From lijr at lzu.edu.cn  Tue Jan  1 01:22:05 2013
From: lijr at lzu.edu.cn (=?GBK?B?wO69qMjZ?=)
Date: Tue, 1 Jan 2013 09:22:05 +0800 (CST)
Subject: [GAP Forum] find maximal subalgebras of a Lie algebra in GAP
Message-ID: <fd5a46.435ec.13bf3b37e9d.Coremail.lijr@lzu.edu.cn>

Dear Forum,

I have a Lie algebra A (the basis of A is given by matrices explicitly). Is there some function in GAP which can compute all subalgebras (in particular, maximal subalgebras of A) in GAP? I searched the manual of GAP, but I am not able to find such functions. Thank you very much.

With best wishes,
Jianrong.



From degraaf at science.unitn.it  Tue Jan  1 09:06:45 2013
From: degraaf at science.unitn.it (Willem de Graaf)
Date: Tue, 1 Jan 2013 10:06:45 +0100
Subject: [GAP Forum] find maximal subalgebras of a Lie algebra in GAP
In-Reply-To: <fd5a46.435ec.13bf3b37e9d.Coremail.lijr@lzu.edu.cn>
References: <fd5a46.435ec.13bf3b37e9d.Coremail.lijr@lzu.edu.cn>
Message-ID: <CAHQ8B2a0s2XnTsSw8neMbEdGKngBM3_5ydAkKZwi3EXRCPAZbg@mail.gmail.com>

Dear Jianrong,

In GAP there is no such functionality. The problem is also very difficult
in general, as there is an infinite number of subalgebras.

Best wishes,

Willem de Graaf

On Tue, Jan 1, 2013 at 2:22 AM, ??? <lijr at lzu.edu.cn> wrote:
> Dear Forum,
>
> I have a Lie algebra A (the basis of A is given by matrices explicitly). Is there some function in GAP which can compute all subalgebras (in particular, maximal subalgebras of A) in GAP? I searched the manual of GAP, but I am not able to find such functions. Thank you very much.
>
> With best wishes,
> Jianrong.
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From lijr at lzu.edu.cn  Tue Jan  1 13:11:23 2013
From: lijr at lzu.edu.cn (=?GBK?B?wO69qMjZ?=)
Date: Tue, 1 Jan 2013 21:11:23 +0800 (CST)
Subject: [GAP Forum] How to check that whether a matrix over GF(2) is
 diagonalizable or not using GAP?
Message-ID: <ce1060.43c00.13bf63ce177.Coremail.lijr@lzu.edu.cn>

Dear Forum,


How to check that whether a matrix over GF(2) is diagonalizable or not using GAP? Is there some function in GAP which can check that whether a matrix over GF(2) is diagonalizable or not? I only find the function DiagonalizeMatrix in GAP. Thank you very much.

With best wishes,
Jianrong.


From dima at ntu.edu.sg  Tue Jan  1 13:55:03 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Tue, 1 Jan 2013 21:55:03 +0800
Subject: [GAP Forum] How to check that whether a matrix over GF(2) is
 diagonalizable or not using GAP?
In-Reply-To: <ce1060.43c00.13bf63ce177.Coremail.lijr@lzu.edu.cn>
References: <ce1060.43c00.13bf63ce177.Coremail.lijr@lzu.edu.cn>
Message-ID: <CAAWYfq1bE+dtkojxJS9PGK1ysQR0DbsFWyU6yEoovjtrcOy+iA@mail.gmail.com>

Dear Jianrong,
In case of GF(2), each diagonalizable square matrix represents a
projection. Thus you just need to check whether the matrix is equal to
its square.
HTH,
Dmitrii

On 1 January 2013 21:11, ??? <lijr at lzu.edu.cn> wrote:
> Dear Forum,
>
>
> How to check that whether a matrix over GF(2) is diagonalizable or not using GAP? Is there some function in GAP which can check that whether a matrix over GF(2) is diagonalizable or not? I only find the function DiagonalizeMatrix in GAP. Thank you very much.
>
> With best wishes,
> Jianrong.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From lijr at lzu.edu.cn  Tue Jan  1 14:04:07 2013
From: lijr at lzu.edu.cn (=?GBK?B?wO69qMjZ?=)
Date: Tue, 1 Jan 2013 22:04:07 +0800 (CST)
Subject: [GAP Forum] multiplication of Lie objects in GAP
Message-ID: <3f7f65.43c6f.13bf66d2a12.Coremail.lijr@lzu.edu.cn>

Dear Forum,

I have a Lie algebra A whose basis is given by matrices explicitly. When I create the algebra A, the matrices in the basis of A are denoted by LieObject... Let x, y in the basis of A. It seems that x*y is the same as [x, y]. How could I compute the usual multiplication of x and y? Thank you very much.

With best wishes,
Jianrong.




From alexk at mcs.st-andrews.ac.uk  Thu Jan  3 12:32:20 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 3 Jan 2013 12:32:20 +0000
Subject: [GAP Forum] Running GAP commnads from a file
In-Reply-To: <CAAWYfq22BLeb=kefOVG43UUZyxbtbi9QwpOqHooLXGEPC28Yaw@mail.gmail.com>
References: <693e31b2.3f35d.13bd954fef6.Webtop.14@optonline.net>
	<CAAWYfq22BLeb=kefOVG43UUZyxbtbi9QwpOqHooLXGEPC28Yaw@mail.gmail.com>
Message-ID: <62FECC18-877B-4264-A76F-E16753958A53@mcs.st-andrews.ac.uk>

Dear Forum, dear Dmitrii,

On 27 Dec 2012, at 03:21, Dmitrii (Dima) Pasechnik wrote:

...

> Do you mean to say that after Read(); you evaluate A at the GAP prompt and don't see
> gap> A;
> 3628800
> 
> but see
> gap> A;
> Variable: 'A' must have a value
> 
> If the latter, it looks as if your file actually didn't get read.
> Please try to modify your file as follows:
> 
> A:=Factorial( 10 );
> B:=Factorial( 20 );
> Print(A);
> 
> Then a successful Read() will also result in 10! being printed.
> If this does not happen,
> post your GAP version and Windows version (not sure if GAP is tested, or even meant to work, on Windows 8) here.

Just to confirm that GAP 4.5.7 works on Windows 8. Moreover, my alternative GAP Installer for Windows <http://www.gap-system.org/ukrgap/wininst/> installed GAP there without difficulties and even created shortcuts in the Start screen (which replaces the Start menu in Windows 8).

Best wishes,
Alexander

 



From alexk at mcs.st-andrews.ac.uk  Thu Jan  3 15:37:54 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 3 Jan 2013 15:37:54 +0000
Subject: [GAP Forum] GAP vs PARI/GP
In-Reply-To: <CAEQWovTcLcR2oU3NEJgeupLOaYNrfnpGLvjvcRk8tX9aOgRKPg@mail.gmail.com>
References: <CAEQWovTcLcR2oU3NEJgeupLOaYNrfnpGLvjvcRk8tX9aOgRKPg@mail.gmail.com>
Message-ID: <38A48C16-33C3-4EAF-9ED7-E9FD46E46562@mcs.st-andrews.ac.uk>

On 16 Dec 2012, at 00:10, Pi wrote:

> Hello
> 
> How do you compare this two free programs: PARI/GP and GAP?
> 
> regards

Hello,

To get an overview of GAP, you may have a look at the Preface from the 
Reference manual http://www.gap-system.org/Manuals/doc/ref/chap1.html
and also at http://www.gap-system.org/Manuals/doc/ref/chap0.html for 
the table of contents. Probably similar materials may be found at PARI/GP
page http://pari.math.u-bordeaux.fr/ - for example, the list of areas 
from http://pari.math.u-bordeaux.fr/dochtml/html.stable/ - maybe someone 
may point out to a better source for PARI/GP.

If you have some particular computations in mind and would like to
check whether they are doable in GAP, please just ask. Also, there is
a GAP package Alnuth <http://www.gap-system.org/Packages/alnuth.html>
providing an interface from GAP to some functions from PARI/GP.

Hope this helps,
Alexander


From lijr at lzu.edu.cn  Fri Jan  4 09:10:24 2013
From: lijr at lzu.edu.cn (=?GBK?B?wO69qMjZ?=)
Date: Fri, 4 Jan 2013 17:10:24 +0800 (CST)
Subject: [GAP Forum] How to determine that a vector is in a vector space or
	not?
Message-ID: <100283c.45e79.13c04d35475.Coremail.lijr@lzu.edu.cn>

Dear Forum,

Let v be a vector and V a vector space. Is there some function in GAP which can determine that v is in V or not? I search the manual of GAP but did not find one. Thank you very much. 

With best wishes,
Jianrong.





From lijr at lzu.edu.cn  Sun Jan  6 13:52:32 2013
From: lijr at lzu.edu.cn (=?GBK?B?wO69qMjZ?=)
Date: Sun, 6 Jan 2013 21:52:32 +0800 (CST)
Subject: [GAP Forum] Coefficients in GAP
Message-ID: <1033a08.47d99.13c10225ae3.Coremail.lijr@lzu.edu.cn>

Dear Forum,

I would like to compute coefficients of a vector in a vector space V with respect to some basis B.
The command in GAP is Coefficients(B, v); 

If B is given by a list, then it seems that it doesn't work. For example, Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3]) will have errors. Here B is a subspace of the vector space A. A consists of matrices. The codes are in the end of the email. How should I correct  Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3])? Thank you very much.

With best wishes,
Jianrong.



for i in complement do
for k in [1..9] do
number:=1;
for l in [Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]] do
if Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]], Basis(B)[k]*l)=fail then number:=0; fi;
od;
od;
if number=1 then Add(new_indices_in_LminusOne, i); fi;
od;


From max at quendi.de  Sun Jan  6 18:10:28 2013
From: max at quendi.de (Max Horn)
Date: Sun, 6 Jan 2013 19:10:28 +0100
Subject: [GAP Forum] How to determine that a vector is in a vector space
	or not?
In-Reply-To: <100283c.45e79.13c04d35475.Coremail.lijr@lzu.edu.cn>
References: <100283c.45e79.13c04d35475.Coremail.lijr@lzu.edu.cn>
Message-ID: <ABB13DC4-E538-4C82-BC1E-B9645A14A3F1@quendi.de>

Dear Jianrong,

On 04.01.2013, at 10:10, ??? wrote:

> Dear Forum,
> 
> Let v be a vector and V a vector space. Is there some function in GAP which can determine that v is in V or not? I search the manual of GAP but did not find one. Thank you very much. 

If a is a vector and V a vectorspace, you can simply write

 a in V

to get a boolean true/false value indicating what you want. For example:

gap> V:=VectorSpace(GF(3), [ [1,0,0,0], [0,1,0,1], [1,-1,0,0] ] * Z(3)^0);
<vector space over GF(3), with 3 generators>
gap> [1,0,0,1] * Z(3)^0 in V;
true
gap> [1,0,1,0] * Z(3)^0 in V;
false


Hope that helps,
Max

From max at quendi.de  Sun Jan  6 18:42:01 2013
From: max at quendi.de (Max Horn)
Date: Sun, 6 Jan 2013 19:42:01 +0100
Subject: [GAP Forum] Coefficients in GAP
In-Reply-To: <1033a08.47d99.13c10225ae3.Coremail.lijr@lzu.edu.cn>
References: <1033a08.47d99.13c10225ae3.Coremail.lijr@lzu.edu.cn>
Message-ID: <A71A2394-734E-4437-B81B-39EA87E4C41F@quendi.de>

Dear Jianrong,

On 06.01.2013, at 14:52, ??? wrote:

> Dear Forum,
> 
> I would like to compute coefficients of a vector in a vector space V with respect to some basis B.
> The command in GAP is Coefficients(B, v); 
> 
> If B is given by a list, then it seems that it doesn't work.

Indeed, because as the documentation of Coefficients states, B must be a basis -- and a "basis" here is a special GAP object, which is more than just a list of basis vectors.

One of the reasons for this is that for an arbitrary list of vectors, such as yours, it is not at all clear whether it actually forms a basis of the space spanned by those vectors, i.e. if they are linearly independent.


> For example, Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3]) will have errors. Here B is a subspace of the vector space A. A consists of matrices. The codes are in the end of the email. How should I correct  Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3])? Thank you very much.

This look as if you want to form a new basis by taking a subset of the existing Basis(B). Here is a sketch of how this could look like.

# Set F to your base field, e.g. GF(3^2)
F := ...;

# Take first 9 basis vectors of B plus second basis vector of A
vecs := Concatenation( Basis(B){[1..9]}, Basis(A){[2]} );

# Compute a basis of the spanned vector space:
bas := ImmutableBasis( MutableBasis( F, vecs ) );

# Optionally, check whether "vecs" really formed a basis.
if Length(vecs) <> Length(bas) then
 Error("vectors do not form a basis"
fi;

# Finally, attempt to rewrite a matrix using this basis
Coefficients( bas, Basis(B)[4]*Basis(A)[3] )


But looking at your example code, and considering your previous question, it seems that perhaps all you want to do is to check whether some vector is contained in the span of some other vectors. Moreover, your code seems to contain a mistake (it sets number:=1 inside the loop over k, but tests it only after that loop; hence, only the result of the last loop iteration has any effect). Supposing all this, you could try something like the following (here I assumed you wanted to set and test "number" outside the k-loop; if the correct thing for you problem is to check "number" on each iteration of that loop, of course you'll have to move things around accordingly):

for i in complement do
 vecs := Concatenation( Basis(B){[1..9]}, Basis(A){[i]} );
 sub := VectorSpace( F, vecs );
 number := true;
 for k in [1..9] do
   for l in vecs do
     if not Basis(B)[k] * l in sub then
       number:=false;
     fi;
   od;
 od;
 if number=true then Add(new_indices_in_LminusOne, i); fi;
od;


The code can actually be simplified a lot more, e.g. by using ForAny or ForAll; and more so if, for example, your space B is actually 9-dimensional. 


Hope that helps,
Max


> 
> With best wishes,
> Jianrong.
> 
> 
> 
> for i in complement do
> for k in [1..9] do
> number:=1;
> for l in [Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]] do
> if Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]], Basis(B)[k]*l)=fail then number:=0; fi;
> od;
> od;
> if number=1 then Add(new_indices_in_LminusOne, i); fi;
> od;
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
> 



From lijr at lzu.edu.cn  Mon Jan  7 03:08:30 2013
From: lijr at lzu.edu.cn (=?utf-8?B?5p2O5bu66I2j?=)
Date: Mon, 7 Jan 2013 11:08:30 +0800 (CST)
Subject: [GAP Forum] [SPAM] Re:  Coefficients in GAP
In-Reply-To: <5ED6DDE9-4C63-4F27-AA1D-6F3DC83EC3D8@quendi.de>
References: <5ED6DDE9-4C63-4F27-AA1D-6F3DC83EC3D8@quendi.de>
	<1033a08.47d99.13c10225ae3.Coremail.lijr@lzu.edu.cn>
Message-ID: <8692d.48590.13c12fb163c.Coremail.lijr@lzu.edu.cn>

Dear Max,

Thank you very much for your help. I will try again.

With best wishes,
Jianrong.


> -----????-----
> ???: "Max Horn" <max at quendi.de>
> ????: 2013?1?7? ???
> ???: "???" <lijr at lzu.edu.cn>
> ??: 
> ??: [SPAM] Re: [GAP Forum] Coefficients in GAP
> 
> Dear Jianrong,
> 
> 
> On 06.01.2013, at 14:52, ??? wrote:
> 
> > Dear Forum,
> > 
> > I would like to compute coefficients of a vector in a vector space V with respect to some basis B.
> > The command in GAP is Coefficients(B, v); 
> > 
> > If B is given by a list, then it seems that it doesn't work.
> 
> Indeed, because as the documentation of Coefficients states, B must be a basis -- and a "basis" here is a special GAP object, which is more than just a list of basis vectors.
> 
> One of the reasons for this is that for an arbitrary list of vectors, such as yours, it is not at all clear whether it actually forms a basis of the space spanned by those vectors, i.e. if they are linearly independent.
> 
> 
> > For example, Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3]) will have errors. Here B is a subspace of the vector space A. A consists of matrices. The codes are in the end of the email. How should I correct  Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[2]], Basis(B)[4]*Basis(A)[3])? Thank you very much.
> 
> This look as if you want to form a new basis by taking a subset of the existing Basis(B). Here is a sketch of how this could look like.
> 
> # Set F to your base field, e.g. GF(3^2)
> F := ...;
> 
> # Take first 9 basis vectors of B plus second basis vector of A
> vecs := Concatenation( Basis(B){[1..9]}, Basis(A){[2]} );
> 
> # Compute a basis of the spanned vector space:
> bas := ImmutableBasis( MutableBasis( F, vecs ) );
> 
> # Optionally, check whether "vecs" really formed a basis.
> if Length(vecs) <> Length(bas) then
>   Error("vectors do not form a basis"
> fi;
> 
> # Finally, attempt to rewrite a matrix using this basis
> Coefficients( bas, Basis(B)[4]*Basis(A)[3] )
> 
> 
> But looking at your example code, and considering your previous question, it seems that perhaps all you want to do is to check whether some vector is contained in the span of some other vectors. Moreover, your code seems to contain a mistake (it sets number:=1 inside the loop over k, but tests it only after that loop; hence, only the result of the last loop iteration has any effect). Supposing all this, you could try something like the following (here I assumed you wanted to set and test "number" outside the k-loop; if the correct thing for you problem is to check "number" on each iteration of that loop, of course you'll have to move things around accordingly):
> 
> for i in complement do
>   vecs := Concatenation( Basis(B){[1..9]}, Basis(A){[i]} );
>   sub := VectorSpace( F, vecs );
>   number := true;
>   for k in [1..9] do
>     for l in vecs do
>       if not Basis(B)[k] * l in sub then
>         number:=false;
>       fi;
>     od;
>   od;
>   if number=true then Add(new_indices_in_LminusOne, i); fi;
> od;
> 
> 
> The code can actually be simplified a lot more, e.g. by using ForAny or ForAll; and more so if, for example, your space B is actually 9-dimensional. 
> 
> 
> Hope that helps,
> Max
> 
> 
> > 
> > With best wishes,
> > Jianrong.
> > 
> > 
> > 
> > for i in complement do
> > for k in [1..9] do
> > number:=1;
> > for l in [Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]] do
> > if Coefficients([Basis(B)[1], Basis(B)[2], Basis(B)[3], Basis(B)[4], Basis(B)[5], Basis(B)[6], Basis(B)[7], Basis(B)[8], Basis(B)[9], Basis(A)[i]], Basis(B)[k]*l)=fail then number:=0; fi;
> > od;
> > od;
> > if number=1 then Add(new_indices_in_LminusOne, i); fi;
> > od;
> > 
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
> > 
> 



From ciobotaru.mircea at gmail.com  Tue Jan  8 12:00:56 2013
From: ciobotaru.mircea at gmail.com (Ciobotaru Mircea)
Date: Tue, 8 Jan 2013 14:00:56 +0200
Subject: [GAP Forum] pkg
Message-ID: <CALHpxBCnFsyHWd5oVd7fHxL+0OueagMTi5qbNZwUCgH6s58ZeQ@mail.gmail.com>

where ist pkg for install GAP4R5/pkg ??
http://picasaweb.google.com/ciobotaru.mircea
http://SEMINEU.sunphoto.ro<http://semineu.sunphoto.ro/>
 http://semineu.sunphoto.ro/design_seminee

mob  0744 804 754   0745 462 970   fix 0264 411 536









]

From gaehler at math.uni-bielefeld.de  Thu Jan 10 14:49:44 2013
From: gaehler at math.uni-bielefeld.de (Franz Gaehler)
Date: Thu, 10 Jan 2013 15:49:44 +0100
Subject: [GAP Forum] Cryst and CrystCat packages
In-Reply-To: <E8BD0813D90B104AB50DD1C9F086AF412BC42B37@sal.ad.unb.ca>
References: <E8BD0813D90B104AB50DD1C9F086AF412BC42B37@sal.ad.unb.ca>
Message-ID: <20130110144944.GA18072@math.uni-bielefeld.de>

Dear Barry Monson,

sorry for the late reply.

> I have a question about the Cryst and CrystCat packages in Gap.  Is
> it possible to classify a given (and legitimate)
> AffineCrystGroupOnRight G according to standard nomenclature?
>
> Of course, I have a 4-dimensional example (whose point group is
> SymmetricGroup(4)). I would like to know where it fits into the
> Brown...Zassenhaus classification. On the other hand, since this is
> really just for my own curiosity, I don't much want to have to read
> that book more carefully. It is a bit daunting.
>
> I understand my G quite well. Besides the faithful affine
> representation I have a nice presentation and a further geometric
> interpretation. G is the so-called monodromy group of the pyramid
> over an apeirogon (infinite sided polygon).

