‣ BoundaryMap( C ) | ( function ) |
Inputs a resolution, chain complex or cochain complex \(C\) and returns the function \(C!.boundary\).
‣ 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
‣ 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
‣ 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:
‣ GroupOfResolution( R ) | ( function ) |
Inputs a \(ZG\)-resolution \(R\) and returns the group \(G\).
Examples:
‣ 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
‣ 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
‣ 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
‣ 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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