### 38.1-9 Target

`‣ Target`( f ) | ( function )

Inputs a chain map, or cochain map, or equivariant chain map, or \(FpG\)-module homomorphism \(f\) and returns its target.

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

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