‣ 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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