Re: [GAP Forum] Regarding Idempotent elements in semigroup

2017-07-06 Thread Shubh Narayan Singh (Assistant Professor, Mathematics)
Thank you sir for providing the code with clarification.

Regards,

\-Shubh

On Fri, Jul 7, 2017 at 11:41 AM, Vinay Wagh  wrote:

> gap> a:= Transformation( [ 2, 3, 4, 1 ] );;
> gap> b:= Transformation( [ 2, 2, 3, 4 ] );;
> gap> s:= Semigroup(a, b);
> 
> 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)  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 *
> > *Mob:   +91- 8404934146*
> > ___
> > Forum mailing list
> > Forum@mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>



-- 
-- 
*Sincerely,*
*Shubh Narayan Singh*


*-Shubh Narayan Singh,
Ph.D.Assistant Professor *



*Department of MathematicsCentral University of South BiharPatna - 800
014-*
*e-mail: sh...@cub.ac.in *
*Mob:   +91- 8404934146*
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Re: [GAP Forum] Regarding Idempotent elements in semigroup

2017-07-06 Thread Vinay Wagh
gap> a:= Transformation( [ 2, 3, 4, 1 ] );;
gap> b:= Transformation( [ 2, 2, 3, 4 ] );;
gap> s:= Semigroup(a, b);

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)  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 *
> *Mob:   +91- 8404934146*
> ___
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

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