Cryst provides a function ConjugatorSpaceGroups, which requires
the package Carat to be installed however. It returns a conjugating
affine transformation if two space groups are equivalent, or fail
otherwise. With this, you can loop over the space group catalogue
in CrystCat and find the right one. In order to make it not too
inefficient, one should skip entire classes of groups as early
as possible. I have attached such a function below.

As the original catalogue consists of left-acting space groups,
my function takes the transpose of a right-acting space group,
and compares it to the left-acting ones from the catalogue.

SpaceGroupTypeBBNWZ := function( S )
  local S1, d, P, c, q, G, z, s, S2;
  if IsAffineCrystGroupOnRight( S ) then
    S1 := TransposedMatrixGroup(S);
  elif IsAffineCrystGroupOnLeft( S )
    S1 := S;
  else
    Error( "S must be an AffineCrystGroup" );
  fi;
  d := DimensionOfMatrixGroup( S1 ) - 1;
  if not d in [2..4] then return fail; fi;
  P := PointGroup( StandardAffineCrystGroup( S1 ) );
  for c in [1 .. NrCrystalSystems( d )] do
    for q in [1 .. NrQClassesCrystalSystem( d, c )] do
      G := MatGroupZClass( d, c, q, 1 );
      if Size( P ) <> Size( G ) then continue; fi;
      if fail = ConjugatorQClass( P, G ) then continue; fi;
      for z in [1 .. NrZClassesQClass( d, c, q )] do
        G := MatGroupZClass( d, c, q, z );
        if fail = RepresentativeAction(GL(d,Integers), P, G) then continue; fi;
        for s in [1 .. NrSpaceGroupTypesZClass( d, c, q, z )] do 
          S2 := SpaceGroupOnLeftBBNWZ( d, c, q, z, s ); 
          if fail <> ConjugatorSpaceGroups( S1, S2 ) then 
            return [d, c, q, z, s];
          fi;
        od;
      od;
    od;
  od;
  return fail;
end;

With best regards,
Franz G?hler

_____________________________________________________________________________
Dr. Franz G?hler          Phone  +49 521 / 106   3876
Faculty of Mathematics    Fax    +49 521 / 106 153876
University of Bielefeld   Email  gaehler at math.uni-bielefeld.de
D-33615 Bielefeld         http://www.math.uni-bielefeld.de/~gaehler/


From marek at mitros.org  Sat Jan 12 20:23:19 2013
From: marek at mitros.org (Marek Mitros)
Date: Sat, 12 Jan 2013 21:23:19 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
Message-ID: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>

Hi,

What is the quickest way to diagonalize symmetric matrix 248x248 with
integral entries. I run Eigenvectors(Rationals, m) but it run long
time on my PC. The matrix is the Gram matrix of Thompson Smith lattice
in dimension 248. See page:
http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html

I would like to obtain the lattice generators or alternatively
orthogonal representation of Thompson sporadic group.

Regards,
Marek


From mathieu.dutour at gmail.com  Sat Jan 12 21:01:24 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Sat, 12 Jan 2013 22:01:24 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
Message-ID: <CADm_teN4H4rEsLO=ukOqmNygbidY+PgJQVq3VKO+hD_tZfcwXA@mail.gmail.com>

Maybe you can try to use real arithmetic for diagonalization using a
Fortran code that implement Jacobi method.

Otherwise, I am not sure if such a diagonalization makes sense.
Such gram matrix are defined up to arithmetic equivalence
A ---> PAP^T   with P an integral matrix of determinant +-1.
The matrix on Nebe's website is just one matrix in the whole equivalence
class and the eigenvalues will be different if you choose another matrix in
the equivalence class.

  Mathieu



On Sat, Jan 12, 2013 at 9:23 PM, Marek Mitros <marek at mitros.org> wrote:

> Hi,
>
> What is the quickest way to diagonalize symmetric matrix 248x248 with
> integral entries. I run Eigenvectors(Rationals, m) but it run long
> time on my PC. The matrix is the Gram matrix of Thompson Smith lattice
> in dimension 248. See page:
> http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
>
> I would like to obtain the lattice generators or alternatively
> orthogonal representation of Thompson sporadic group.
>
> Regards,
> Marek
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From dima at ntu.edu.sg  Sun Jan 13 06:28:57 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Sun, 13 Jan 2013 14:28:57 +0800
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
Message-ID: <CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>

Dear Marek,

On 13 January 2013 04:23, Marek Mitros <marek at mitros.org> wrote:
> Hi,
>
> What is the quickest way to diagonalize symmetric matrix 248x248 with
> integral entries. I run Eigenvectors(Rationals, m) but it run long
> time on my PC.
the eigenvalues (and, therefore, eigenvectors) need not be rational.
To achieve this, you might need to extend the field of rationals.

HTH,
Dmitrii

> The matrix is the Gram matrix of Thompson Smith lattice
> in dimension 248. See page:
> http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
>
> I would like to obtain the lattice generators or alternatively
> orthogonal representation of Thompson sporadic group.
>
> Regards,
> Marek
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From marek at mitros.org  Sun Jan 13 10:39:59 2013
From: marek at mitros.org (Marek Mitros)
Date: Sun, 13 Jan 2013 11:39:59 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
	<CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>
Message-ID: <CAOng4KiUwxZvYN-aM6KDGgn-7DhE4m_7zLt10RuczvXjLYOw4w@mail.gmail.com>

In general you are right. In this case I've got information from G. Nebe,
that matrix is diagonalizable over rationals. So orthogonal representation
of Th group would have rational entries.

Regards,
Marek
13-01-2013 07:29, "Dmitrii (Dima) Pasechnik" <dima at ntu.edu.sg> napisa?(a):

> Dear Marek,
>
> On 13 January 2013 04:23, Marek Mitros <marek at mitros.org> wrote:
> > Hi,
> >
> > What is the quickest way to diagonalize symmetric matrix 248x248 with
> > integral entries. I run Eigenvectors(Rationals, m) but it run long
> > time on my PC.
> the eigenvalues (and, therefore, eigenvectors) need not be rational.
> To achieve this, you might need to extend the field of rationals.
>
> HTH,
> Dmitrii
>
> > The matrix is the Gram matrix of Thompson Smith lattice
> > in dimension 248. See page:
> > http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
> >
> > I would like to obtain the lattice generators or alternatively
> > orthogonal representation of Thompson sporadic group.
> >
> > Regards,
> > Marek
> >
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
> CONFIDENTIALITY:This email is intended solely for the person(s) named and
> may be confidential and/or privileged.If you are not the intended
> recipient,please delete it,notify us and do not copy,use,or disclose its
> content.
>
> Towards A Sustainable Earth:Print Only When Necessary.Thank you.
>

From Bill.Allombert at math.u-bordeaux1.fr  Sun Jan 13 12:16:41 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Sun, 13 Jan 2013 13:16:41 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <CAOng4KiUwxZvYN-aM6KDGgn-7DhE4m_7zLt10RuczvXjLYOw4w@mail.gmail.com>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
	<CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>
	<CAOng4KiUwxZvYN-aM6KDGgn-7DhE4m_7zLt10RuczvXjLYOw4w@mail.gmail.com>
Message-ID: <20130113121641.GF8968@yellowpig>

On Sun, Jan 13, 2013 at 11:39:59AM +0100, Marek Mitros wrote:
> In general you are right. In this case I've got information from G. Nebe,
> that matrix is diagonalizable over rationals. So orthogonal representation
> of Th group would have rational entries.

With PARI/GP, I found that the eigenvalues are:
[238 230 228 220 218 216 214 212 210 208 206 204 202 200 198 196 194 192 190 188 186 184 182 180
178 176 174 172 170 168 166 160 158 156 24]
with multiplicities
[1 3 2 6 2 4 7 3 6 3 5 5 5 5 2 5 3 9 3 3 2 2 3 2 1 2 3 4 2 1 1 1 1 1 140]

Maybe this will allow you to complete the computation with gap.

Cheers,
Bill.


From Bill.Allombert at math.u-bordeaux1.fr  Sun Jan 13 12:54:16 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Sun, 13 Jan 2013 13:54:16 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <20130113121641.GF8968@yellowpig>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
	<CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>
	<CAOng4KiUwxZvYN-aM6KDGgn-7DhE4m_7zLt10RuczvXjLYOw4w@mail.gmail.com>
	<20130113121641.GF8968@yellowpig>
Message-ID: <20130113125416.GH8968@yellowpig>

On Sun, Jan 13, 2013 at 01:16:41PM +0100, Bill Allombert wrote:
> On Sun, Jan 13, 2013 at 11:39:59AM +0100, Marek Mitros wrote:
> > In general you are right. In this case I've got information from G. Nebe,
> > that matrix is diagonalizable over rationals. So orthogonal representation
> > of Th group would have rational entries.
> 
> With PARI/GP, I found that the eigenvalues are:
> [238 230 228 220 218 216 214 212 210 208 206 204 202 200 198 196 194 192 190 188 186 184 182 180
> 178 176 174 172 170 168 166 160 158 156 24]
> with multiplicities
> [1 3 2 6 2 4 7 3 6 3 5 5 5 5 2 5 3 9 3 3 2 2 3 2 1 2 3 4 2 1 1 1 1 1 140]

Bah, obviously this is garbage, I did not input the matrix correctly.
Is it possible to dowload the matrix without doing a big copy-paste ?

Cheers,
Bill.


From dima at ntu.edu.sg  Sun Jan 13 13:50:50 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Sun, 13 Jan 2013 21:50:50 +0800
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <20130113125416.GH8968@yellowpig>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
	<CAAWYfq2sNbqNm8A0e6AnQpBN0S5hrTB7wRLNjMEN62Cu+wNVnQ@mail.gmail.com>
	<CAOng4KiUwxZvYN-aM6KDGgn-7DhE4m_7zLt10RuczvXjLYOw4w@mail.gmail.com>
	<20130113121641.GF8968@yellowpig> <20130113125416.GH8968@yellowpig>
Message-ID: <CAAWYfq3x=5MF0XZEOszZkW9U04cSBxF8+HugxP+NR7V=TP0tew@mail.gmail.com>

Dmitrii Pasechnik
On 13 January 2013 20:54, Bill Allombert
<Bill.Allombert at math.u-bordeaux1.fr> wrote:
> On Sun, Jan 13, 2013 at 01:16:41PM +0100, Bill Allombert wrote:
>> On Sun, Jan 13, 2013 at 11:39:59AM +0100, Marek Mitros wrote:
>> > In general you are right. In this case I've got information from G. Nebe,
>> > that matrix is diagonalizable over rationals. So orthogonal representation
>> > of Th group would have rational entries.
>>
>> With PARI/GP, I found that the eigenvalues are:
>> [238 230 228 220 218 216 214 212 210 208 206 204 202 200 198 196 194 192 190 188 186 184 182 180
>> 178 176 174 172 170 168 166 160 158 156 24]
>> with multiplicities
>> [1 3 2 6 2 4 7 3 6 3 5 5 5 5 2 5 3 9 3 3 2 2 3 2 1 2 3 4 2 1 1 1 1 1 140]
>
> Bah, obviously this is garbage, I did not input the matrix correctly.
> Is it possible to dowload the matrix without doing a big copy-paste ?

save the html file, then edit it...

HTH,
Dima
>
> Cheers,
> Bill.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From marek at mitros.org  Tue Jan 15 09:35:28 2013
From: marek at mitros.org (Marek Mitros)
Date: Tue, 15 Jan 2013 10:35:28 +0100
Subject: [GAP Forum] Diagonalize of symmetric matrix 248x248
In-Reply-To: <CADm_teN4H4rEsLO=ukOqmNygbidY+PgJQVq3VKO+hD_tZfcwXA@mail.gmail.com>
References: <CAOng4KjSXLACyOdgLG5UgchMOiGN5e169i5jdrwfPPz+-yS=AA@mail.gmail.com>
	<CADm_teN4H4rEsLO=ukOqmNygbidY+PgJQVq3VKO+hD_tZfcwXA@mail.gmail.com>
Message-ID: <CAOng4KhBAwwA3Q6nJ4Lor-aJ_v6eYTD2ZWKuPwy6ijTQrNCA_g@mail.gmail.com>

Hello again,

I would like to thank you all the people who answered on my post.
Thanks to Gabrielle Nebe I was able to obtain orthogonal
representation of Th group. This makes me happy and I am able to
continue my research in this group.

My method was wrong. You do not need to look for eigenvectors of Gram
matrix in order to do orthogonalization. Prof. Nebe has sent me the
magic matrix using which I obtained orthogonal generators from the
linear ones present on lattice catalogue web page.

Best regards,
Marek Mitros


On 1/12/13, Mathieu Dutour <mathieu.dutour at gmail.com> wrote:
> Maybe you can try to use real arithmetic for diagonalization using a
> Fortran code that implement Jacobi method.
>
> Otherwise, I am not sure if such a diagonalization makes sense.
> Such gram matrix are defined up to arithmetic equivalence
> A ---> PAP^T   with P an integral matrix of determinant +-1.
> The matrix on Nebe's website is just one matrix in the whole equivalence
> class and the eigenvalues will be different if you choose another matrix in
> the equivalence class.
>
>   Mathieu
>
>
>
> On Sat, Jan 12, 2013 at 9:23 PM, Marek Mitros <marek at mitros.org> wrote:
>
>> Hi,
>>
>> What is the quickest way to diagonalize symmetric matrix 248x248 with
>> integral entries. I run Eigenvectors(Rationals, m) but it run long
>> time on my PC. The matrix is the Gram matrix of Thompson Smith lattice
>> in dimension 248. See page:
>> http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
>>
>> I would like to obtain the lattice generators or alternatively
>> orthogonal representation of Thompson sporadic group.
>>
>> Regards,
>> Marek
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>


From group.compute at gmail.com  Thu Jan 17 07:52:21 2013
From: group.compute at gmail.com (A L)
Date: Thu, 17 Jan 2013 01:52:21 -0600
Subject: [GAP Forum] efficient hamming distance computation
Message-ID: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>

Hello,

For a project, I need to compute the minimal Hamming distance between a
fixed permutation and a (large) permutation group. What is the "correct"
way to do this in GAP? I am looking for the most efficient method, both for
the Hamming distance computation between individual elements, as well as
ways to avoid brute-force comparison with each element in the group
(perhaps utilizing information about the group's structure).

Any help or pointers/references would be appreciated. I am new to GAP and
have tried my best to wade through the extensive documentation.

From dima at ntu.edu.sg  Thu Jan 17 10:52:10 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Thu, 17 Jan 2013 18:52:10 +0800
Subject: [GAP Forum] efficient hamming distance computation
In-Reply-To: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>
References: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>
Message-ID: <CAAWYfq3rB9+eOT6hfGgPCw-WB0=9V2gQi-Hj6TWV2f3oPKqxdw@mail.gmail.com>

On 17 January 2013 15:52, A L <group.compute at gmail.com> wrote:
> Hello,
>
> For a project, I need to compute the minimal Hamming distance between a
> fixed permutation and a (large) permutation group.
it would be good to know how large the group can be, and what is its degree n.


> What is the "correct"
> way to do this in GAP? I am looking for the most efficient method, both for
> the Hamming distance computation between individual elements, as well as
> ways to avoid brute-force comparison with each element in the group
> (perhaps utilizing information about the group's structure).

Note that if H is your group and g your permutation, then the Hamming
distance d(H,g) between H and g equals d(H,HgH), for HgH the double
coset of H in <H,g>, or in S_n, does not matter.
(This holds as d(f,g)=d(hf,hg)=d(hfh',hgh') for any f,h,h' in H.)
So you might begin by trying to find a "nicer" element in Hg.
E.g. you might want to find such an element with maximum (or just
large) number of fixed points. Then the pointwise stabilizer of these
points in H will contain the closest to g element, as far as I can
see.
Another point of view might be useful if you can construct the set of
double cosets of H in S_n. Then you can create a graph structure on
them using transpositions: H is connected to HtH for a transposition t
not in H (and so for any g in HtH one has d(H,g)=2, for g in Htt'H one
would have d(H,g)=3 or 4,... ), etc.

Perhaps there are even better methods for your problem: indeed,
computing d(,) seems to be an extension of a procedure to check
whether g is in H, and this is studied very extensively.

Seems to be a natural and interesting problem, IMHO!

HTH,
Dmitrii


>
> Any help or pointers/references would be appreciated. I am new to GAP and
> have tried my best to wade through the extensive documentation.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From group.compute at gmail.com  Thu Jan 17 17:50:14 2013
From: group.compute at gmail.com (A L)
Date: Thu, 17 Jan 2013 11:50:14 -0600
Subject: [GAP Forum] efficient hamming distance computation
In-Reply-To: <CAAWYfq3rB9+eOT6hfGgPCw-WB0=9V2gQi-Hj6TWV2f3oPKqxdw@mail.gmail.com>
References: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>
	<CAAWYfq3rB9+eOT6hfGgPCw-WB0=9V2gQi-Hj6TWV2f3oPKqxdw@mail.gmail.com>
Message-ID: <CABZttPRT7BkRNxeuJZFEyU1hEvYxD4VigDo450qd+dvMz-VKBA@mail.gmail.com>

Thanks for the enthusiastic response, Dmitrii. I have tried to respond in
the body of your email, below.
I also wanted to point out that I am (somewhat) familiar with the
theoretical literature related to this problem, and I am mostly interested
in learning more about the specific implementation in GAP. For instance, if
the most efficient way to compute d(a,b) in GAP is to compute the fixed
points of ab^-1, which efficient functions should I call to perform this
computation?


On Thu, Jan 17, 2013 at 4:52 AM, Dmitrii (Dima) Pasechnik
<dima at ntu.edu.sg>wrote:

> On 17 January 2013 15:52, A L <group.compute at gmail.com> wrote:
> > Hello,
> >
> > For a project, I need to compute the minimal Hamming distance between a
> > fixed permutation and a (large) permutation group.
> it would be good to know how large the group can be, and what is its
> degree n.
>
> Let me be a little more specific. At the moment, I am looking at the
families of groups PGL(2,q) where q ~ 50, so let's say n ~ 100k.

>
> > What is the "correct"
> > way to do this in GAP? I am looking for the most efficient method, both
> for
> > the Hamming distance computation between individual elements, as well as
> > ways to avoid brute-force comparison with each element in the group
> > (perhaps utilizing information about the group's structure).
>
> Note that if H is your group and g your permutation, then the Hamming
> distance d(H,g) between H and g equals d(H,HgH), for HgH the double
> coset of H in <H,g>, or in S_n, does not matter.
> (This holds as d(f,g)=d(hf,hg)=d(hfh',hgh') for any f,h,h' in H.)
>

Can you clarify what you mean in the section starting here:

> So you might begin by trying to find a "nicer" element in Hg.
> E.g. you might want to find such an element with maximum (or just
> large) number of fixed points. Then the pointwise stabilizer of these
> points in H will contain the closest to g element, as far as I can
> see.
>
and ending here.

Another point of view might be useful if you can construct the set of
> double cosets of H in S_n. Then you can create a graph structure on
> them using transpositions: H is connected to HtH for a transposition t
> not in H (and so for any g in HtH one has d(H,g)=2, for g in Htt'H one
> would have d(H,g)=3 or 4,... ), etc.
>
> Perhaps there are even better methods for your problem: indeed,
> computing d(,) seems to be an extension of a procedure to check
> whether g is in H, and this is studied very extensively.
>
Which (specific) references do you have in mind?

> Seems to be a natural and interesting problem, IMHO!
>
> HTH,
> Dmitrii
>
>
> >
> > Any help or pointers/references would be appreciated. I am new to GAP and
> > have tried my best to wade through the extensive documentation.
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
> CONFIDENTIALITY:This email is intended solely for the person(s) named and
> may be confidential and/or privileged.If you are not the intended
> recipient,please delete it,notify us and do not copy,use,or disclose its
> content.
>
> Towards A Sustainable Earth:Print Only When Necessary.Thank you.
>

From nagyg at math.u-szeged.hu  Thu Jan 17 19:01:18 2013
From: nagyg at math.u-szeged.hu (Nagy Gabor)
Date: Thu, 17 Jan 2013 20:01:18 +0100
Subject: [GAP Forum] efficient hamming distance computation
In-Reply-To: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>
References: <CABZttPQs7xdOMtFasqggqdLdH+DCQRWHm1-LrLb7=X76MMfe5w@mail.gmail.com>
Message-ID: <50F84A7E.20907@math.u-szeged.hu>

Hi,

I am used to do a lot of calculation with distances of permutations.

