gap> a:= Transformation( [ 2, 3, 4, 1 ] );; gap> b:= Transformation( [ 2, 2, 3, 4 ] );; gap> s:= Semigroup(a, b); <transformation semigroup of degree 4 with 2 generators> gap> l := Idempotents( s ); [ Transformation( [ 2, 2 ] ), IdentityTransformation, Transformation( [ 1, 1, 3, 3 ] ), Transformation( [ 4, 2, 2, 4 ] ), Transformation( [ 1, 2, 3, 1 ] ), Transformation( [ 1, 2, 4, 4 ] ), Transformation( [ 1, 3, 3 ] ), Transformation( [ 1, 1 ] ), Transformation( [ 2, 2, 2 ] ), Transformation( [ 2, 2, 3, 3 ] ), Transformation( [ 2, 2, 4, 4 ] ), Transformation( [ 3, 3, 3 ] ), Transformation( [ 4, 2, 3, 4 ] ), Transformation( [ 1, 3, 3, 1 ] ), Transformation( [ 2, 2, 3, 2 ] ), Transformation( [ 2, 2, 2, 2 ] ), Transformation( [ 1, 1, 1 ] ), Transformation( [ 1, 1, 4, 4 ] ), Transformation( [ 3, 3, 3, 3 ] ), Transformation( [ 4, 4, 3, 4 ] ), Transformation( [ 1, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1 ] ), Transformation( [ 4, 3, 3, 4 ] ), Transformation( [ 1, 2, 3, 3 ] ), Transformation( [ 3, 2, 3, 3 ] ), Transformation( [ 4, 2, 4, 4 ] ), Transformation( [ 1, 2, 1, 1 ] ), Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 3, 3, 3 ] ), Transformation( [ 1, 4, 4, 4 ] ), Transformation( [ 4, 4, 4, 4 ] ), Transformation( [ 1, 1, 1, 1 ] ), Transformation( [ 1, 2, 2, 2 ] ) ] gap> Size( l ); 33
Hope this helps! VInay On 7 July 2017 at 06:56, Shubh Narayan Singh (Assistant Professor, Mathematics) <sh...@cub.ac.in> wrote: > Please can someone tell the gap code, if exists, for > > 1. listing all the idempotent elements > > 2. cardinality of the set of all idempotent elements > > in a finite semigroup. > > Thank you in advance. > > > *Regards,* > > *Shubh* > > > *-----------------------------------------------------Shubh Narayan Singh, > Ph.D.Assistant Professor * > > > > *Department of MathematicsCentral University of South BiharPatna - 800 > 014-----------------------------------------* > *e-mail: sh...@cub.ac.in <sh...@cub.ac.in>* > *Mob: +91- 8404934146* > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
