62.9 Kernel for transformations

Kernel( t )

For a transformation t on X, the kernel of t is defined as an equivalence relation Kernel(t) as: forall x,y in X: (x,y) in Kernel(t) {rm if/f} t(x) = t(y).

Kernel returns the kernel of the transformation t as a list l of lists where each sublist of l represents an equivalence class of the equivalence relation Kernel(t).

 
  gap> t:=Transformation( [1..5], [2,3,2,4,4] );
  Transformation( [ 1, 2, 3, 4, 5 ], [ 2, 3, 2, 4, 4 ] )
  gap> Kernel( t );
  [ [ 1, 3 ], [ 2 ], [ 4, 5 ] ] 

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