According to me,

NrMovedPoints(a/b)

is very efficient to compute d(a,b).

More difficult is to find the element b of G which is "closest" to a. I 
would do it rather straightforward.

G:=PGL(2,53); Size(G);

closest:=function(G,a)
     local md,x,b;
     md:=NrMovedPoints(G); b:="";
     for x in G do
         if NrMovedPoints(x/a)<md then
             md:=NrMovedPoints(x/a);
             b:=x;
         fi;
     od;
     return b;
end;

a:=Random(SymmetricGroup(NrMovedPoints(G)));
b:=closest(G,a);
time;

You can check the result by

NrMovedPoints(a/b);
Collected(List(G,u->NrMovedPoints(a/u)));

I hope this helps.

Bye,

Gabor


On 01/17/2013 08:52 AM, A L wrote:
> Hello,
>
> For a project, I need to compute the minimal Hamming distance between a
> fixed permutation and a (large) permutation group. What is the "correct"
> way to do this in GAP? I am looking for the most efficient method, both for
> the Hamming distance computation between individual elements, as well as
> ways to avoid brute-force comparison with each element in the group
> (perhaps utilizing information about the group's structure).
>
> Any help or pointers/references would be appreciated. I am new to GAP and
> have tried my best to wade through the extensive documentation.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From degraaf at science.unitn.it  Thu Jan 17 21:24:29 2013
From: degraaf at science.unitn.it (Willem de Graaf)
Date: Thu, 17 Jan 2013 22:24:29 +0100
Subject: [GAP Forum] naming convention for basis of highest weight
	modules
In-Reply-To: <1355986153.39583.YahooMailNeo@web121202.mail.ne1.yahoo.com>
References: <1355986153.39583.YahooMailNeo@web121202.mail.ne1.yahoo.com>
Message-ID: <CAHQ8B2Zvk4=D5Jdoj3Z-3TbTDjmG2G8sSKD20zDrvRK=3S8rig@mail.gmail.com>

Dear R.N. Tsai,

You asked about the way the basis elements of a highest weight module
are printed. This is described in the manual section: 64.14-4
IsWeightRepElement.

A basis vector is printed as mon*v0. Here 'v0' is the highest weight vector
and 'mon' is a monomial in the root vectors corresponding to the negative
roots (sometimes called lowering operators).

Example:

gap> L:= SimpleLieAlgebra("A", 2, Rationals);;
gap> V:= HighestWeightModule( L, [1,1] );;
gap> v0:=Basis(V)[1];
1*v0
gap> y:= ChevalleyBasis(L)[2];;
gap> y[1]^(y[2]^v0);
y1*y2*v0


If you have questions about this, then please ask.

Best wishes,

Willem de Graaf

On Thu, Dec 20, 2012 at 7:49 AM, R.N. Tsai <r_n_tsai at yahoo.com> wrote:
> Dear gap-forum,
>
> Is the naming convention for the basis of highest weight modules described anywhere?
>
> For example :
>
> gap>L:=SimpleLieAlgebra("A",2,Rationals);;
> gap>M1:=HighestWeightModule(L,[1,0]);;
> gap>B1:=Basis(M1);;
> gap>M2:=TensorProductOfAlgebraModules(M1,M1);;
> gap>B2:=Basis(M2);;
>
> gap> BasisVectors(B1);
> [ 1*v0, y1*v0, y3*v0 ]
> gap> BasisVectors(B2);
> [ 1*(1*v0<x>1*v0), 1*(1*v0<x>y1*v0), 1*(1*v0<x>y3*v0), 1*(y1*v0<x>1*v0), 1*(y1*v0<x>y1*v0), 1*(y1*v0<x>y3*v0),
>   1*(y3*v0<x>1*v0), 1*(y3*v0<x>y1*v0), 1*(y3*v0<x>y3*v0) ]
>
> 1*v0,y1*v0,y3*v0 seems an odd choice without knowing where it came from.
>
> Thanks,
> r.n.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From w_becker at hotmail.com  Mon Jan 21 23:07:25 2013
From: w_becker at hotmail.com (Walter Becker)
Date: Mon, 21 Jan 2013 14:07:25 -0900
Subject: [GAP Forum] correspondence betrween Small group lib and Hall Senior
	tables
Message-ID: <BAY002-W429F31F08170B9FA46E504FF170@phx.gbl>

Gap Forum
 
I know there exists a table listing the correspondence 
for the groups of order 2^n for n less than or equal to 6
given in the Hall-Senior Tables and the corresponding 
group number in the Small Group Library. Could you direct me to
an on-line source for this table ---or send me one via e-mail ?
 
Walter Becker 		 	   		  

From mbg.nimda at gmail.com  Mon Jan 21 22:54:02 2013
From: mbg.nimda at gmail.com (Mbg Nimda)
Date: Mon, 21 Jan 2013 23:54:02 +0100
Subject: [GAP Forum] Fwd:
Message-ID: <50fdd522.c71a700a.5488.3ae5@mx.google.com>

http://www.illuminazioneconled.it/7robnn.php


From mbg.nimda at gmail.com  Mon Jan 21 22:55:00 2013
From: mbg.nimda at gmail.com (Mbg Nimda)
Date: Mon, 21 Jan 2013 23:55:00 +0100
Subject: [GAP Forum] Fwd:
Message-ID: <50fdd55e.637b980a.055f.ffff96cd@mx.google.com>

http://www.illuminazioneconled.it/7robnn.php


From suskudar at gmail.com  Tue Jan 22 00:05:50 2013
From: suskudar at gmail.com (sumeyra uskudar)
Date: Tue, 22 Jan 2013 02:05:50 +0200
Subject: [GAP Forum] Fwd:  hall-senior number vs small group id
In-Reply-To: <4F8E3342.8050104@auckland.ac.nz>
References: <CADUzUOhgOHRKhSDWa0XViNkwbbVqbsAVF+NU4B9DQsatUQ78vQ@mail.gmail.com>
	<alpine.LRH.2.00.1204170854440.18149@rzlogin03.rz.tu-bs.de>
	<4F8E3342.8050104@auckland.ac.nz>
Message-ID: <CADUzUOipzq5_jxTKoyCb_Jt+xOtX621R3T30axAE-Kf-Sfyd-g@mail.gmail.com>

---------- Forwarded message ----------
From: Eamonn O'Brien <e.obrien at auckland.ac.nz>
Date: 2012/4/18
Subject: Re: [GAP Forum] hall-senior number vs small group id
To: forum at gap-system.org
Cc: sumeyra uskudar <suskudar at gmail.com>


Dear Forum:

Attached is the correspondence between Hall-Senior identifiers
for the groups of order dividing 64 and the corresponding
SmallGroup identifiers. I determined this in the 1980s.

HallSeniorToSmallGroup[n][x] returns the SmallGroup id
of the H-S group (2^n)#x.

gap> HallSeniorToSmallGroup[6][187]**;
245

SmallGroupToHallSenior[m][y] returns the HallSenior id
of the SmallGroup  (2^m)#y.

gap> SmallGroupToHallSenior[6][245]**;
187

Best wishes.
Eamonn

# Given a SmallGroup id of a group of order 2^n, print
# SmallGroupToHallSenior[n][x] to obtain the Hall-Senior number of the
group.

# Given a Hall-Senior number y of a group of order 2^n, print
# HallSeniorToSmallGroup[n][y] to obtain the SmallGroup id of the group.

SmallGroupToHallSenior := [
     [ 1 ],
     [ 2, 1 ],
     [ 3, 2, 4, 5, 1 ],
     [ 5, 3, 9, 10, 4, 11, 12, 13, 14, 2, 6, 7, 8, 1 ],
     [ 7, 18, 5, 19, 20, 46, 47, 48, 27, 28, 31, 21, 30, 29, 32, 6, 22, 49,
          50, 51, 3, 11, 12, 16, 14, 15, 33, 36, 37, 38, 39, 40, 41, 34, 35,
          4, 13, 17, 23, 24, 25, 26, 44, 45, 2, 8, 9, 10, 42, 43, 1 ],
     [ 11, 8, 38, 131, 132, 62, 63, 237, 238, 239, 240, 234, 235, 236, 65,
          64, 37, 180, 181, 60, 59, 61, 128, 129, 130, 9, 39, 182, 40, 133,
66,           250, 251, 252, 253, 254, 255, 138, 139, 142, 248, 247, 249,
41, 67,
          246, 140, 141, 143, 10, 42, 265, 266, 267, 5, 22, 30, 28, 29, 81,
83,
          89, 90, 93, 82, 86, 84, 92, 91, 88, 85, 87, 144, 147, 146, 145,
150,
          151, 149, 148, 152, 153, 6, 23, 31, 32, 24, 94, 96, 123, 126, 124,
          125, 127, 47, 48, 53, 114, 113, 115, 51, 120, 25, 95, 97, 50, 49,
54,
          116, 52, 121, 33, 98, 102, 34, 99, 100, 55, 56, 57, 118, 119, 117,
          58, 122, 35, 101, 201, 203, 217, 202, 204, 218, 261, 263, 262,
264,
          259, 260, 205, 206, 208, 211, 219, 220, 196, 195, 197, 229, 228,
230,
          257, 256, 258, 207, 210, 209, 212, 221, 222, 213, 214, 223, 215,
216,
          224, 193, 194, 200, 232, 231, 233, 189, 188, 192, 198, 225, 226,
191,
          199, 190, 227, 7, 26, 36, 134, 135, 136, 137, 244, 245, 3, 15, 16,
          20, 18, 19, 27, 106, 108, 107, 68, 71, 72, 73, 77, 74, 75, 76, 80,
          69, 70, 78, 79, 169, 170, 172, 171, 175, 177, 176, 179, 178, 173,
          174, 154, 157, 160, 159, 155, 158, 163, 167, 164, 161, 166, 168,
162,
          156, 165, 184, 183, 185, 186, 187, 4, 17, 21, 109, 43, 44, 45, 46,
          110, 111, 112, 241, 242, 243, 2, 12, 13, 14, 103, 104, 105, 1 ] ];

HallSeniorToSmallGroup := [
     [ 1 ],
     [ 2, 1 ],
     [ 5, 2, 1, 3, 4 ],
     [ 14, 10, 2, 5, 1, 11, 12, 13, 3, 4, 6, 7, 8, 9 ],
     [ 51, 45, 21, 36, 3, 16, 1, 46, 47, 48, 22, 23, 37, 25, 26, 24, 38, 2,
          4, 5, 12, 17, 39, 40, 41, 42, 9, 10, 14, 13, 11, 15, 27, 34, 35,
28,
          29, 30, 31, 32, 33, 49, 50, 43, 44, 6, 7, 8, 18, 19, 20 ],
     [ 267, 260, 192, 246, 55, 83, 183, 2, 26, 50, 1, 261, 262, 263, 193,
          194, 247, 196, 197, 195, 248, 56, 84, 87, 103, 184, 198, 58, 59,
57,
          85, 86, 112, 115, 126, 185, 17, 3, 27, 29, 44, 51, 250, 251, 252,
          253, 95, 96, 107, 106, 101, 110, 97, 108, 118, 119, 120, 124, 21,
20,
          22, 6, 7, 16, 15, 31, 45, 202, 211, 212, 203, 204, 205, 207, 208,
          209, 206, 213, 214, 210, 60, 65, 61, 67, 71, 66, 72, 70, 62, 63,
69,
          68, 64, 88, 104, 89, 105, 113, 116, 117, 127, 114, 264, 265, 266,
          199, 201, 200, 249, 254, 255, 256, 99, 98, 100, 109, 123, 121,
122,
          102, 111, 125, 90, 92, 93, 91, 94, 23, 24, 25, 4, 5, 30, 186, 187,
          188, 189, 38, 39, 47, 48, 40, 49, 73, 76, 75, 74, 80, 79, 77, 78,
81,
          82, 226, 230, 239, 227, 231, 229, 228, 235, 238, 232, 234, 240,
236,
          233, 237, 215, 216, 218, 217, 224, 225, 219, 221, 220, 223, 222,
18,
          19, 28, 242, 241, 243, 244, 245, 174, 173, 181, 179, 175, 167,
168,
          147, 146, 148, 176, 180, 169, 128, 131, 129, 132, 140, 141, 155,
142,
          157, 156, 143, 158, 161, 162, 164, 165, 130, 133, 144, 145, 159,
160,
          163, 166, 177, 178, 182, 150, 149, 151, 171, 170, 172, 12, 13,
14, 8,
          9, 10, 11, 257, 258, 259, 190, 191, 46, 42, 41, 43, 32, 33, 34,
35,
          36, 37, 153, 152, 154, 138, 139, 134, 136, 135, 137, 52, 53, 54 ]
];




-- 
*S?meyra Bedir*
-------------- next part --------------
# Given a SmallGroup id of a group of order 2^n, print 
# SmallGroupToHallSenior[n][x] to obtain the Hall-Senior number of the group. 

# Given a Hall-Senior number y of a group of order 2^n, print 
# HallSeniorToSmallGroup[n][y] to obtain the SmallGroup id of the group.

SmallGroupToHallSenior := [ 
     [ 1 ], 
     [ 2, 1 ], 
     [ 3, 2, 4, 5, 1 ], 
     [ 5, 3, 9, 10, 4, 11, 12, 13, 14, 2, 6, 7, 8, 1 ], 
     [ 7, 18, 5, 19, 20, 46, 47, 48, 27, 28, 31, 21, 30, 29, 32, 6, 22, 49,
          50, 51, 3, 11, 12, 16, 14, 15, 33, 36, 37, 38, 39, 40, 41, 34, 35, 
          4, 13, 17, 23, 24, 25, 26, 44, 45, 2, 8, 9, 10, 42, 43, 1 ], 
     [ 11, 8, 38, 131, 132, 62, 63, 237, 238, 239, 240, 234, 235, 236, 65, 
          64, 37, 180, 181, 60, 59, 61, 128, 129, 130, 9, 39, 182, 40, 133, 66,           250, 251, 252, 253, 254, 255, 138, 139, 142, 248, 247, 249, 41, 67, 
          246, 140, 141, 143, 10, 42, 265, 266, 267, 5, 22, 30, 28, 29, 81, 83,
          89, 90, 93, 82, 86, 84, 92, 91, 88, 85, 87, 144, 147, 146, 145, 150,
          151, 149, 148, 152, 153, 6, 23, 31, 32, 24, 94, 96, 123, 126, 124, 
          125, 127, 47, 48, 53, 114, 113, 115, 51, 120, 25, 95, 97, 50, 49, 54,
          116, 52, 121, 33, 98, 102, 34, 99, 100, 55, 56, 57, 118, 119, 117, 
          58, 122, 35, 101, 201, 203, 217, 202, 204, 218, 261, 263, 262, 264, 
          259, 260, 205, 206, 208, 211, 219, 220, 196, 195, 197, 229, 228, 230,
          257, 256, 258, 207, 210, 209, 212, 221, 222, 213, 214, 223, 215, 216,
          224, 193, 194, 200, 232, 231, 233, 189, 188, 192, 198, 225, 226, 191,
          199, 190, 227, 7, 26, 36, 134, 135, 136, 137, 244, 245, 3, 15, 16, 
          20, 18, 19, 27, 106, 108, 107, 68, 71, 72, 73, 77, 74, 75, 76, 80, 
          69, 70, 78, 79, 169, 170, 172, 171, 175, 177, 176, 179, 178, 173, 
          174, 154, 157, 160, 159, 155, 158, 163, 167, 164, 161, 166, 168, 162,
          156, 165, 184, 183, 185, 186, 187, 4, 17, 21, 109, 43, 44, 45, 46, 
          110, 111, 112, 241, 242, 243, 2, 12, 13, 14, 103, 104, 105, 1 ] ];

HallSeniorToSmallGroup := [ 
     [ 1 ], 
     [ 2, 1 ], 
     [ 5, 2, 1, 3, 4 ], 
     [ 14, 10, 2, 5, 1, 11, 12, 13, 3, 4, 6, 7, 8, 9 ], 
     [ 51, 45, 21, 36, 3, 16, 1, 46, 47, 48, 22, 23, 37, 25, 26, 24, 38, 2,
          4, 5, 12, 17, 39, 40, 41, 42, 9, 10, 14, 13, 11, 15, 27, 34, 35, 28,
          29, 30, 31, 32, 33, 49, 50, 43, 44, 6, 7, 8, 18, 19, 20 ], 
     [ 267, 260, 192, 246, 55, 83, 183, 2, 26, 50, 1, 261, 262, 263, 193, 
          194, 247, 196, 197, 195, 248, 56, 84, 87, 103, 184, 198, 58, 59, 57,
          85, 86, 112, 115, 126, 185, 17, 3, 27, 29, 44, 51, 250, 251, 252, 
          253, 95, 96, 107, 106, 101, 110, 97, 108, 118, 119, 120, 124, 21, 20,
          22, 6, 7, 16, 15, 31, 45, 202, 211, 212, 203, 204, 205, 207, 208, 
          209, 206, 213, 214, 210, 60, 65, 61, 67, 71, 66, 72, 70, 62, 63, 69,
          68, 64, 88, 104, 89, 105, 113, 116, 117, 127, 114, 264, 265, 266, 
          199, 201, 200, 249, 254, 255, 256, 99, 98, 100, 109, 123, 121, 122, 
          102, 111, 125, 90, 92, 93, 91, 94, 23, 24, 25, 4, 5, 30, 186, 187, 
          188, 189, 38, 39, 47, 48, 40, 49, 73, 76, 75, 74, 80, 79, 77, 78, 81,
          82, 226, 230, 239, 227, 231, 229, 228, 235, 238, 232, 234, 240, 236, 
          233, 237, 215, 216, 218, 217, 224, 225, 219, 221, 220, 223, 222, 18, 
          19, 28, 242, 241, 243, 244, 245, 174, 173, 181, 179, 175, 167, 168, 
          147, 146, 148, 176, 180, 169, 128, 131, 129, 132, 140, 141, 155, 142,
          157, 156, 143, 158, 161, 162, 164, 165, 130, 133, 144, 145, 159, 160,
          163, 166, 177, 178, 182, 150, 149, 151, 171, 170, 172, 12, 13, 14, 8,
          9, 10, 11, 257, 258, 259, 190, 191, 46, 42, 41, 43, 32, 33, 34, 35, 
          36, 37, 153, 152, 154, 138, 139, 134, 136, 135, 137, 52, 53, 54 ] ];

From w_becker at hotmail.com  Thu Jan 24 02:43:50 2013
From: w_becker at hotmail.com (Walter Becker)
Date: Wed, 23 Jan 2013 17:43:50 -0900
Subject: [GAP Forum] diagonalization of a matrix
Message-ID: <BAY002-W1907722AD87CBABA778C3A1FF140@phx.gbl>

I am not sure if this is an appropriate question for the gap-forum 
but it might be an interesting math question anyway.
 
 The following four by four matrix reperesents the action of an order
five element on the elementary abelian group of order 11^4.   Call the 
following matrix e:
 
            [ 7 10  4  1]
            [ 5  1  9  7]
            [ 8  9  4  9]
            [ 9  8  8  5]
 
One reads this action as follows: 
      a^e*a^(-7)*b^(-10}*c^(-4)*d^(-1) =
      b^e*a^(-5)*b^(-1)*c^(-9)*d^(-7)=  
 
etc for c^e and d^e.  
 
The group generated by (a,b,c,,d,e) and 
with this action is equivalent (ie isomorphic)
to one in which the action by an
order 5 matrix takes the form:
 
a^e*a^(-x)=b^e*b^(-x)=c^e*c^(-y)=d^e*d^)-z)=1
 
where x=3, y=3^2, and z=3^3 mod(11).
 
This correspondence was found by asking for groups with the 
presentation in the form 
 
a^e*a^(-x)-b^e*b^(-y)=c^e*c^(-z)=d^e*d^(-w)=1.
 
Four cases of this type were found for the above given matrix. 
One knows that these exponents must be chosen from the set
of numbers 1,3,4,5,9.  
 
If a matrix is a real symmetric  (or hermitian) matrix then one knows
how to diagonalize it ---find its eigenvalues and eigenvectors and 
then the matrix of eigenvectors will enable one to get the diagonal form.
 
Does there exist a corresponding construction for a general matrix over
a finite field ?   Note here that even though the initial matrix is not 
symmetric it is equivalent to a diagonal matrix as far as the group is concerned.   
 
  		 	   		  

From nagyg at math.u-szeged.hu  Mon Jan 28 11:08:56 2013
From: nagyg at math.u-szeged.hu (Nagy Gabor)
Date: Mon, 28 Jan 2013 12:08:56 +0100
Subject: [GAP Forum] Filter by family
Message-ID: <51065C48.7090809@math.u-szeged.hu>

Dear Forum,

I have a fixed monoid M.

