# Re: [GAP Forum] Listing idempotents in terms of generators

```Dear Shubh,

Thanks for the clarification, the answer I gave in my last email tells you
how to achieve what you are trying to do.```
```
Best wishes,

James

On Mon, 17 Jul 2017 at 06:33 Shubh Narayan Singh (Assistant Professor,
Mathematics) <sh...@cub.ac.in> wrote:

> Dear Sir,
>
> I am trying to elaborate my question:
>
> Let f:= Transformation([2,3,4,5,1])    g:=Transformation([5,4,5,1,1]),
> and S:=Semigroup(f, g);
>
> We observed that the idempotent h:= Transformation([1,1,1,1,1]) belongs to
> the semigroup S
> which can be written in terms of functions f and g. That is   h = g^2 f^4
> g.
>
> I am searching for the gap code for listing the idempotents in terms of
> the transformations f and g as above example.
>
>
> On Fri, Jul 14, 2017 at 4:45 PM, James Mitchell <j...@st-andrews.ac.uk>
> wrote:
>
>> Dear Shubh,
>>
>> Do you mean you want to factorise the idempotents over the
>> transformations f and g? If so, then you can do this using the semigroups
>> package as follows:
>>
>> S := Semigroup(f, g);
>> List(Idempotents(S), x -> Factorisation(S, x));
>>
>> Best wishes,
>>
>> James
>>
>> On Fri, 14 Jul 2017 at 12:08 Shubh Narayan Singh (Assistant Professor,
>> Mathematics) <sh...@cub.ac.in> wrote:
>>
>>> Let M be transformation monoid generated by two transformations f and g
>>> on
>>> the finite set.
>>>
>>> Please can someone tell the gap code, if exists, for listing all the
>>> idempotents in terms of the transformations f and g.
>>>
>>>
>>>
>>> \-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 <+91%2084049%2034146>*
>>> _______________________________________________
>>> 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 Mathematics Central University of South Bihar Patna - 800
> 014 -----------------------------------------*
> *e-mail: sh...@cub.ac.in <sh...@cub.ac.in>*
> *Mob:   +91- 8404934146 <+91%2084049%2034146>*
>
>
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```