[GAP Forum] Combination of generators

[James Mitchell]

Dear Shubh,

If you are using GAP 4.5, then the answer is yes. In the Citrus package (
http://www-groups.mcs.st-andrews.ac.uk/~jamesm/citrus/index.html) you can
find the command Factorization which does what you want. For example,

gap> f:=RandomTransformation(7);
Transformation( [ 6, 4, 2, 3, 4, 3, 1 ] )
gap> g:=RandomTransformation(7);
Transformation( [ 1, 6, 4, 4, 7, 4, 6 ] )
gap> M:=Monoid(f,g);
<monoid with 2 generators>
gap> h:=Random(M);
Transformation( [ 1, 6, 4, 4, 7, 4, 6 ] )
gap> Factorization(M, h);
[ 2 ]
gap> h:=Random(M);
Transformation( [ 6, 3, 3, 3, 1, 3, 3 ] )
gap> Factorization(M, h);
[ 2, 1 ]
gap> g*f;
Transformation( [ 6, 3, 3, 3, 1, 3, 3 ] )
gap> h:=Random(M);
Transformation( [ 1, 4, 4, 4, 6, 4, 4 ] )
gap> Factorization(M, h);
[ 2, 2 ]
gap> h:=Random(M);
Transformation( [ 4, 4, 4, 4, 4, 4, 4 ] )
gap> Factorization(M, h);
[ 1, 1, 2, 1, 2 ]
gap> f^2*g*f*g;
Transformation( [ 4, 4, 4, 4, 4, 4, 4 ] )

The list that is returned is  a  list  of  positive  integers  where  i
corresponds to GeneratorsOfSemigroups(S)[i].

Regards,

James



Date: Tue, 24 Jan 2012 16:54:58 +0530
From: shubh at iitg.ernet.in
To: forum at gap-system.org
Subject: [GAP Forum] Combination of generators
Message-ID:
       <fd6edcbdafc85cd9397ac6d0200e8001.squirrel at webmail.iitg.ernet.in>
Content-Type: text/plain;charset=iso-8859-1

Dear Sir,

I have a finitely generated transformation monoid M on a finite set X
generated by two transformations f and g on X. Also I have another
transformation h in M. Is there any method to tell what type of
combination of f and g give h.


With Regards,
Shubh

--
Shubh N. Singh
Research Scholar
Department of Mathematics
IIT Guwahati - 781039
Email: shubh at iitg.ernet.in
Mob. no.: +91-9864221370

-- 
James Mitchell
tinyurl.com/jdmitchell

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