All the elements of M have the same family Fam.

I would like to construct a filter "IsElementOfM" which returns true if 
and only if the object is in M.

Is this feasible?

Thanks in advance,

Gabor





From alexk at mcs.st-andrews.ac.uk  Mon Jan 28 16:30:01 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 28 Jan 2013 16:30:01 +0000
Subject: [GAP Forum] Compiling GAP code in a Windows environment
In-Reply-To: <CAEJjAo1LABpTRuQWC95g+NWekUZ34vMyFbihsKjxUngAEPzidg@mail.gmail.com>
References: <CAEJjAo1LABpTRuQWC95g+NWekUZ34vMyFbihsKjxUngAEPzidg@mail.gmail.com>
Message-ID: <4E9784E6-1A22-49CE-A44C-3E4C99C8F48A@mcs.st-andrews.ac.uk>

Dear David,

I've noticed that this question remains unanswered in the Forum. I'm 
not even sure that compiling GAP code was ever possible under Windows.
Anyhow, as http://www.gap-system.org/Manuals//doc/changes/chap2.html 
says,

"... we no longer recommend using the GAP compiler gac to compile 
GAP code to C, and may withdraw it in future releases. Compiling 
GAP code only ever gave a substantial speedup for rather specific 
types of calculation, and much more benefit can usually be achieved 
quite easily by writing a small number of key functions in C and 
loading them into the kernel as described in LoadDynamicModule 
(Reference: LoadDynamicModule). The gac script will remain available 
as a convenient way of compiling such kernel modules from C."

The latter way is used by some packages whose Windows binaries are 
supplied with GAP (EDIM, orb, Browse, io and cvec), though their 
development is happening under Linux, and Windows binaries are 
compiled on a Windows machine with a full Cygwin installation. 
You may look at those packages, if you would be interested in going 
that way.

Best regards,
Alexander





On 13 Nov 2012, at 07:59, David Harden wrote:

> I have GAP installed on my Windows machine. I am interested in doing a
> computation which makes use of a long list (of permutations on 32 points)
> and repeating the same operations many times over, so I think compiling my
> code can give me a substantial speed-up. How do I compile?
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From khersham.lim at mpi-hd.mpg.de  Fri Feb  1 11:33:03 2013
From: khersham.lim at mpi-hd.mpg.de (Kher Sham Lim)
Date: Fri, 01 Feb 2013 12:33:03 +0100
Subject: [GAP Forum] Finding certain subgroups from very large group
In-Reply-To: <510BA69C.5070800@mpi-hd.mpg.de>
References: <510BA69C.5070800@mpi-hd.mpg.de>
Message-ID: <510BA7EF.4050904@mpi-hd.mpg.de>

Dear GAP forum

I have a very large group to study, say G (it is an automorphism group 
of a small group). G has order of 10 million and I am interested in 
knowing whether a certain known group, say H is a subgroup in G. To find 
H is impossible in GAP, as GAP tries to calculate all the subgroups and 
this process exceeds my computer's memory. Is there another command or 
algorithm in GAP to compute subgroup of specific order only, or at least 
limit the subgroup order? I used SONATA to obtain the subgroups by the 
way. Thanks in advanced.

Sincerely

Kher Sham Lim

From alexk at mcs.st-andrews.ac.uk  Fri Feb  1 11:50:18 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 1 Feb 2013 11:50:18 +0000
Subject: [GAP Forum] Finding certain subgroups from very large group
In-Reply-To: <510BA7EF.4050904@mpi-hd.mpg.de>
References: <510BA69C.5070800@mpi-hd.mpg.de> <510BA7EF.4050904@mpi-hd.mpg.de>
Message-ID: <0D967CBF-7B02-4552-8B34-36D376D5F084@mcs.st-andrews.ac.uk>

Dear Kher Sham Lim,

Thank you for your question. In fact, the very first hint is contained in the documentation of 'AllSubgroups' from the manual of the SONATA package:

  For  a  finite  group  G  AllSubgroups returns a list of all subgroups of G,
  intended  primarily  for  use  in  class  for small examples. This list will
  quickly  get  very  long  and  in  general  use of ConjugacyClassesSubgroups
  (39.19-3) is recommended

Further hints may be found in the GAP F.A.Q. at http://www.gap-system.org/Faq/faq.html#7.7 - for convenience, that text is also pasted below:

---------

7.7: How do I get the subgroups of my group?

Everything said for elements holds even more so for subgroups: You probably want only representatives of the conjugacy classes or even just of subgroups of a given size.

For groups of moderate size (up to 10^4/10^5, this depends a bit on the group structure) the commands LatticeSubgroups or ConjugacyClassesSubgroups will compute representatives of all subgroups up to conjugacy. If the group gets bigger, however, this will either run out of space or take too long to be feasible.

In this case it is likely that you are only interested in certain types of subgroups. Try to use the restricting conditions to reduce the calculation (for example p-subgroups can be found inside a Sylow subgroup). GAP commands that might come useful to obtain specific subgroups are for example NormalSubgroups,SylowSubgroup, HallSubgroup, or MaximalSubgroupClassReps.

----------

Hope this helps. There may be better suggestions, if more details would be known about the groups in question.

Best wishes,
Alexander



On 1 Feb 2013, at 11:33, Kher Sham Lim wrote:

> Dear GAP forum
> 
> I have a very large group to study, say G (it is an automorphism group of a small group). G has order of 10 million and I am interested in knowing whether a certain known group, say H is a subgroup in G. To find H is impossible in GAP, as GAP tries to calculate all the subgroups and this process exceeds my computer's memory. Is there another command or algorithm in GAP to compute subgroup of specific order only, or at least limit the subgroup order? I used SONATA to obtain the subgroups by the way. Thanks in advanced.
> 
> Sincerely
> 
> Kher Sham Lim
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From Sven.Reichard at tu-dresden.de  Fri Feb  1 11:57:06 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Fri, 01 Feb 2013 12:57:06 +0100
Subject: [GAP Forum] Finding certain subgroups from very large group
In-Reply-To: <510BA7EF.4050904@mpi-hd.mpg.de>
References: <510BA69C.5070800@mpi-hd.mpg.de> <510BA7EF.4050904@mpi-hd.mpg.de>
Message-ID: <510BAD92.3000109@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

What do we know about the structure of H?

Sven Reichard.

Am 01.02.2013 12:33, schrieb Kher Sham Lim:
> Dear GAP forum
> 
> I have a very large group to study, say G (it is an automorphism
> group of a small group). G has order of 10 million and I am
> interested in knowing whether a certain known group, say H is a
> subgroup in G. To find H is impossible in GAP, as GAP tries to
> calculate all the subgroups and this process exceeds my computer's
> memory. Is there another command or algorithm in GAP to compute
> subgroup of specific order only, or at least limit the subgroup
> order? I used SONATA to obtain the subgroups by the way. Thanks in
> advanced.
> 
> Sincerely
> 
> Kher Sham Lim _______________________________________________ Forum
> mailing list Forum at mail.gap-system.org 
> http://mail.gap-system.org/mailman/listinfo/forum

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From sl4 at st-andrews.ac.uk  Fri Feb  1 12:09:04 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Fri, 1 Feb 2013 12:09:04 +0000
Subject: [GAP Forum] Finding certain subgroups from very large group
In-Reply-To: <093121d5cf284410ac80fcfb90968b62@UOS-DUN-CAS5.st-andrews.ac.uk>
References: <510BA69C.5070800@mpi-hd.mpg.de>
	<093121d5cf284410ac80fcfb90968b62@UOS-DUN-CAS5.st-andrews.ac.uk>
Message-ID: <BD2E85EE-9AD7-4F7D-8834-2734948777A4@st-andrews.ac.uk>

Dear Kher Sham Lim,

I assume you actually want to know if G has a subgroup isomorphic to H.
If so, the command you want is IsomorphicSubgroups(G,H).

This is enormously more efficient than simply listing all [conjugacy classes of] subgroups of G in most cases.

It might also be helpful to first replace G by an isomorphic permutation group (using IsomorphismPermGroup).

All of these commands are documented in the reference manual (equivalently in the on-line help).

	Steve

On 1 Feb 2013, at 11:33, Kher Sham Lim <khersham.lim at mpi-hd.mpg.de> wrote:

> Dear GAP forum
> 
> I have a very large group to study, say G (it is an automorphism group 
> of a small group). G has order of 10 million and I am interested in 
> knowing whether a certain known group, say H is a subgroup in G. To find 
> H is impossible in GAP, as GAP tries to calculate all the subgroups and 
> this process exceeds my computer's memory. Is there another command or 
> algorithm in GAP to compute subgroup of specific order only, or at least 
> limit the subgroup order? I used SONATA to obtain the subgroups by the 
> way. Thanks in advanced.
> 
> Sincerely
> 
> Kher Sham Lim
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From johannes.hahn at uni-jena.de  Fri Feb  1 14:38:08 2013
From: johannes.hahn at uni-jena.de (Johannes Hahn)
Date: Fri, 01 Feb 2013 15:38:08 +0100
Subject: [GAP Forum] Modules over general and not so general algebras
Message-ID: <510BD350.3070301@uni-jena.de>

Hi everyone.

Is there an elegant way to implement (finite-dimensional) modules over 
my favorite algebra? My algebra is finite dimensional and I would GAP 
tell this if it needs to know, but I don't want to spell out an explicit 
basis and structure constants for the algebra. (More to the point: I 
work with Hecke algebras and they get way to big for this, if the 
Coxeter group is big, say E_7, E_8)

I do not actually need the algebra, I just want to do some computations 
with the matrices of the representation. There seems no way to define an 
algebra by generators and relations because GAP seemingly wants to do 
some calculations and of course this goes wrong in the general case and 
even in my special case GAP doesn't know that there are normalforms for 
the elements of my algebra etc. (And I cannot find a way to tell GAP this)

The next best thing would be to just forget the relations for a moment 
and think of the modules as algebra morphisms from the free algebra on 
the (small) set of generators into a full matrix algebra. If you have 
that, one could implement a filter that checks the defining relations of 
my favorite algebra for such morphisms manually.
GAP knows free algebras and it knows matrix algebras and it has an 
operation for defining algebra morphisms by their images, but 
interestingly, even this does not work.

If I just try to get the morphism Q<x,y> \to Q, x \mapsto 1, y\mapsto 1 
doing this:
 > F:=FreeAssociativeAlgebraWithOne(Rationals,2);
<algebra-with-one over Rationals, with 2 generators>
 > f := AlgebraHomomorphismByImages(F,FullMatrixAlgebra(Rationals,1), 
GeneratorsOfAlgebraWithOne(F),[ [[1]], [[1]] ]);
then GAP enters an infinite loop for some reason.
This behaviour is completely mysterious to me. Why on earth would GAP 
even consider to do *any* computation in that situation? There is 
exactly nothing else to know about a general algebra morphism on a free 
algebra other than the data that already has been given. The only thing 
to do here is to take the input data, wrap it into an object, set some 
filters to true and return that object.
Why does GAP try to compute anything here instead of just giving me my 
morphism so I can start working with it?

Should there be a compelling reason for GAP to behave this way (although 
I really can't think of any...), then my question immediatly changes 
into: What is an elegant way to implement matrix representation of Hecke 
algebras without having to tell GAP an explicit basis and structure 
constants for the algebra?

Right now I'm just working with plain records to store information about 
the representation but this seems very inelegant to me. There are no 
"real" objects, no types, no possibility for method-selection based on 
additional information... (and I can't figure out how to implement 
Hecke-Matrix-Representation objects for myself... I'm not sure yet if 
GAP really behaves differently than the manual claims or if I'm just to 
stupid to read the manual correctly.)

Best wishes
Johannes Hahn.


From jmichel at math.jussieu.fr  Fri Feb  1 14:53:36 2013
From: jmichel at math.jussieu.fr (Jean MICHEL)
Date: Fri, 1 Feb 2013 15:53:36 +0100
Subject: [GAP Forum] Modules over general and not so general algebras
In-Reply-To: <510BD350.3070301@uni-jena.de>
References: <510BD350.3070301@uni-jena.de>
Message-ID: <20130201145335.GA6430@math.jussieu.fr>

On Fri, Feb 01, 2013 at 03:38:08PM +0100, Johannes Hahn wrote:
> Is there an elegant way to implement (finite-dimensional) modules over my 
> favorite algebra? My algebra is finite dimensional and I would GAP tell 
> this if it needs to know, but I don't want to spell out an explicit basis 
> and structure constants for the algebra. (More to the point: I work with 
> Hecke algebras and they get way to big for this, if the Coxeter group is 
> big, say E_7, E_8)
>
> I do not actually need the algebra, I just want to do some computations 
> with the matrices of the representation. There seems no way to define an 
> algebra by generators and relations because GAP seemingly wants to do some 
> calculations and of course this goes wrong in the general case and even in 
> my special case GAP doesn't know that there are normalforms for the 
> elements of my algebra etc. (And I cannot find a way to tell GAP this)

Matrices  for  all  irreducible  representations  of  the Hecke algebras of
finite  Coxeter group are implemented in  the GAP3 package CHEVIE. There is
also an implementation of various bases of these algebras.

See www.math.jussieu.fr/~jmichel/chevie
------------------------------------------------------------------------------
Jean MICHEL, Groupes et representations, IMJ-PRG UMR7586 tel.(33)157279144
Bureau 639 Bat. Sophie Germain Case 7012 - 75205 PARIS Cedex 13


From khersham.lim at mpi-hd.mpg.de  Fri Feb  1 15:44:27 2013
From: khersham.lim at mpi-hd.mpg.de (Kher Sham Lim)
Date: Fri, 01 Feb 2013 16:44:27 +0100
Subject: [GAP Forum] Finding certain subgroups from very large group
In-Reply-To: <BD2E85EE-9AD7-4F7D-8834-2734948777A4@st-andrews.ac.uk>
References: <510BA69C.5070800@mpi-hd.mpg.de>
	<093121d5cf284410ac80fcfb90968b62@UOS-DUN-CAS5.st-andrews.ac.uk>
	<BD2E85EE-9AD7-4F7D-8834-2734948777A4@st-andrews.ac.uk>
Message-ID: <510BE2DB.7000606@mpi-hd.mpg.de>

Dear Stephen,

Thanks, the command IsomorphicSubgroups(G,H) does exactly what I need.

Best regards,

Kher Sham


On 02/01/2013 01:09 PM, Stephen Linton wrote:
> Dear Kher Sham Lim,
>
> I assume you actually want to know if G has a subgroup isomorphic to H.
> If so, the command you want is IsomorphicSubgroups(G,H).
>
> This is enormously more efficient than simply listing all [conjugacy classes of] subgroups of G in most cases.
>
> It might also be helpful to first replace G by an isomorphic permutation group (using IsomorphismPermGroup).
>
> All of these commands are documented in the reference manual (equivalently in the on-line help).
>
> 	Steve
>
> On 1 Feb 2013, at 11:33, Kher Sham Lim <khersham.lim at mpi-hd.mpg.de> wrote:
>
>> Dear GAP forum
>>
>> I have a very large group to study, say G (it is an automorphism group
>> of a small group). G has order of 10 million and I am interested in
>> knowing whether a certain known group, say H is a subgroup in G. To find
>> H is impossible in GAP, as GAP tries to calculate all the subgroups and
>> this process exceeds my computer's memory. Is there another command or
>> algorithm in GAP to compute subgroup of specific order only, or at least
>> limit the subgroup order? I used SONATA to obtain the subgroups by the
>> way. Thanks in advanced.
>>
>> Sincerely
>>
>> Kher Sham Lim
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum


From denisetorrao at hotmail.com  Mon Feb  4 11:38:28 2013
From: denisetorrao at hotmail.com (=?iso-8859-1?B?RGVuaXNlIFRvcnLjbw==?=)
Date: Mon, 4 Feb 2013 11:38:28 +0000
Subject: [GAP Forum] list of list
Message-ID: <SNT145-W61472F6783B58AC63A1A1FCA010@phx.gbl>


Hello, my name is Denise and I'm starting to work in GAP. I'm trying to compute a simple program, but I'm with some dificulty, because I implement a cycle for, and my values of the list change. The program is the following:
algoritmo14:=function(p,D,c)
local soma, soma2, aux, aux3,i,A,x;
A:=[];A[1]:=[];x:=[];
for j in [1..p-1] do	A[1][j]:=0;od;A[1][p]:=c;

for i in [1..p-1] do	x[i]:=0;od;x[p]:=c;
i:=p-1;
soma:=0;
while (i>0) do	for aux in [i+1..p] do		soma:=soma+D[aux]*x[aux];	od;	if (soma >= D[i]) then		x[i]:=x[i]+1;				x[p]:=soma-D[i];
		for aux3 in [i+1..p-1] do			x[aux3]:=0;		od;Print("A1-> ",A,"\n");
		Add(A,x);Print("A2-> ",A,"\n");		i:=p-1;	else		i:=i-1;	fi;	soma:=0;od;

return A;end;	
My problem is with the list A, that changes, and in the final all it's elements (except for the first one) are equal. Can someone help me? I guess is something very trivial, but as I said before, I'm taking my first steps with GAP, so I still have a lot of dificulties with this program.
Very very thanks,
Denise Torr?o 		 	   		  

From sl4 at st-andrews.ac.uk  Mon Feb  4 12:10:34 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Mon, 4 Feb 2013 12:10:34 +0000
Subject: [GAP Forum] list of list
In-Reply-To: <839dafcc26e04851a0e6f48ebcaedf3e@UOS-DUN-CAS3.st-andrews.ac.uk>
References: <839dafcc26e04851a0e6f48ebcaedf3e@UOS-DUN-CAS3.st-andrews.ac.uk>
Message-ID: <FE1252CE-D5D3-4671-AFAB-AE9E3C54F85A@st-andrews.ac.uk>

Dear GAP Forum,


On 4 Feb 2013, at 11:38, Denise Torr?o <denisetorrao at hotmail.com> wrote:

> 
> Hello, my name is Denise and I'm starting to work in GAP. I'm trying to compute a simple program, but I'm with some dificulty, because I implement a cycle for, and my values of the list change. The program is the following:
> algoritmo14:=function(p,D,c)
> local soma, soma2, aux, aux3,i,A,x;
> A:=[];A[1]:=[];x:=[];
> for j in [1..p-1] do	A[1][j]:=0;od;A[1][p]:=c;
> 
> for i in [1..p-1] do	x[i]:=0;od;x[p]:=c;
> i:=p-1;
> soma:=0;
> while (i>0) do	for aux in [i+1..p] do		soma:=soma+D[aux]*x[aux];	od;	if (soma >= D[i]) then		x[i]:=x[i]+1;				x[p]:=soma-D[i];
> 		for aux3 in [i+1..p-1] do			x[aux3]:=0;		od;Print("A1-> ",A,"\n");
> 		Add(A,x);Print("A2-> ",A,"\n");		i:=p-1;	else		i:=i-1;	fi;	soma:=0;od;
> 
> return A;end;	
> My problem is with the list A, that changes, and in the final all it's elements (except for the first one) are equal. Can someone help me? I guess is something very trivial, but as I said before, I'm taking my first steps with GAP, so I still have a lot of dificulties with this program.
> Very very thanks,
> Denise Torr?o 		 	   		  

I think the problem is the statement "Add(A,x)". This DOES NOT make a copy of x.

A simple example is 

gap> l := [1];
[ 1 ]
gap> m := [];
[  ]
gap> Add(m,l);
gap> l[1] := 2;
2
gap> m;
[ [ 2 ] ]
gap> 

Here m[1] and l are THE SAME list and changes to that list can be seen through both routes. What you probably want is 

Add(A, ShallowCopy(x));

which does make a copy.

	Steve




From hatlam at gmail.com  Wed Feb  6 06:52:25 2013
From: hatlam at gmail.com (Ha T. Lam)
Date: Wed, 6 Feb 2013 01:52:25 -0500
Subject: [GAP Forum] Coefficients of basis elements for Galois field
Message-ID: <CAFxJ0MzES8Q_SkgnFTxgLH2hVeRRSjMbqVDkO5hXiLR7CyTufg@mail.gmail.com>

Dear GAP forum,

I built a Galois field over F2 with irreducible polynomial f

x:=Indeterminate(GF(2), "x");
> x
f:=x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0;
> x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0
gf:=GF(2,f);
> Field( [ a ] )
BasisVectors(Basis(gf));
> [ !Z(2)^0, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12,
a^13, a^14, a^15, a^16, a^17, a^18, a^19, a^20, a^21 ]

I'm trying to get the basis elements as polynomials, in particular, I want
their coefficients, but I'm not sure how to do this. My guess is that since
they are all powers of the primitive root, if I know the coefficients
representing the primitive root, I will be able to compute their
coefficients. The next thing I tried was to extract the primitive root:

PrimitiveRoot(gf);

but I get the message "Error, no method found!"

