62.28 LibrarySemigroup

LibrarySemigroup( size, num )

The semigroup library contains all semigroups of sizes 1 up to 5, classified into classes of isomorphic semigroups. LibrarySemigroup retrieves a representative of an isomorphism class from the semigroup library and returns it as a transformation semigroup. The parameters of LibrarySemigroup are two positive integers: size must be in {1,2,3,4,5} and indicates the size of the semigroup to be retrieved, num indicates the number of an isomorphism class.

  gap> ls := LibrarySemigroup( 4, 123 );
  TransformationSemigroup( Transformation( [ 1, 2, 3, 4 ], 
  [ 1, 1, 3, 3 ] ), Transformation( [ 1, 2, 3, 4 ], 
  [ 1, 2, 3, 4 ] ), Transformation( [ 1, 2, 3, 4 ], 
  [ 1, 3, 3, 1 ] ), Transformation( [ 1, 2, 3, 4 ], [ 1, 4, 3, 2 ] ) ) 
  gap> DisplayCayleyTable( ls );
  Let:
  s0 := Transformation( [ 1, 2, 3, 4 ], [ 1, 1, 3, 3 ] )
  s1 := Transformation( [ 1, 2, 3, 4 ], [ 1, 2, 3, 4 ] )
  s2 := Transformation( [ 1, 2, 3, 4 ], [ 1, 3, 3, 1 ] )
  s3 := Transformation( [ 1, 2, 3, 4 ], [ 1, 4, 3, 2 ] )

    *  

  s0 s1 s2 s3 
   ------------------
    s0 

 s0 s0 s0 s0 
    s1 

 s0 s1 s2 s3 
    s2 

 s2 s2 s2 s2 
    s3 

 s2 s3 s0 s1 

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