62.37 Elements for near-rings

Elements( nr )

The function Elements computes the elements of the near-ring nr. As for semigroups the GAP standard library dispatcher function Elements calls nr.op-er-a-tions.El-e-ments which simply returns the elements of nr.-group if nr is not a transformation near-ring or -- if nr is a transformation near-ring -- performs a simple closure algorithm and returns a set of transformations which are the elements of nr.

  gap> t := Transformation( Group( (1,2) ), [2,1] );
  Transformation( Group( (1,2) ), [ 2, 1 ] )
  gap> Elements( Nearring( t ) );
  [ Transformation( Group( (1,2) ), [ 1, 1 ] ), 
    Transformation( Group( (1,2) ), [ 1, 2 ] ), 
    Transformation( Group( (1,2) ), [ 2, 1 ] ), 
    Transformation( Group( (1,2) ), [ 2, 2 ] ) ]
  gap> Elements( LibraryNearring( "C3", 4 ) );
  [ (), (1,2,3), (1,3,2) ]

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