I'm not sure what to try next, do you have any advise?

Best regards,

Ha T. Lam

From hulpke at me.com  Wed Feb  6 14:42:54 2013
From: hulpke at me.com (Alexander Hulpke)
Date: Wed, 06 Feb 2013 07:42:54 -0700
Subject: [GAP Forum] Coefficients of basis elements for Galois field
In-Reply-To: <CAFxJ0MzES8Q_SkgnFTxgLH2hVeRRSjMbqVDkO5hXiLR7CyTufg@mail.gmail.com>
References: <CAFxJ0MzES8Q_SkgnFTxgLH2hVeRRSjMbqVDkO5hXiLR7CyTufg@mail.gmail.com>
Message-ID: <F76BE002-F8D6-4FC0-A045-7EA4BCE29EA6@me.com>

Dear Forum,

On Feb 5, 2013, at 11:52 PM, Ha T. Lam <hatlam at gmail.com> wrote:

> I built a Galois field over F2 with irreducible polynomial f
> 
> x:=Indeterminate(GF(2), "x");
>> x
> f:=x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0;
>> x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0
> gf:=GF(2,f);
>> Field( [ a ] )
> BasisVectors(Basis(gf));
>> [ !Z(2)^0, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12,
> a^13, a^14, a^15, a^16, a^17, a^18, a^19, a^20, a^21 ]
> 
> I'm trying to get the basis elements as polynomials, in particular, I want
> their coefficients, but I'm not sure how to do this. My guess is that since
> they are all powers of the primitive root, if I know the coefficients
> representing the primitive root, I will be able to compute their
> coefficients. The next thing I tried was to extract the primitive root:

This function is called PrimitiveElement in GAP:

gap> a:=PrimitiveElement(gf);
a

To see how elements of gf are represented as polynomials, you need to look at an elements internal representation:

gap> IsAlgBFRep(a^0); 
true
gap> IsAlgBFRep(a^1);
false

If it is in IsAlgBFRep (base field), then elm![1] (note the exclamation mark)returns the element of the base field:

gap> z:=a^0;
!Z(2)^0
gap> z![1];
Z(2)^0


If it is in IsAlgExtRep, z![1] returns the coefficient vector of the polynomial representing the element.
gap> z:=a^5+a+Z(2);
a^5+a+Z(2)^0
gap> IsAlgExtRep(z);  
true
gap> z![1];
<a GF2 vector of length 22>
gap> Print(z![1]);
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 
0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 
0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ]

I believe this is the data you were looking for.

Best wishes,

    Alexander Hulpke




From s.witzel at gmx.net  Thu Feb  7 15:34:07 2013
From: s.witzel at gmx.net (Stefan Witzel)
Date: Thu, 07 Feb 2013 16:34:07 +0100
Subject: [GAP Forum] ConjugacyClasses
Message-ID: <20130207153407.310280@gmx.net>

Hi gap forum,

can anyone explain the following behavior to me (saying that PSL(3,2) has to distinct conjugacy classes that are conjugate)?

vec1:=[1,0,0]*Z(2)^0;;
sl:=SL(3,2);;
orb:=Orbit(sl,vec1,OnLines);;
act:=ActionHomomorphism(sl,orb,OnLines);;
psl:=Image(act);;
ConjugacyClasses(psl); 

[ ()^G, (3,4)(6,7)^G, (2,3,5,4)(6,7)^G, (2,3,6)(4,7,5)^G, (1,2,3,4,7,5,6)^G, (1,2,3,5,6,7,4)^G ]

g:=Representative(ConjugacyClasses(psl)[5]);;
h:=Representative(ConjugacyClasses(psl)[6]);;
c:=(2,6,4)(3,5,7);;
c*g^(-1)*c^(-1)=h;

true

IsSubgroup(psl,Group(c));

true

I guess one could as well use PSL(3,2) out of the box but that gives a different permutation presentation and I didn't want to work out c anew. I also know that PSL(3,2)=SL(3,2)=GL(3,2) etc., but that's not the point of the question. (I do not know what would be the right way to say "IsElement(psl,c)" in the end, so I would be interested in that.)
Thanks for the help!

Best regards,
Stefan

P.S.: In case you are wondering, I'm using GAP version 4.4.12.


From stefan at mcs.st-and.ac.uk  Thu Feb  7 15:47:46 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Thu, 7 Feb 2013 15:47:46 -0000 (UTC)
Subject: [GAP Forum] ConjugacyClasses
In-Reply-To: <20130207153407.310280@gmx.net>
References: <20130207153407.310280@gmx.net>
Message-ID: <submission.1U3ThS-0006za-I3@mail-gap.mcs.st-and.ac.uk>

On Thu, February 7, 2013 3:34 pm, Stefan Witzel wrote:
> can anyone explain the following behavior to me (saying that PSL(3,2) has to distinct
> conjugacy classes that are conjugate)?
>
> vec1:=[1,0,0]*Z(2)^0;;
> sl:=SL(3,2);;
> orb:=Orbit(sl,vec1,OnLines);;
> act:=ActionHomomorphism(sl,orb,OnLines);;
> psl:=Image(act);;
> ConjugacyClasses(psl);
>
> [ ()^G, (3,4)(6,7)^G, (2,3,5,4)(6,7)^G, (2,3,6)(4,7,5)^G, (1,2,3,4,7,5,6)^G,
> (1,2,3,5,6,7,4)^G ]
>
> g:=Representative(ConjugacyClasses(psl)[5]);;
> h:=Representative(ConjugacyClasses(psl)[6]);;
> c:=(2,6,4)(3,5,7);;
> c*g^(-1)*c^(-1)=h;
>
> true
>
> IsSubgroup(psl,Group(c));
>
> true

The point is that the 6th conjugacy class in the list consists of the
inverses of the elements of the 5th conjugacy class (in particular the
elements in these classes are not conjugate to their inverses):

gap> ccl := ConjugacyClasses(psl);
[ ()^G, (3,4)(6,7)^G, (2,3,5,4)(6,7)^G, (2,3,6)(4,7,5)^G, (1,2,3,4,7,5,6)^G,
  (1,2,3,5,6,7,4)^G ]
gap> Set(AsList(ccl[6])) = Set(List(AsList(ccl[5]),g->g^-1));
true
gap> IsConjugate(psl,Representative(ccl[5]),Representative(ccl[6]));
false
gap> IsConjugate(psl,Representative(ccl[5]),Representative(ccl[6])^-1);
true

Hope this helps,

    Stefan Kohl




From member at linkedin.com  Fri Feb  8 04:07:56 2013
From: member at linkedin.com (Mohammad sarwar via LinkedIn)
Date: Fri, 8 Feb 2013 04:07:56 +0000 (UTC)
Subject: [GAP Forum] Join my network on LinkedIn
Message-ID: <632497681.15328845.1360296476634.JavaMail.app@ela4-app2322.prod>

LinkedIn
------------




    Mohammad sarwar requested to add you as a connection on LinkedIn:
  

------------------------------------------

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I'd like to add you to my professional network on LinkedIn.

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Accept invitation from Mohammad sarwar
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From gordon.royle at uwa.edu.au  Fri Feb  8 09:10:44 2013
From: gordon.royle at uwa.edu.au (Gordon Royle)
Date: Fri, 8 Feb 2013 17:10:44 +0800
Subject: [GAP Forum] Strange output
Message-ID: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>

I have a simple program that uses SmallestImageSet to find the lex least representative of orbits of a graph on k-sets.

The output has suddenly started to look odd, in that in among all the "regular" sets, there are sets that print out with a strange syntax


[ 1, 5, 51 ]
[ 1, 6 .. 11 ]
[ 1, 6, 12 ]

The set [ 1, 6 .. 11 ] is equal to [1, 6, 11] but why does it print this way?

Thanks

Gordon

Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>














From stefan at mcs.st-and.ac.uk  Fri Feb  8 10:10:25 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Fri, 8 Feb 2013 10:10:25 -0000 (UTC)
Subject: [GAP Forum] Strange output
In-Reply-To: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
Message-ID: <submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>

On Fri, February 8, 2013 9:10 am, Gordon Royle wrote:
> I have a simple program that uses SmallestImageSet to find the lex least representative
> of orbits of a graph on k-sets.
>
> The output has suddenly started to look odd, in that in among all the "regular" sets,
> there are sets that print out with a strange syntax
>
>
> [ 1, 5, 51 ]
> [ 1, 6 .. 11 ]
> [ 1, 6, 12 ]
>
> The set [ 1, 6 .. 11 ] is equal to [1, 6, 11] but why does it print this way?

The second list prints in this way because it is in `IsRangeRep' (as opposed
to `IsPlistRep'), and neither short ranges are automatically converted to
`IsPlistRep' nor the output routine deals with that special case. We have:

gap> l1 := [ 1, 6 .. 11 ];
[ 1, 6 .. 11 ]
gap> l2 := [ 1, 6, 11 ];
[ 1, 6, 11 ]
gap> l1=l2;
true
gap> IsPlistRep(l1);
false
gap> IsPlistRep(l2);
true
gap> IsRangeRep(l1);
true
gap> IsRangeRep(l2);
false
gap> TNUM_OBJ(l1);
[ 64, "list (range,ssort)" ]
gap> TNUM_OBJ(l2);
[ 54, "list (plain,cyc)" ]
gap> MemoryUsage(l1); # saves already a tiny bit of memory
28
gap> MemoryUsage(l2);
32
gap> l3 := [1,6..1000001];
[ 1, 6 .. 1000001 ]
gap> MemoryUsage(l3); # for longer ranges, more memory is saved
28
gap> MemoryUsage(AsSet(l3));
800024

If there is a real need, I guess at least the output routine could be
adjusted as to print [ 1, 6, 11 ] rather than [ 1, 6 .. 11 ].

Best regards,

    Stefan





From alexk at mcs.st-andrews.ac.uk  Fri Feb  8 12:20:09 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 8 Feb 2013 12:20:09 +0000
Subject: [GAP Forum] GAP 4.6.2 release announcement
Message-ID: <E728F1E7-826A-4803-A27B-A6655FA87FCB@mcs.st-andrews.ac.uk>

Dear GAP Forum,

We have just released the next major release, GAP 4.6.2, which is 
available now for download from the GAP website

	http://www.gap-system.org

and is also available via alternative GAP distributions listed at

	http://www.gap-system.org/Download/#alternatives
	
You may access the overview of changes in GAP 4.6.2 by entering 
'?Changes between GAP 4.5 and GAP 4.6' in GAP 4.6.2, or view it 
online at

http://www.gap-system.org/Manuals/doc/changes/chap2.html#X8175857F79C8AD8E

In addition to improved and extended functionality and fixed bugs, 
GAP 4.6.2 contains 106 GAP packages, whereas at the time of the 
first public release of GAP 4.5 there were 99 packages redistributed 
with GAP.

We encourage all users to upgrade to GAP 4.6.2. If you need any help 
or would like to report any problems, please do not hesitate to 
contact us at support at gap-system.org.

Please note that we are regularly updating the GAP distribution to 
include new versions of GAP packages, but we may not announce each 
of them to the Forum. We intend to use the Forum to announce updates 
of the core GAP system and only of some packages which may fix 
serious issues or have major influence on GAP. 

Wishing you fun and success using GAP,
The GAP Group


From alexk at mcs.st-andrews.ac.uk  Fri Feb  8 12:25:01 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 8 Feb 2013 12:25:01 +0000
Subject: [GAP Forum] multiplication of Lie objects in GAP
In-Reply-To: <3f7f65.43c6f.13bf66d2a12.Coremail.lijr@lzu.edu.cn>
References: <3f7f65.43c6f.13bf66d2a12.Coremail.lijr@lzu.edu.cn>
Message-ID: <22AB3E68-EEA4-4E89-8349-8EA7FD9F53EF@mcs.st-andrews.ac.uk>

Dear Jianrong,

GAP 4.6.2 which was just announced in the GAP Forum, has a new attribute
'UnderlyingRingElement'. If x and y are Lie objects, then the 'usual'
multiplication may be computed with 

UnderlyingRingElement(x)*UnderlyingRingElement(y) 

(note that the result will NOT be a Lie object).

Hope this helps,
Alexander


On 1 Jan 2013, at 14:04, ??? wrote:

> Dear Forum,
> 
> I have a Lie algebra A whose basis is given by matrices explicitly. When I create the algebra A, the matrices in the basis of A are denoted by LieObject... Let x, y in the basis of A. It seems that x*y is the same as [x, y]. How could I compute the usual multiplication of x and y? Thank you very much.
> 
> With best wishes,
> Jianrong.



From gordon.royle at uwa.edu.au  Sun Feb 10 02:52:02 2013
From: gordon.royle at uwa.edu.au (Gordon Royle)
Date: Sun, 10 Feb 2013 10:52:02 +0800
Subject: [GAP Forum] Strange output
In-Reply-To: <submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
Message-ID: <7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>

Well, thanks for the feedback, but I remain somewhat confused?

Firstly,  why does GAP unilaterally choose to change the format .. .the program is simply a recursive program with a single Print statement, and yet the output changes format , and then changes back again, without me asking it to...

[ 1, 5, 51 ]
[ 1, 6 .. 11 ]
[ 1, 6, 12 ]




Secondly, why is

6 .. 11

the "range representation" for

6, 11

In most languages that support it, the ".." means "everything from the first to the last (or perhaps the first to the last-minus-one)"


Actually, it means the same in GAP too:

gap> for x in [6 .. 11] do
> Print(x," ");
> od;
6 7 8 9 10 11

So, naively I would expect

[1, 6 .. 11]

to be a fancy way of saying

[1, 6, 7, 8, 9, 10, 11]


But it's not:

gap> for x in [1, 6 .. 11] do
> Print(x," ");
> od;
1 6 11


It seems dangerous to me to have the expression   a .. b mean something different to (a) other uses in the same language, (b) mathematical usage and (c ) other programming languages.


Thirdly, why has this happened RIGHT NOW, when I've been using this program for years without ever seeing anything like this before?


Thanks again

Gordon



Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>














From dima at ntu.edu.sg  Sun Feb 10 04:58:39 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Sun, 10 Feb 2013 12:58:39 +0800
Subject: [GAP Forum] Strange output
In-Reply-To: <7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
	<7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
Message-ID: <CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>

On 10 February 2013 10:52, Gordon Royle <gordon.royle at uwa.edu.au> wrote:
> Well, thanks for the feedback, but I remain somewhat confused?

I think this is definitely a bug, and must be fixed ASAP...

Best,
Dima

>
> Firstly,  why does GAP unilaterally choose to change the format .. .the program is simply a recursive program with a single Print statement, and yet the output changes format , and then changes back again, without me asking it to...
>
> [ 1, 5, 51 ]
> [ 1, 6 .. 11 ]
> [ 1, 6, 12 ]
>
>
>
>
> Secondly, why is
>
> 6 .. 11
>
> the "range representation" for
>
> 6, 11
>
> In most languages that support it, the ".." means "everything from the first to the last (or perhaps the first to the last-minus-one)"
>
>
> Actually, it means the same in GAP too:
>
> gap> for x in [6 .. 11] do
>> Print(x," ");
>> od;
> 6 7 8 9 10 11
>
> So, naively I would expect
>
> [1, 6 .. 11]
>
> to be a fancy way of saying
>
> [1, 6, 7, 8, 9, 10, 11]
>
>
> But it's not:
>
> gap> for x in [1, 6 .. 11] do
>> Print(x," ");
>> od;
> 1 6 11
>
>
> It seems dangerous to me to have the expression   a .. b mean something different to (a) other uses in the same language, (b) mathematical usage and (c ) other programming languages.
>
>
> Thirdly, why has this happened RIGHT NOW, when I've been using this program for years without ever seeing anything like this before?
>
>
> Thanks again
>
> Gordon
>
>
>
> Professor Gordon Royle
> School of Mathematics and Statistics
> University of Western Australia
> Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>
>
>
>
>
>
>
>
>
>
>
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From laurent.bartholdi at gmail.com  Sun Feb 10 06:25:37 2013
From: laurent.bartholdi at gmail.com (Laurent Bartholdi)
Date: Sun, 10 Feb 2013 07:25:37 +0100
Subject: [GAP Forum] [Devel]  Strange output
In-Reply-To: <CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
	<7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
	<CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>
Message-ID: <CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com>

The [a, b .. c] in GAP means { a, b, 2b-a, ..., a+i(b-a), ..., c } in
mathematics.

GAP is not exactly a programming language; there are *objects* and their
*representations*, and GAP is allowed to change a representation to another
one in case it's provably more efficient (i.e. there are more or faster
algorithms for it).

Hope this helps,
Laurent


On Sun, Feb 10, 2013 at 5:58 AM, Dmitrii (Dima) Pasechnik
<dima at ntu.edu.sg>wrote:

> On 10 February 2013 10:52, Gordon Royle <gordon.royle at uwa.edu.au> wrote:
> > Well, thanks for the feedback, but I remain somewhat confused?
>
> I think this is definitely a bug, and must be fixed ASAP...
>
> Best,
> Dima
>
> >
> > Firstly,  why does GAP unilaterally choose to change the format .. .the
> program is simply a recursive program with a single Print statement, and
> yet the output changes format , and then changes back again, without me
> asking it to...
> >
> > [ 1, 5, 51 ]
> > [ 1, 6 .. 11 ]
> > [ 1, 6, 12 ]
> >
> >
> >
> >
> > Secondly, why is
> >
> > 6 .. 11
> >
> > the "range representation" for
> >
> > 6, 11
> >
> > In most languages that support it, the ".." means "everything from the
> first to the last (or perhaps the first to the last-minus-one)"
> >
> >
> > Actually, it means the same in GAP too:
> >
> > gap> for x in [6 .. 11] do
> >> Print(x," ");
> >> od;
> > 6 7 8 9 10 11
> >
> > So, naively I would expect
> >
> > [1, 6 .. 11]
> >
> > to be a fancy way of saying
> >
> > [1, 6, 7, 8, 9, 10, 11]
> >
> >
> > But it's not:
> >
> > gap> for x in [1, 6 .. 11] do
> >> Print(x," ");
> >> od;
> > 1 6 11
> >
> >
> > It seems dangerous to me to have the expression   a .. b mean something
> different to (a) other uses in the same language, (b) mathematical usage
> and (c ) other programming languages.
> >
> >
> > Thirdly, why has this happened RIGHT NOW, when I've been using this
> program for years without ever seeing anything like this before?
> >
> >
> > Thanks again
> >
> > Gordon
> >
> >
> >
> > Professor Gordon Royle
> > School of Mathematics and Statistics
> > University of Western Australia
> > Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
> CONFIDENTIALITY:This email is intended solely for the person(s) named and
> may be confidential and/or privileged.If you are not the intended
> recipient,please delete it,notify us and do not copy,use,or disclose its
> content.
>
> Towards A Sustainable Earth:Print Only When Necessary.Thank you.
>
> _______________________________________________
> Devel mailing list
> Devel at gap-system.org
> http://mail.gap-system.org/mailman/listinfo/devel
>



-- 
Prof. Dr. Laurent Bartholdi   \ laurent.bartholdi<at>gmail<dot>com
G.-A. Universit?t zu G?ttingen \ Phone: +49 551 39 7826
Bunsenstra?e 3-5                \ Secr: +49 551 39 7752
D-37073 G?ttingen, Germany       \ Fax: +49 551 39 22674

From sl4 at st-andrews.ac.uk  Sun Feb 10 08:30:51 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Sun, 10 Feb 2013 08:30:51 +0000
Subject: [GAP Forum] Strange output
In-Reply-To: <a35d8dcd45c54210a1fdef0af3a97a51@UOS-DUN-CAS1.st-andrews.ac.uk>
References: <a35d8dcd45c54210a1fdef0af3a97a51@UOS-DUN-CAS1.st-andrews.ac.uk>
Message-ID: <F39EA6E9-CF4C-447A-8CE0-950124CA6DB6@st-andrews.ac.uk>

Hi Gordon,

Could you let me have your programme so I can look into this?

In terms of correctness, though, this is not a bug. The range [1,6..11] which has length 3 offset 1 and step 5 is equal to the plain list [1,6,11].  GAP range notation only makes sense with the brackets and the three entry notation [a,b..c] implies a step of b-a. b..c does not mean anything outside brackets.

As Laurent says, GAP in general, is allowed to, and benefits by being able to, choose what representation to return a result in, so long as the result is correct according to the documentation.

If there isn't a good performance reason, though, then this is needless complication, so I'll look into it. 

	Steve

On 8 Feb 2013, at 09:10, Gordon Royle <Gordon.Royle at uwa.edu.au> wrote:

> I have a simple program that uses SmallestImageSet to find the lex least representative of orbits of a graph on k-sets.
> 
> The output has suddenly started to look odd, in that in among all the "regular" sets, there are sets that print out with a strange syntax
> 
> 
> [ 1, 5, 51 ]
> [ 1, 6 .. 11 ]
> [ 1, 6, 12 ]
> 
> The set [ 1, 6 .. 11 ] is equal to [1, 6, 11] but why does it print this way?
> 
> Thanks
> 
> Gordon
> 
> Professor Gordon Royle
> School of Mathematics and Statistics
> University of Western Australia
> Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From dima at ntu.edu.sg  Sun Feb 10 11:25:14 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Sun, 10 Feb 2013 19:25:14 +0800
Subject: [GAP Forum] [Devel]  Strange output
In-Reply-To: <CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
	<7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
	<CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>
	<CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com>
Message-ID: <CAAWYfq3ULYhDMRn1pqX4-Ov97dCEf99hXQ9ZMAakR5LZ45HGaA@mail.gmail.com>

On 10 February 2013 14:25, Laurent Bartholdi
<laurent.bartholdi at gmail.com> wrote:
> The [a, b .. c] in GAP means { a, b, 2b-a, ..., a+i(b-a), ..., c } in
> mathematics.

I've been using GAP for 20 years, and I never saw or heard about this
one. Sorry.
IMHO it is confusing, counter-intuitive, goes against well-established practices
in other programming languages and CAS's, etc...

I can probably list a dozen programming languages / CAS's, where such
lists (or/and loops) are constructed by the triple of parameters
("beginning","end","step"), in this order.


May I humbly propose syntax [a .. c, b-a] instead?

Best,
Dmitrii


>
> GAP is not exactly a programming language; there are *objects* and their
> *representations*, and GAP is allowed to change a representation to another
> one in case it's provably more efficient (i.e. there are more or faster
> algorithms for it).
>
> Hope this helps,
> Laurent
>
>
> On Sun, Feb 10, 2013 at 5:58 AM, Dmitrii (Dima) Pasechnik <dima at ntu.edu.sg>
> wrote:
>>
>> On 10 February 2013 10:52, Gordon Royle <gordon.royle at uwa.edu.au> wrote:
>> > Well, thanks for the feedback, but I remain somewhat confused?
>>
>> I think this is definitely a bug, and must be fixed ASAP...
>>
>> Best,
>> Dima
>>
>> >
>> > Firstly,  why does GAP unilaterally choose to change the format .. .the
>> > program is simply a recursive program with a single Print statement, and yet
>> > the output changes format , and then changes back again, without me asking
>> > it to...
>> >
>> > [ 1, 5, 51 ]
>> > [ 1, 6 .. 11 ]
>> > [ 1, 6, 12 ]
>> >
>> >
>> >
>> >
>> > Secondly, why is
>> >
>> > 6 .. 11
>> >
>> > the "range representation" for
>> >
>> > 6, 11
>> >
>> > In most languages that support it, the ".." means "everything from the
>> > first to the last (or perhaps the first to the last-minus-one)"
>> >
>> >
>> > Actually, it means the same in GAP too:
>> >
>> > gap> for x in [6 .. 11] do
>> >> Print(x," ");
>> >> od;
>> > 6 7 8 9 10 11
>> >
>> > So, naively I would expect
>> >
>> > [1, 6 .. 11]
>> >
>> > to be a fancy way of saying
>> >
>> > [1, 6, 7, 8, 9, 10, 11]
>> >
>> >
>> > But it's not:
>> >
>> > gap> for x in [1, 6 .. 11] do
>> >> Print(x," ");
>> >> od;
>> > 1 6 11
>> >
>> >
>> > It seems dangerous to me to have the expression   a .. b mean something
>> > different to (a) other uses in the same language, (b) mathematical usage and
>> > (c ) other programming languages.
>> >
>> >
>> > Thirdly, why has this happened RIGHT NOW, when I've been using this
>> > program for years without ever seeing anything like this before?
>> >
>> >
>> > Thanks again
>> >
>> > Gordon
>> >
>> >
>> >
>> > Professor Gordon Royle
>> > School of Mathematics and Statistics
>> > University of Western Australia
>> > Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> > _______________________________________________
>> > Forum mailing list
>> > Forum at mail.gap-system.org
>> > http://mail.gap-system.org/mailman/listinfo/forum
>>
>> CONFIDENTIALITY:This email is intended solely for the person(s) named and
>> may be confidential and/or privileged.If you are not the intended
>> recipient,please delete it,notify us and do not copy,use,or disclose its
>> content.
>>
>> Towards A Sustainable Earth:Print Only When Necessary.Thank you.
>>
>> _______________________________________________
>> Devel mailing list
>> Devel at gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/devel
>
>
>
>
> --
> Prof. Dr. Laurent Bartholdi   \ laurent.bartholdi<at>gmail<dot>com
> G.-A. Universit?t zu G?ttingen \ Phone: +49 551 39 7826
> Bunsenstra?e 3-5                \ Secr: +49 551 39 7752
> D-37073 G?ttingen, Germany       \ Fax: +49 551 39 22674


From Bill.Allombert at math.u-bordeaux1.fr  Sun Feb 10 12:11:46 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Sun, 10 Feb 2013 13:11:46 +0100
Subject: [GAP Forum] [Devel]  Strange output
In-Reply-To: <CAAWYfq3ULYhDMRn1pqX4-Ov97dCEf99hXQ9ZMAakR5LZ45HGaA@mail.gmail.com>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
	<7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
	<CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>
	<CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com>
	<CAAWYfq3ULYhDMRn1pqX4-Ov97dCEf99hXQ9ZMAakR5LZ45HGaA@mail.gmail.com>
Message-ID: <20130210121146.GD7044@yellowpig>

On Sun, Feb 10, 2013 at 07:25:14PM +0800, Dmitrii (Dima) Pasechnik wrote:
> On 10 February 2013 14:25, Laurent Bartholdi
> <laurent.bartholdi at gmail.com> wrote:
> > The [a, b .. c] in GAP means { a, b, 2b-a, ..., a+i(b-a), ..., c } in
> > mathematics.
> 
> I've been using GAP for 20 years, and I never saw or heard about this
> one. Sorry.
> IMHO it is confusing, counter-intuitive, goes against well-established practices
> in other programming languages and CAS's, etc...
> 
> I can probably list a dozen programming languages / CAS's, where such
> lists (or/and loops) are constructed by the triple of parameters
> ("beginning","end","step"), in this order.

Haskell works like GAP too: [1,3..11] give [1,3,5,7,9,11]

Cheers,
Bill.


From dima at ntu.edu.sg  Sun Feb 10 12:49:11 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Sun, 10 Feb 2013 20:49:11 +0800
Subject: [GAP Forum] [Devel] Strange output
In-Reply-To: <20130210121146.GD7044@yellowpig>
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au>
	<submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk>
	<7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au>
	<CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com>
	<CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com>
	<CAAWYfq3ULYhDMRn1pqX4-Ov97dCEf99hXQ9ZMAakR5LZ45HGaA@mail.gmail.com>
	<20130210121146.GD7044@yellowpig>
Message-ID: <CAAWYfq1riReUMr4F+FDXjZebzMDVnLfzjD-4AsaoXt_MED7GRw@mail.gmail.com>

On 10 February 2013 20:11, Bill Allombert
<Bill.Allombert at math.u-bordeaux1.fr> wrote:
> On Sun, Feb 10, 2013 at 07:25:14PM +0800, Dmitrii (Dima) Pasechnik wrote:
>> On 10 February 2013 14:25, Laurent Bartholdi
>> <laurent.bartholdi at gmail.com> wrote:
>> > The [a, b .. c] in GAP means { a, b, 2b-a, ..., a+i(b-a), ..., c } in
>> > mathematics.
>>
>> I've been using GAP for 20 years, and I never saw or heard about this
>> one. Sorry.
>> IMHO it is confusing, counter-intuitive, goes against well-established practices
>> in other programming languages and CAS's, etc...
>>
>> I can probably list a dozen programming languages / CAS's, where such
>> lists (or/and loops) are constructed by the triple of parameters
>> ("beginning","end","step"), in this order.
>
> Haskell works like GAP too: [1,3..11] give [1,3,5,7,9,11]

not quite:

gap> [1,3..16];
Error, Range: <last>-<first> (15) must be divisible by <inc> (2)
not in any function at line 1 of *stdin*

(Using a recent Haskell (ghci)):

Prelude> [1,3..16]
[1,3,5,7,9,11,13,15]

(why  <last>-<first>  must be divisible by <inc> in GAP is another
good question).

Anyway, syntactically Haskell is much closer to "usual" mathematical
notation than GAP.
While it would be great if GAP had many more Haskell features, it's
too far from it...

Best,
Dima


>
> Cheers,
> Bill.

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From roberto.radina at tiscali.it  Sun Feb 10 19:48:43 2013
From: roberto.radina at tiscali.it (=?iso-8859-1?Q?Roberto_R=E0dina?=)
Date: Sun, 10 Feb 2013 20:48:43 +0100
Subject: [GAP Forum] [Devel] Strange output
References: <D9F688DE-8CB4-421F-9A06-BA8E025F127A@uwa.edu.au><submission.1U3kuX-0007Bt-CT@mail-gap.mcs.st-and.ac.uk><7A1A9969-4819-4917-B7A4-B00470AC62F6@uwa.edu.au><CAAWYfq3f0YK_wYMZ8vv8D2w04f+Qw7iW5TXYR4v+GQudf399ig@mail.gmail.com><CABBpeGBfMuk9M_Ckh_qZSK3z53xNjKGd0Q=RKTkbitRt1dbU5g@mail.gmail.com><CAAWYfq3ULYhDMRn1pqX4-Ov97dCEf99hXQ9ZMAakR5LZ45HGaA@mail.gmail.com><20130210121146.GD7044@yellowpig>
	<CAAWYfq1riReUMr4F+FDXjZebzMDVnLfzjD-4AsaoXt_MED7GRw@mail.gmail.com>
Message-ID: <E64A6C667D5E45DA8D1A1CAEAEA37F30@carnia>

> gap> [1,3..16];
> Error, Range: <last>-<first> (15) must be divisible by <inc> (2)
> not in any function at line 1 of *stdin*

> (why  <last>-<first>  must be divisible by <inc> in GAP is another
> good question).

because when in a math book I see 1+3+...+n and n=9 I think it means 
1+3+5+7+9, when n=8 I think there is an error somewhere



From jjm at mcs.st-and.ac.uk  Tue Feb 12 12:41:34 2013
From: jjm at mcs.st-and.ac.uk (John McDermott)
Date: Tue, 12 Feb 2013 12:41:34 +0000
Subject: [GAP Forum] Computational Group Theory: LMS-EPSRC Short Course
Message-ID: <E8E7C5B8-019C-4DB1-9CD7-26F84066B857@mcs.st-andrews.ac.uk>


Dear Forum,

this summer from 29 July to 2 August as part of the LMS-EPSRC Short Instructional Course series, the University of St Andrews will host a short course in Computational Group Theory.

The courses in this series aim to provide training for postgraduate students in core areas of mathematics. They are also open to postdocs and those working in industry.

The course is timed to happen in the week before Groups St Andrews 2013, in St Andrews (http://www.groupsstandrews.org/2013/).

Some brief details about the course are appended below but please see the course website at http://www-circa.mcs.st-and.ac.uk/cgt2013 for more information and links to the appropriate part of the LMS website for registration.

John.



29 July - 2 August 2013: LMS-EPSRC Short Course

Computational Group Theory, St. Andrews


The course will consist of the following lecture series:

Permutation Groups (Alexander Hulpke, Colorado State University)

Soluble Groups and p-Groups (Bettina Eick, Technische Universit?t Braunschweig)

Matrix Groups/Constructive Recognition (Derek Holt, University of Warwick)

Finitely Presented Groups (Max Neunh?ffer, University of St Andrews)

These lecture courses will be supplemented by tutorial sessions. 


Organisers: J. McDermott, A. Miguel, M. Neunh?ffer, A. Konovalov

Application Deadline: 17 June 2013




--
John McDermott
Scientific Officer
Centre for Interdisciplinary Research in Computational Algebra
School of Computer Science
University of St Andrews
North Haugh, St Andrews, Fife
KY16 9SX
SCOTLAND

(Room 330, Mathematical Institute)

tel +44 1334 463813
mob +44 7941 507531

The University of St Andrews is committed to sustainable practices and the preservation of the environment.
Please do not print this email unless absolutely necessary.

The University of St Andrews is a charity registered in Scotland : No SC013532



From tendshumba at yahoo.com  Thu Feb 14 09:28:14 2013
From: tendshumba at yahoo.com (tendai shumba)
Date: Thu, 14 Feb 2013 01:28:14 -0800 (PST)
Subject: [GAP Forum] Computational Group Theory: LMS-EPSRC Short Course
In-Reply-To: <E8E7C5B8-019C-4DB1-9CD7-26F84066B857@mcs.st-andrews.ac.uk>
References: <E8E7C5B8-019C-4DB1-9CD7-26F84066B857@mcs.st-andrews.ac.uk>
Message-ID: <1360834094.54989.YahooMailNeo@web162104.mail.bf1.yahoo.com>





________________________________
 From: John McDermott <jjm at mcs.st-and.ac.uk>
To: "Forum at mail.gap-system.org" <forum at gap-system.org> 
Sent: Tuesday, February 12, 2013 2:41 PM
Subject: [GAP Forum] Computational Group Theory: LMS-EPSRC Short Course
 

Dear Forum,

this summer from 29 July to 2 August as part of the LMS-EPSRC Short Instructional Course series, the University of St Andrews will host a short course in Computational Group Theory.

The courses in this series aim to provide training for postgraduate students in core areas of mathematics. They are also open to postdocs and those working in industry.

The course is timed to happen in the week before Groups St Andrews 2013, in St Andrews (http://www.groupsstandrews.org/2013/).

Some brief details about the course are appended below but please see the course website at http://www-circa.mcs.st-and.ac.uk/cgt2013 for more information and links to the appropriate part of the LMS website for registration.

John.



29 July - 2 August 2013: LMS-EPSRC Short Course

Computational Group Theory, St. Andrews


The course will consist of the following lecture series:

Permutation Groups (Alexander Hulpke, Colorado State University)

Soluble Groups and p-Groups (Bettina Eick, Technische Universit?t Braunschweig)

Matrix Groups/Constructive Recognition (Derek Holt, University of Warwick)

Finitely Presented Groups (Max Neunh?ffer, University of St Andrews)

These lecture courses will be supplemented by tutorial sessions. 


Organisers: J. McDermott, A. Miguel, M. Neunh?ffer, A. Konovalov

Application Deadline: 17 June 2013




--
John McDermott
Scientific Officer
Centre for Interdisciplinary Research in Computational Algebra
School of Computer Science
University of St Andrews
North Haugh, St Andrews, Fife
KY16 9SX
SCOTLAND

(Room 330, Mathematical Institute)

tel +44 1334 463813
mob +44 7941 507531

The University of St Andrews is committed to sustainable practices and the preservation of the environment.
Please do not print this email unless absolutely necessary.

The University of St Andrews is a charity registered in Scotland : No SC013532


_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum

From stefanosaivazidis at gmail.com  Thu Feb 14 16:56:55 2013
From: stefanosaivazidis at gmail.com (Stefanos Aivazidis)
Date: Thu, 14 Feb 2013 16:56:55 +0000
Subject: [GAP Forum] Construction of a group
Message-ID: <CAPCTGEOejZe+g1dvGh202ZDSdrFYeKGLk+Ja4V6sGH7ScUr7EQ@mail.gmail.com>

Dear Forum,

I wish to construct a family of groups parametrised by a variable n, to be
specified by the user. Let me describe the steps:

0) Specify a value for n,

1) construct the finite field F=F_q with q=2^(2n+1) elements,

2) construct the automorphism f of F mapping each element x to x^(2^a),
where a=n+1,

3) define an operation * on FxF (as a set) via the rule:
(x,y)*(x',y')=(x+x',y+y'+xf(x')), where the operations on the
right-hand-side are those of the underlying field F,

Now P=(FxF,*) is a group, but I don't know if I can assure GAP this is the
case. Perhaps I can ask her to test this somehow (GAP is a woman in my
world).

4) assuming that GAP now knows P is a group, define the semi-direct product
S=P]C, where C is the multiplicative group of F and acts on P (via
automorphisms) by the rule:c.(x,y)=(cx,cf(c)y), where f is as in 2) and
concatenation on the right-hand-side is just multiplication in F.

To give some motivation for the above construction, P thus constructed is
the Sylow 2-subgroup of Sz(q), while S is its normaliser in Sz(q). Of
course I can access both P and S via P:=SylowSubgroup(Sz(q),2) and
S:=Normaliser(Sz(q),P) respectively, but I would prefer to work with P and
S constructed as per the above "algorithm". The reason is that I mainly
want to count subgroups and conjugacy classes of subgroups of P and S for
(at least) n=4, since for smaller values of n, the order of C is a prime
(thus C uninteresting), but GAP is unable to handle this in terms of memory.

I have serious doubts that constructing P and S as above will be more
memory-efficient than the permutation representation already in
Sz(IsPermGroup,q), but I can't decide this issue in advance.

If it is indeed non-trivial to decide beforehand, I would appreciate any
help in how to write the code for the construction as explained above.

Many thanks,
Stefanos

From e.obrien at auckland.ac.nz  Fri Feb 15 08:43:03 2013
From: e.obrien at auckland.ac.nz (Eamonn O'Brien)
Date: Fri, 15 Feb 2013 21:43:03 +1300
Subject: [GAP Forum] Akos Seress (1958-2013)
Message-ID: <511DF517.7040300@auckland.ac.nz>

Dear Friends,

We have learned with great sadness that Akos Seress passed away
Wednesday evening, February 13, in Columbus, Ohio.

Akos was an outstanding mathematician, author of a book on
algorithmic group theory and over a hundred papers on asymptotic
and algorithmic group theory and combinatorics.  He was an invited
speaker at the 2006 International Congress of Mathematicians in
Madrid.  In addition to his theoretical work, he was a major
contributor to the GAP computational algebra system.  He was an
indefatigable architect of bridges between the computational group
theory and the theory of computing communities.

Born in Budapest on November 24, 1958, Akos studied mathematics at
Eotvos University, Budapest where he began publishing in
combinatorics while an undergraduate.  He completed his Ph.D.  at
the Ohio State University under Dijen Ray-Chaudhury.  Subsequently
he entered the field of algorithmic group theory in a series of
joint papers with Babai and Luks on the complexity of permutation
group algorithms and wrote the definitive monograph on the subject.
He continued with a series of important papers on the statistical
theory of finite simple groups with Bill Kantor and others; this
line of work contributed to a recent definitive result on the
complexity of algorithms for matrix groups over finite fields by
Akos and coauthors.  He has also extensively contributed to the
asymptotic theory of permutation groups, vertex-transitive graphs,
extremal combinatorics, and the theory of designs.

Motivated by the theoretical results on algorithms for permutation
groups, Akos pioneered the implementation of these algorithms in
the GAP computational algebra system.  Developed in the 1990s, with
the cooperation and support of the Aachen group, Akos's packages
delivered, for the first time, practical performance backed up by
theoretical analysis.  His modular design and black-box techniques
allow an easy adaptation to other representations; his work is
widely used today as infrastructure both for permutation groups and
for matrix groups.  More recently Akos and Max Neunhoeffer have
developed efficient implementations of a suite of algorithms for
matrix groups.

Akos has been a tireless builder of communities, his own work and
example demonstrating the bridge between the "red-hats," those who
create "paper-algorithms" with proven asymptotic performance
guarantees, and the "green-hats," the computational group theorists
who demand working code to study the stucture of concrete groups.
Akos, along with Bill Kantor, has been a chief organizer of a
series of meetings that brought these two communities together.

Akos spent most of his professional career at the Ohio State
University, with extended visits to the University of Western
Australia.  He died at the age of 54 of renal cell carcinoma, a
particularly aggressive form of cancer, diagnosed only six months
ago.  The disease struck him at the height of his creative powers.
His paper "Construction of 2-Closed M-Representations" received the
Distinguished paper award at ISSAC 2012 (Intl. Symp. on Symbolic
and Algebraic Manipulation) and was hailed as "a groundbreaking
work" that "marks a turning point in Majorana Theory."  His most
recent work, with Harald Helfgott, under publication in the Annals
of Mathematics, gives a long-sought bound on the diameter of the
alternating and symmetric groups and represents a tour de force in
the study of the geometry of finite simple groups.

Akos has been a most generous friend, colleague, and mentor.  His
passing will be felt deeply by all around the globe whose lives he
touched and whose careers he enriched.  Our hearts go out to his
wife Sherry and his son Laszlo.

     -- Laszlo Babai and Eamonn O'Brien





From rahul.kitture at gmail.com  Fri Feb 15 09:02:05 2013
From: rahul.kitture at gmail.com (rahul kitture)
Date: Fri, 15 Feb 2013 14:32:05 +0530
Subject: [GAP Forum] Product of Subgroups in a Group
Message-ID: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>

Given two subgroups $H$ and $K$ of a finite group (say Symmetric/
Alternating Group), how do we
compute the product $HK$ in the group? I couldn't find anything from Help
or topics in online library.
Also, given finite number of square (invertible) matrices over a finite
field, how do we get the (multiplicative) group, generated by them?
(The command "GroupWithGenerators(); " does not work with the
elements(generators) to be matrices.

-- 
Rahul D. Kitture
Senior Research Fellow (CSIR),
Bhaskaracharya Pratishthana,
(Research Institute for Mathematics)
www.bprim.org
Pune: 411 004 (India)*.
*

From Sven.Reichard at tu-dresden.de  Fri Feb 15 09:35:50 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Fri, 15 Feb 2013 10:35:50 +0100
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
Message-ID: <511E0176.5020107@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 15.02.2013 10:02, schrieb rahul kitture:
> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/ 
> Alternating Group), how do we compute the product $HK$ in the
> group? I couldn't find anything from Help or topics in online
> library.

This may not be the most elegant way, but
gap> Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
should do the trick.

> Also, given finite number of square (invertible) matrices over a
> finite field, how do we get the (multiplicative) group, generated
> by them? (The command "GroupWithGenerators(); " does not work with
> the elements(generators) to be matrices.
> 
Works for me.

gap> GL(3, GF(2));
SL(3,2)
gap> List([1..3], x -> Random(last));
[ <an immutable 3x3 matrix over GF2>, <an immutable 3x3 matrix over GF2>,
  <an immutable 3x3 matrix over GF2> ]
gap> Group(last);
<matrix group with 3 generators>
gap> GroupWithGenerators(last2);
<matrix group with 3 generators>
gap> last=last2;
true

Are the entries of your matrices elements of the finite field? If not,
multiply the matrices by One(field).

HTH
Sven Reichard

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From sandeepr.murthy at gmail.com  Fri Feb 15 13:27:15 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Fri, 15 Feb 2013 13:27:15 +0000
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <511E0176.5020107@tu-dresden.de>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
	<511E0176.5020107@tu-dresden.de>
Message-ID: <511E37B3.8060903@gmail.com>

Hi,

If H, K are subgroups of G then

ListX( H, K, PROD )

will return a (mutable) list of
the elements of the set HK in
G.

Sincerely, Sandeep.

Sven Reichard wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Am 15.02.2013 10:02, schrieb rahul kitture:
>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/
>> Alternating Group), how do we compute the product $HK$ in the
>> group? I couldn't find anything from Help or topics in online
>> library.
>
> This may not be the most elegant way, but
> gap>  Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
> should do the trick.
>
>> Also, given finite number of square (invertible) matrices over a
>> finite field, how do we get the (multiplicative) group, generated
>> by them? (The command "GroupWithGenerators(); " does not work with
>> the elements(generators) to be matrices.
>>
> Works for me.
>
> gap>  GL(3, GF(2));
> SL(3,2)
> gap>  List([1..3], x ->  Random(last));
> [<an immutable 3x3 matrix over GF2>,<an immutable 3x3 matrix over GF2>,
>    <an immutable 3x3 matrix over GF2>  ]
> gap>  Group(last);
> <matrix group with 3 generators>
> gap>  GroupWithGenerators(last2);
> <matrix group with 3 generators>
> gap>  last=last2;
> true
>
> Are the entries of your matrices elements of the finite field? If not,
> multiply the matrices by One(field).
>
> HTH
> Sven Reichard
>
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.5 (GNU/Linux)
> Comment: Using GnuPG with Thunderbird - http://www.enigmail.net/
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> =VVZt
> -----END PGP SIGNATURE-----
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From burkhard at hoefling.name  Fri Feb 15 14:10:17 2013
From: burkhard at hoefling.name (=?iso-8859-1?Q?Burkhard_H=F6fling?=)
Date: Fri, 15 Feb 2013 15:10:17 +0100
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <511E0176.5020107@tu-dresden.de>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
	<511E0176.5020107@tu-dresden.de>
Message-ID: <05B25004-DA47-457E-8D22-17C52138C9B3@hoefling.name>


On 2013-02-15, at 10:35 , Sven Reichard <Sven.Reichard at tu-dresden.de> wrote:

> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
> 
> Am 15.02.2013 10:02, schrieb rahul kitture:
>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/ 
>> Alternating Group), how do we compute the product $HK$ in the
>> group? I couldn't find anything from Help or topics in online
>> library.
> 
> This may not be the most elegant way, but
> gap> Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
> should do the trick.


This gives the subgroup generated by H and K but not, in general, the set HK. If you know that HK is a subgroup, then this will work. ClosureGroup (H,K) might be a bit more efficient.

On 2013-02-15, at 14:27 , Sandeep Murthy <sandeepr.murthy at gmail.com> wrote:

> Hi,
> 
> If H, K are subgroups of G then
> 
> ListX( H, K, PROD )
> 
> will return a (mutable) list of
> the elements
> of the set HK in
> G.

But note that the list will have duplicates if H and K don't intersect trivially.

I would suggest DoubleCoset (H, One(H), K)  to represent HK more efficiently. You can turn the double coset into a list via AsList/ AsSSortedList.

Cheers

Burkhard.
  

From sandeepr.murthy at gmail.com  Fri Feb 15 14:47:52 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Fri, 15 Feb 2013 14:47:52 +0000
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <05B25004-DA47-457E-8D22-17C52138C9B3@hoefling.name>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
	<511E0176.5020107@tu-dresden.de>
	<05B25004-DA47-457E-8D22-17C52138C9B3@hoefling.name>
Message-ID: <511E4A98.6030608@gmail.com>

the duplicates can be removed using

Unique( ListX( H, K, PROD ) ).

Seems fairly quick, but maybe for large products
DoubleCoset (H, One(H), K), suggested by Burkhard,
is quicker.

Sincerely, Sandeep.

Burkhard H?fling wrote:
> On 2013-02-15, at 10:35 , Sven Reichard<Sven.Reichard at tu-dresden.de>  wrote:
>
>> -----BEGIN PGP SIGNED MESSAGE-----
>> Hash: SHA1
>>
>> Am 15.02.2013 10:02, schrieb rahul kitture:
>>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/
>>> Alternating Group), how do we compute the product $HK$ in the
>>> group? I couldn't find anything from Help or topics in online
>>> library.
>> This may not be the most elegant way, but
>> gap>  Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
>> should do the trick.
>
>
> This gives the subgroup generated by H and K but not, in general, the set HK. If you know that HK is a subgroup, then this will work. ClosureGroup (H,K) might be a bit more efficient.
>
> On 2013-02-15, at 14:27 , Sandeep Murthy<sandeepr.murthy at gmail.com>  wrote:
>
>> Hi,
>>
>> If H, K are subgroups of G then
>>
>> ListX( H, K, PROD )
>>
>> will return a (mutable) list of
>> the elements
>> of the set HK in
>> G.
>
> But note that the list will have duplicates if H and K don't intersect trivially.
>
> I would suggest DoubleCoset (H, One(H), K)  to represent HK more efficiently. You can turn the double coset into a list via AsList/ AsSSortedList.
>
> Cheers
>
> Burkhard.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From benjamin.sambale at gmail.com  Fri Feb 15 15:51:14 2013
From: benjamin.sambale at gmail.com (Benjamin Sambale)
Date: Fri, 15 Feb 2013 16:51:14 +0100
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <511E4A98.6030608@gmail.com>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
	<511E0176.5020107@tu-dresden.de>
	<05B25004-DA47-457E-8D22-17C52138C9B3@hoefling.name>
	<511E4A98.6030608@gmail.com>
Message-ID: <511E5972.1090000@gmail.com>

See also SetX(H,K,PROD)

Benjamin

Am 15.02.2013 15:47, schrieb Sandeep Murthy:
> the duplicates can be removed using
>
> Unique( ListX( H, K, PROD ) ).
>
> Seems fairly quick, but maybe for large products
> DoubleCoset (H, One(H), K), suggested by Burkhard,
> is quicker.
>
> Sincerely, Sandeep.
>
> Burkhard H?fling wrote:
>> On 2013-02-15, at 10:35 , Sven Reichard<Sven.Reichard at tu-dresden.de>  
>> wrote:
>>
>>> -----BEGIN PGP SIGNED MESSAGE-----
>>> Hash: SHA1
>>>
>>> Am 15.02.2013 10:02, schrieb rahul kitture:
>>>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/
>>>> Alternating Group), how do we compute the product $HK$ in the
>>>> group? I couldn't find anything from Help or topics in online
>>>> library.
>>> This may not be the most elegant way, but
>>> gap>  Group(Concatenation(List([H,K], GeneratorsOfGroup)), 
>>> Identity(H));
>>> should do the trick.
>>
>>
>> This gives the subgroup generated by H and K but not, in general, the 
>> set HK. If you know that HK is a subgroup, then this will work. 
>> ClosureGroup (H,K) might be a bit more efficient.
>>
>> On 2013-02-15, at 14:27 , Sandeep Murthy<sandeepr.murthy at gmail.com>  
>> wrote:
>>
>>> Hi,
>>>
>>> If H, K are subgroups of G then
>>>
>>> ListX( H, K, PROD )
>>>
>>> will return a (mutable) list of
>>> the elements
>>> of the set HK in
>>> G.
>>
>> But note that the list will have duplicates if H and K don't 
>> intersect trivially.
>>
>> I would suggest DoubleCoset (H, One(H), K)  to represent HK more 
>> efficiently. You can turn the double coset into a list via AsList/ 
>> AsSSortedList.
>>
>> Cheers
>>
>> Burkhard.
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From williamdemeo at gmail.com  Fri Feb 15 17:22:07 2013
From: williamdemeo at gmail.com (William DeMeo)
Date: Fri, 15 Feb 2013 12:22:07 -0500
Subject: [GAP Forum] Product of Subgroups in a Group
In-Reply-To: <511E5972.1090000@gmail.com>
References: <CALU+QdeDo0dm32Um58h4KpWGvbJNrOi8GpDoyYkSXPHoopYNiQ@mail.gmail.com>
	<511E0176.5020107@tu-dresden.de>
	<05B25004-DA47-457E-8D22-17C52138C9B3@hoefling.name>
	<511E4A98.6030608@gmail.com> <511E5972.1090000@gmail.com>
Message-ID: <CAHO_k7QLmSkw4DiScokVgyf=XNTOh_9PfmjWD2LfRn5eLqEN9g@mail.gmail.com>

See also the thread "complex product of two groups" in the forum archive:

http://mail.gap-system.org/pipermail/forum/2012/thread.html#3628

Cheers,
William



On Fri, Feb 15, 2013 at 10:51 AM, Benjamin Sambale
<benjamin.sambale at gmail.com> wrote:
> See also SetX(H,K,PROD)
>
> Benjamin
>
> Am 15.02.2013 15:47, schrieb Sandeep Murthy:
>
>> the duplicates can be removed using
>>
>> Unique( ListX( H, K, PROD ) ).
>>
>> Seems fairly quick, but maybe for large products
>> DoubleCoset (H, One(H), K), suggested by Burkhard,
>> is quicker.
>>
>> Sincerely, Sandeep.
>>
>> Burkhard H?fling wrote:
>>>
>>> On 2013-02-15, at 10:35 , Sven Reichard<Sven.Reichard at tu-dresden.de>
>>> wrote:
>>>
>>>> -----BEGIN PGP SIGNED MESSAGE-----
>>>> Hash: SHA1
>>>>
>>>> Am 15.02.2013 10:02, schrieb rahul kitture:
>>>>>
>>>>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/
>>>>> Alternating Group), how do we compute the product $HK$ in the
>>>>> group? I couldn't find anything from Help or topics in online
>>>>> library.
>>>>
>>>> This may not be the most elegant way, but
>>>> gap>  Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
>>>> should do the trick.
>>>
>>>
>>>
>>> This gives the subgroup generated by H and K but not, in general, the set
>>> HK. If you know that HK is a subgroup, then this will work. ClosureGroup
>>> (H,K) might be a bit more efficient.
>>>
>>> On 2013-02-15, at 14:27 , Sandeep Murthy<sandeepr.murthy at gmail.com>
>>> wrote:
>>>
>>>> Hi,
>>>>
>>>> If H, K are subgroups of G then
>>>>
>>>> ListX( H, K, PROD )
>>>>
>>>> will return a (mutable) list of
>>>> the elements
>>>> of the set HK in
>>>> G.
>>>
>>>
>>> But note that the list will have duplicates if H and K don't intersect
>>> trivially.
>>>
>>> I would suggest DoubleCoset (H, One(H), K)  to represent HK more
>>> efficiently. You can turn the double coset into a list via AsList/
>>> AsSSortedList.
>>>
>>> Cheers
>>>
>>> Burkhard.
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From sandeepr.murthy at gmail.com  Sat Feb 16 17:51:21 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Sat, 16 Feb 2013 17:51:21 +0000
Subject: [GAP Forum] Algebras
Message-ID: <511FC719.9010604@gmail.com>

Hi,

1. I can't make sense of the following result on GAP:

gap> IsAlgebraWithOne( MatAlgebra( Rationals, 1 ) );
true
gap> IsAlgebraWithOne( MatAlgebra( Rationals, 2 ) );
true
gap> IsAlgebraWithOne( DirectSumOfAlgebras( MatAlgebra( Rationals, 1 ), 
MatAlgebra( Rationals, 2 ) ) );
false

Surely the result should also be an algebra with one.

2. Is there a way to test for isomorphism between two
algebras indirectly, in the same way as for groups
(i.e. IsomorphismGroups( G, H ))?

Sincerely, Sandeep.












From max at quendi.de  Wed Feb 20 14:08:57 2013
From: max at quendi.de (Max Horn)
Date: Wed, 20 Feb 2013 15:08:57 +0100
Subject: [GAP Forum] Construction of a group
In-Reply-To: <CAPCTGEOejZe+g1dvGh202ZDSdrFYeKGLk+Ja4V6sGH7ScUr7EQ@mail.gmail.com>
References: <CAPCTGEOejZe+g1dvGh202ZDSdrFYeKGLk+Ja4V6sGH7ScUr7EQ@mail.gmail.com>
Message-ID: <0491335A-91B5-453D-8316-B1EF87FA233E@quendi.de>

Dear Stefanos,

you asked about constructing the (normalizer of) the 2-Sylow subgroup of the Suzuki groups without first constructing the Suzuki groups. Moreover, you expressed interest in counting their (classes of) subgroups. I will try to address both below.


On 14.02.2013, at 17:56, Stefanos Aivazidis wrote:

> Dear Forum,
> 
> I wish to construct a family of groups parametrised by a variable n, to be
> specified by the user. Let me describe the steps:
> 
> 0) Specify a value for n,
> 
> 1) construct the finite field F=F_q with q=2^(2n+1) elements,
> 
> 2) construct the automorphism f of F mapping each element x to x^(2^a),
> where a=n+1,

Let's record what we have so far:

n := 4;   # later you mention n=4, but other values work, too
q := 2^(2*n+1);
F := GF(q);
a := n+1;
f := x -> x^(2^a);


> 
> 3) define an operation * on FxF (as a set) via the rule:
> (x,y)*(x',y')=(x+x',y+y'+xf(x')), where the operations on the
> right-hand-side are those of the underlying field F,
> 
> Now P=(FxF,*) is a group, but I don't know if I can assure GAP this is the
> case. Perhaps I can ask her to test this somehow (GAP is a woman in my
> world).

The above group (the root group of a Moufang set in my world ;-) is a
p-group, hence polycyclic. And thus a natural way to construct it is as
a pc group (or, in my case, as a "pcp group", which is what the
"polycyclic" package for GAP provides). For large p-groups, permutation
representations (at least as computed by GAP) tend to have huge degree
and working with them quickly becomes problematic. But pc presentations
don't suffer from that problem (they have other computation drawbacks,
though).

Anyway, let's first collect some basic observations about this product:

 (a) (0,y)*(0,y') = (0,y+y')
     => 0xF is a subgroup isomorphic to (F,+)
 (b) (x,0)*(0,y') = (x,y') = (0,y')*(0,x)
     => 0xF is in fact central.
 (c) (x,0)*(x',0) = (x+x', xf(x')) 
     => the factor group FxF/0xF is abelian.
 (d) (x,0)^2 = (0,xf(x))
     => the relative order of (x,0) is 2
 (e) (x,0)^-1 = (x,xf(x))
 (f) (x,0)^(x',0) = (x',0)^-1*(x,0)*(x',0)
          = (x',x'f(x'))*(x+x', xf(x'))
          = (x, x'f(x+x')+x'f(x')+xf(x'))
          = (x, x'f(x)+xf(x'))

The last two relations tell us how conjugation between element of Fx0
looks like. Next, choose a basis b_1,...b_{2n+1} of F viewed as
GF(2)-vector space, and let x_1,...,x_{2n+1} be the corresponding basis
of Fx0, and let y_1,...,y_{2n+1} be the corresponding basis of 0xF.


We are now equipped with everything to construct a polycyclic presentation for
the group P. But wait, you want more:

> 
> 4) assuming that GAP now knows P is a group, define the semi-direct product
> S=P]C, where C is the multiplicative group of F and acts on P (via
> automorphisms) by the rule:c.(x,y)=(cx,cf(c)y), where f is as in 2) and
> concatenation on the right-hand-side is just multiplication in F.

We could try to construct P first and then use GAP's SemidirectProduct(),
but that would be very expensive, and in fact, unnecessary. After all, the
unit group F^* of F is cyclic (in particular, poly-cyclic ;-) and Z(q) is
a generator for it in GAP. Semidirect products of finite polycyclic groups
are again finite polycyclic.


So let's get busy:

LoadPackage("polycyclic");
b:=Basis(F);

# Helper taking a pair (x,y) in FxF and, using the basis b, mapping it to a
# generator-exponent vector.
F_to_genexp := function(x,y)
    local ge, k;
    ge:=[];
    x := Coefficients(b,x);
    y := Coefficients(b,y);
    for k in [1..2*n+1] do
        if not IsZero(x[k]) then Append(ge, [k+1, IntFFE(x[k])]); fi;
    od;
    for k in [1..2*n+1] do
        if not IsZero(y[k]) then Append(ge, [k+2*n+2, IntFFE(y[k])]); fi;
    od;
    return ge;
end;

# We need 1 + 2*dim(F) = 4*n+3 generators
coll:=FromTheLeftCollector(1 + 4*n+2);

# First comes the generator of the cyclic group F^*.
# It has order |F|-1, and acts as you described.
SetRelativeOrder(coll, 1, Size(F)-1);
for j in [1..2*n+1] do
    # action on x_j
    exp := F_to_genexp( Z(q)*b[j], Zero(F) );
    SetConjugate(coll, j+1, 1, exp);

    # action on y_j
    exp := F_to_genexp( Zero(F), Z(q)*f(Z(q))*b[j] );
    SetConjugate(coll, j+2*n+2, 1, exp);
od;

# Next, the "upper" part Fx0: x_i acts on x_j non-trivially,
# but centralizes the y_k (since the default is that a generator
# centralizes another, we don't need to tell GAP what y_k^x_i is)
for i in [1..2*n+1] do
    # relative order of x_i is 2, and (x,0)^2=(0,xf(x))
    SetRelativeOrder(coll, i+1, 2);
    exp := F_to_genexp(Zero(F), b[i] * f(b[i]));
    SetPower(coll, i+1, exp);
    # (x_j,0)^(x_i,0) = ...
    for j in [i+1..2*n+1] do
        exp := F_to_genexp(b[j], b[i] * f(b[j]) + b[j] * f(b[i]));
        SetConjugate(coll, j+1, i+1, exp);
    od;
od;

# Finally the "lower" and central part 0xF
for i in [2*n+2..4*n+2] do
    SetRelativeOrder(coll, i+1, 2);
od;

# Now we can construct the group S
S := PcpGroupByCollector(coll);
#S := PcpGroupByCollectorNC(coll); # For large n this is faster by skipping checks

# P is the subgroup of S on the generators 2 .. 4*n+3:
P := Subgroup(S,GeneratorsOfGroup(S){[2..4*n+3]});

# And C is generated by the first generator
C := Subgroup(S,[S.1]);


> 
> To give some motivation for the above construction, P thus constructed is
> the Sylow 2-subgroup of Sz(q), while S is its normaliser in Sz(q). Of
> course I can access both P and S via P:=SylowSubgroup(Sz(q),2) and
> S:=Normaliser(Sz(q),P) respectively, but I would prefer to work with P and
> S constructed as per the above "algorithm". The reason is that I mainly
> want to count subgroups and conjugacy classes of subgroups of P and S for
> (at least) n=4, since for smaller values of n, the order of C is a prime
> (thus C uninteresting), but GAP is unable to handle this in terms of memory.
> 
> I have serious doubts that constructing P and S as above will be more
> memory-efficient than the permutation representation already in
> Sz(IsPermGroup,q), but I can't decide this issue in advance.

The polycyclic presentation constructed above should be a lot more
efficient. However, constructing all (classes of) subgroup is still a
difficult business, as there simply are so many of them, at least for P.
After all, 0xY is a central elementary abelian subgroup of order q =
2^(2*n+1). For n=4 it has size 2^9=512; and each subspace corresponds to
a normal subgroup of P. But there are 8283458 subspaces, each yielding a
subgroup conjugacy class in P. The situation should be somewhat better
in S, at least in the sense that there are fewer conjugacy classes (e.g.
all 1-dimensional subspaces of 0xY are conjugate in S; in general, .

Similarly, the factor group P/0xY has 8283458 normal subgroups. Each
lifts to at least one conjugacy class in P. In other words, GAP will
have to compute in excess of 16 million subgroups, together with their
normalizers, and will have to store them all in memory. Hence I do not
expect ConjugacyClassesSubgroups(P) or ConjugacyClassesSubgroups(S) to
work "out of the box", no matter how you present P and S to GAP. But if
you just want to take specific subgroups and look at them to, say you
want to compute their normalizes, check if a few of them are conjugate
etc., the above can still be helpful.

If you truly want to count the (classes of) subgroups, and indeed only
need the count, then it might still be possible to achieve that by
taking the special structure of the group into account. The first thing
I would try: For each subgroup A of P/0xY, identify all subgroups U of P
for which U/0xY = A holds. The fact that the map F\to F : c \mapsto c
f(c) is bijective and non-linear, plus that we have (x,y)^2 = (0,xf(x)),
should help with that. And of course if you work inside S (where you
have fewer conjugacy classes overall, I guess), things should get a bit
better, too.



Hope that helps,
Max

> 
> If it is indeed non-trivial to decide beforehand, I would appreciate any
> help in how to write the code for the construction as explained above.
> 
> Many thanks,
> Stefanos
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
> 



From max at quendi.de  Wed Feb 20 14:23:50 2013
From: max at quendi.de (Max Horn)
Date: Wed, 20 Feb 2013 15:23:50 +0100
Subject: [GAP Forum] Algebras
In-Reply-To: <511FC719.9010604@gmail.com>
References: <511FC719.9010604@gmail.com>
Message-ID: <55D68BDE-ED41-44D7-B40C-E88848413EBD@quendi.de>

Dear Sandeep,

let me try to address your first question.

On 16.02.2013, at 18:51, Sandeep Murthy wrote:

> Hi,
> 
> 1. I can't make sense of the following result on GAP:
> 
> gap> IsAlgebraWithOne( MatAlgebra( Rationals, 1 ) );
> true
> gap> IsAlgebraWithOne( MatAlgebra( Rationals, 2 ) );
> true
> gap> IsAlgebraWithOne( DirectSumOfAlgebras( MatAlgebra( Rationals, 1 ), MatAlgebra( Rationals, 2 ) ) );
> false
> 
> Surely the result should also be an algebra with one.

Not quite. This (admittedly irritating) behavior is due to the fact that IsAlgebraWithOne does not really check whether its argument is an "algebra with an identity element".

Rather, it checks whether its argument has the *type* AlgebraWithOne, e.g. was created using the constructor AlgebraWithOne() as opposed to Algebra(). Perhaps thinking of it in terms of (mathematical) categories helps: The real numbers certainly are objects in both the category of real associate algebras, and its subcategory of real associative  algebras with identity. Or perhaps think of the difference between a topological space, and a pointed topological space, where single out one specific point.

Here is another, perhaps even more succinct GAP example to emphasis this point:

gap> F:=GF(2);;g:=IdentityMat(4,F);;
gap> IsAlgebra(Algebra(F,[g]));
true
gap> IsAlgebraWithOne(Algebra(F,[g]));
false
gap> IsAlgebra(AlgebraWithOne(F,[g]));
true
gap> IsAlgebraWithOne(AlgebraWithOne(F,[g]));
true


The problem in your example is that DirectSumOfAlgebras is defined in the category of algebras, not of algebras-with-one. You have to coerce the result into an algebra with one:

gap> alg := DirectSumOfAlgebras( MatAlgebra( Rationals, 1 ), MatAlgebra( Rationals, 2 ) );
<algebra over Rationals, with 6 generators>
gap> IsAlgebraWithOne(alg);
false
gap> alg := AsAlgebraWithOne(Rationals,alg);
<algebra-with-one over Rationals, with 6 generators>
gap> IsAlgebraWithOne(alg);
true


Perhaps there should be a DirectSumOfAlgebrasWithOne, or perhaps DirectSumOfAlgebras should simply be enhanced to check if its arguments all are algebras with one, and if so, carry this information through...


Best regards,
Max

From max at quendi.de  Wed Feb 20 15:06:25 2013
From: max at quendi.de (Max Horn)
Date: Wed, 20 Feb 2013 16:06:25 +0100
Subject: [GAP Forum] Modules over general and not so general algebras
In-Reply-To: <510BD350.3070301@uni-jena.de>
References: <510BD350.3070301@uni-jena.de>
Message-ID: <8B0EEC18-9ADE-4FED-89FF-28A1518C7893@quendi.de>

Dear Johannes,

On 01.02.2013, at 15:38, Johannes Hahn wrote:

> Hi everyone.
> 
> Is there an elegant way to implement (finite-dimensional) modules over my favorite algebra? My algebra is finite dimensional and I would GAP tell this if it needs to know, but I don't want to spell out an explicit basis and structure constants for the algebra. (More to the point: I work with Hecke algebras and they get way to big for this, if the Coxeter group is big, say E_7, E_8)
> 
> I do not actually need the algebra, I just want to do some computations with the matrices of the representation. There seems no way to define an algebra by generators and relations because GAP seemingly wants to do some calculations and of course this goes wrong in the general case and even in my special case GAP doesn't know that there are normalforms for the elements of my algebra etc. (And I cannot find a way to tell GAP this)

If you know how to compute normal forms for your algebras effectively, you could implement your own algebra(-with-one) type and teach GAP about that. But I am not sure if that is really what you wanted to hear ;-)..


> 
> The next best thing would be to just forget the relations for a moment and think of the modules as algebra morphisms from the free algebra on the (small) set of generators into a full matrix algebra. If you have that, one could implement a filter that checks the defining relations of my favorite algebra for such morphisms manually.
> GAP knows free algebras and it knows matrix algebras and it has an operation for defining algebra morphisms by their images, but interestingly, even this does not work.
> 
> If I just try to get the morphism Q<x,y> \to Q, x \mapsto 1, y\mapsto 1 doing this:
> > F:=FreeAssociativeAlgebraWithOne(Rationals,2);
> <algebra-with-one over Rationals, with 2 generators>
> > f := AlgebraHomomorphismByImages(F,FullMatrixAlgebra(Rationals,1), GeneratorsOfAlgebraWithOne(F),[ [[1]], [[1]] ]);
> then GAP enters an infinite loop for some reason.

The reason is that it wants to verify that what you specified there is really an algebra homomorphism (which is sensible), but it then attempts to compute a "nice" presentation of the algebra F as a module... which is of course not sensible, as that module would be infinite dimensional. So I'd consider this a bug, or perhaps a missing feature. This is essentially due to the fact that GAP is lacking a lot of (sometimes even relatively basic) functionality when it comes to algebras other than those defined by a structure constant table (sct). :-(.

One can avoid this by using the NC variant:

gap>  f := AlgebraHomomorphismByImagesNC(F,FullMatrixAlgebra(Rationals,1), GeneratorsOfAlgebraWithOne(F),[ [[1]], [[1]] ]);
[ (1)*x.1, (1)*x.2 ] -> [ [ [ 1 ] ], [ [ 1 ] ] ]


But that doesn't quite help, as it still does not know how to actually compute the image. The following code snippet should fix this. Also note that you may actually want to use AlgebraWithOneHomomorphismByImagesNC (see also my other email to Sandeep for more about that),

InstallMethod( ImagesRepresentative,
    FamSourceEqFamElm,
    [ IsAlgebraHomomorphism, IsElementOfFreeMagmaRing ],
    function( hom, elm )
    local mgi;
    mgi := MappingGeneratorsImages(hom);
    return MappedExpressionForElementOfFreeAssociativeAlgebra( elm, mgi[1], mgi[2] );
    end );

But note that this is a hack: It does not verify that the generators you specified when defining the homomorphism are indeed the canonical generators (returned by GeneratorsOfAlgebraWithOne()) of F. But with some work, it should be possible to enhance GAP to use something like that above. I'll log a feature request for this all in the GAP tracker.



> This behaviour is completely mysterious to me. Why on earth would GAP even consider to do *any* computation in that situation? There is exactly nothing else to know about a general algebra morphism on a free algebra other than the data that already has been given. The only thing to do here is to take the input data, wrap it into an object, set some filters to true and return that object.
> Why does GAP try to compute anything here instead of just giving me my morphism so I can start working with it?

Well, because GAP is just a dumb computer program, and nobody has so far taught it about this particular property of free algebras and morphisms from them... in other words: because nobody implemented this so far... ;-). But I do agree that this is irritating and somewhat frustrating. In fact, I have been bitten by similar problems before.

BTW, in a somewhat tangential note: It would be nice if e.g. the GBNP package (which provides non-commutative Groebner basis computations) could be enhanced as to install suitable methods for fp rings / algebras -- with GBNP, it is actually possible to compute bases of fp algebras in many cases, and compute with them without providing structure constant tables -- except that doing so produces highly unreadable code, because no methods for things like \+, \* etc. are installed :-(.

> 
> Should there be a compelling reason for GAP to behave this way (although I really can't think of any...), then my question immediatly changes into: What is an elegant way to implement matrix representation of Hecke algebras without having to tell GAP an explicit basis and structure constants for the algebra?
> 
> Right now I'm just working with plain records to store information about the representation but this seems very inelegant to me. There are no "real" objects, no types, no possibility for method-selection based on additional information... (and I can't figure out how to implement Hecke-Matrix-Representation objects for myself... I'm not sure yet if GAP really behaves differently than the manual claims or if I'm just to stupid to read the manual correctly.)

If the manual truly claims that the above should work, then this is a mistake in the manual, and should be corrected (until such functionality is actually implemented, at least). Any pointers to such incorrect or at least misleading parts of the manual would be greatly appreciated!



Cheers,
Max

From cotton at alum.mit.edu  Sat Feb 23 19:02:20 2013
From: cotton at alum.mit.edu (Cotton Seed)
Date: Sat, 23 Feb 2013 14:02:20 -0500
Subject: [GAP Forum] sorted index of group element
Message-ID: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>

Is there way to get the sorted index of a group element?  More
specifically, let G be a group, and g an element of G.  Is there a function
that will give me the index i so that MagmaElement(G,i) = g?  Thanks!

Best,
Cotton

From alexk at mcs.st-andrews.ac.uk  Sun Feb 24 20:38:44 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Sun, 24 Feb 2013 20:38:44 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
Message-ID: <06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>


On 23 Feb 2013, at 19:02, Cotton Seed <cotton at alum.mit.edu> wrote:

> Is there way to get the sorted index of a group element?  More
> specifically, let G be a group, and g an element of G.  Is there a function
> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
> 
> Best,
> Cotton


Dear Cotton,

Let me first start with a hint how the source code of the MagmaElement 
function may be explored to find an answer, and then suggest a more 
efficient approach.

First, looking at the code of MagmaElement function - this may be done by 
typing `ViewSource(MagmaElement);' in GAP - you may spot the call to 
AsSSortedList:

InstallGlobalFunction( MagmaElement, function( M, i )
   M:= AsSSortedList( M );
   if Length( M ) < i then
     return fail;
   else
     return M[i];
   fi;
end );

Thus, MagmaElement returns the i-th element of AsSSortedList(M), where 
the latter contains all elements of M in strictly sorted order, w.r.t. 
the canonical ordering defined on M (depending on the type of M). 
Therefore, the index in which you're interested will be returned by 

Position( AsSSortedList( G ), g ) 

For example,

gap> G:=SmallGroup(8,3);
<pc group of size 8 with 3 generators>
gap> g:=Random(G);
f1*f3
gap> s:=AsSSortedList(G);;
gap> Position(s,g);
6
gap> MagmaElement(G,6);
f1*f3
gap> MagmaElement(G,6)=g;
true

Creating the list of all elements may not be very efficient, especially
when the group is very large. However, if the method for `Enumerator' 
exists for such a group (see `?Enumerator), then there is another
approach. Enumerator(G) need not to store its elements explicitly, 
but it knows how to determine the i-th element and the position of a 
given object. For example, this works:

gap> S:=SymmetricGroup(50);
Sym( [ 1 .. 50 ] )
gap> g:=Random(S);
(1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
gap> enum:=Enumerator(S);
<enumerator of perm group>
gap> pos:=Position(enum,g);
19748951512546719853008099372809900742253637283670495935197327991
gap> enum[pos]=g;
true

while AsSSortedList(S) will run out of memory. There are methods for 
enumerators of various types of algebraic structures defined in the
GAP library.

Please note that the order in which MagmaElement and Enumerator will
sort elements of a domain sometimes may be different: the one for 
MagmaElement is determined by the '\<' relation defined on the domain, 
while the one for Enumerator depends on the algorithm used to enumerate
elements of a domain of some particular type. For example,

gap> F:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> AssignGeneratorVariables(F);
#I  Assigned the global variables [ a, b ]
gap> G:=F/[a^32,b^2,b^-1*a*b*a];
<fp group on the generators [ a, b ]>
gap> First([1..Size(G)],i -> not MagmaElement(G,i)=Enumerator(G)[i]);
3
gap> MagmaElement(G,3);
b
gap> Enumerator(G)[3];
a^-1

However, in most applications it is not the particular order that matters,
but the ability to determine the position of an element in the fixed 
list of elements, and to retrieve the i-th element of that list.

Hope this helps,
Alexander



From roberto.radina at tiscali.it  Mon Feb 25 17:09:08 2013
From: roberto.radina at tiscali.it (=?iso-8859-1?Q?Roberto_R=E0dina?=)
Date: Mon, 25 Feb 2013 18:09:08 +0100
Subject: [GAP Forum] md5 sum needed
Message-ID: <FC62F680364248A5B18E325B5B06A737@carnia>

Dear forum,
I need md5 or sha1 sums of  gap4r6p2_2013_02_02-01_00-win.zip  for a check. 
It is the file for installing the last version of GAP.
Can someone post it here? 



From alexk at mcs.st-andrews.ac.uk  Mon Feb 25 18:51:24 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 25 Feb 2013 18:51:24 +0000
Subject: [GAP Forum] md5 sum needed
In-Reply-To: <FC62F680364248A5B18E325B5B06A737@carnia>
References: <FC62F680364248A5B18E325B5B06A737@carnia>
Message-ID: <46F12B85-B660-478B-B1AE-E11E6021FF04@mcs.st-andrews.ac.uk>

Dear Roberto,

On 25 Feb 2013, at 17:09, Roberto R?dina <roberto.radina at tiscali.it> wrote:

> Dear forum,
> I need md5 or sha1 sums of  gap4r6p2_2013_02_02-01_00-win.zip  for a check.
> It is the file for installing the last version of GAP.
> Can someone post it here? 
> 

Here it is:

/ftp/pub/gap/gap46/win.zip > md5sum gap4r6p2_2013_02_02-01_00-win.zip 
0c5d44f306f3013d1da7f22a0cc37398  gap4r6p2_2013_02_02-01_00-win.zip

Also, if you wish to use the Windows installer from 

	http://www.gap-system.org/ukrgap/wininst/

then its checksum is here:

/ftp/pub/gap/windowsinstaller > md5sum gap4r6p2_2013_02_02-01_00.exe 
64ac87c35de7c2da562643db9ec7112c  gap4r6p2_2013_02_02-01_00.exe

Best wishes,
Alexander










From vipul at math.uchicago.edu  Mon Feb 25 20:16:30 2013
From: vipul at math.uchicago.edu (Vipul Naik)
Date: Mon, 25 Feb 2013 14:16:30 -0600
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
Message-ID: <20130225201630.GA20677@math.uchicago.edu>

Hi,

I'm not able to run ViewSource on GAP -- it does not recognize the command.

I'm using GAP 4.5.6.

Vipul

* Quoting Alexander Konovalov who at 2013-02-24 20:38:44+0000 (Sun) wrote
> 
> On 23 Feb 2013, at 19:02, Cotton Seed <cotton at alum.mit.edu> wrote:
> 
> > Is there way to get the sorted index of a group element?  More
> > specifically, let G be a group, and g an element of G.  Is there a function
> > that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
> > 
> > Best,
> > Cotton
> 
> 
> Dear Cotton,
> 
> Let me first start with a hint how the source code of the MagmaElement 
> function may be explored to find an answer, and then suggest a more 
> efficient approach.
> 
> First, looking at the code of MagmaElement function - this may be done by 
> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to 
> AsSSortedList:
> 
> InstallGlobalFunction( MagmaElement, function( M, i )
>    M:= AsSSortedList( M );
>    if Length( M ) < i then
>      return fail;
>    else
>      return M[i];
>    fi;
> end );
> 
> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where 
> the latter contains all elements of M in strictly sorted order, w.r.t. 
> the canonical ordering defined on M (depending on the type of M). 
> Therefore, the index in which you're interested will be returned by 
> 
> Position( AsSSortedList( G ), g ) 
> 
> For example,
> 
> gap> G:=SmallGroup(8,3);
> <pc group of size 8 with 3 generators>
> gap> g:=Random(G);
> f1*f3
> gap> s:=AsSSortedList(G);;
> gap> Position(s,g);
> 6
> gap> MagmaElement(G,6);
> f1*f3
> gap> MagmaElement(G,6)=g;
> true
> 
> Creating the list of all elements may not be very efficient, especially
> when the group is very large. However, if the method for `Enumerator' 
> exists for such a group (see `?Enumerator), then there is another
> approach. Enumerator(G) need not to store its elements explicitly, 
> but it knows how to determine the i-th element and the position of a 
> given object. For example, this works:
> 
> gap> S:=SymmetricGroup(50);
> Sym( [ 1 .. 50 ] )
> gap> g:=Random(S);
> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
> gap> enum:=Enumerator(S);
> <enumerator of perm group>
> gap> pos:=Position(enum,g);
> 19748951512546719853008099372809900742253637283670495935197327991
> gap> enum[pos]=g;
> true
> 
> while AsSSortedList(S) will run out of memory. There are methods for 
> enumerators of various types of algebraic structures defined in the
> GAP library.
> 
> Please note that the order in which MagmaElement and Enumerator will
> sort elements of a domain sometimes may be different: the one for 
> MagmaElement is determined by the '\<' relation defined on the domain, 
> while the one for Enumerator depends on the algorithm used to enumerate
> elements of a domain of some particular type. For example,
> 
> gap> F:=FreeGroup("a","b");
> <free group on the generators [ a, b ]>
> gap> AssignGeneratorVariables(F);
> #I  Assigned the global variables [ a, b ]
> gap> G:=F/[a^32,b^2,b^-1*a*b*a];
> <fp group on the generators [ a, b ]>
> gap> First([1..Size(G)],i -> not MagmaElement(G,i)=Enumerator(G)[i]);
> 3
> gap> MagmaElement(G,3);
> b
> gap> Enumerator(G)[3];
> a^-1
> 
> However, in most applications it is not the particular order that matters,
> but the ability to determine the position of an element in the fixed 
> list of elements, and to retrieve the i-th element of that list.
> 
> Hope this helps,
> Alexander
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From sandeepr.murthy at gmail.com  Mon Feb 25 20:23:28 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Mon, 25 Feb 2013 20:23:28 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <20130225201630.GA20677@math.uchicago.edu>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
	<20130225201630.GA20677@math.uchicago.edu>
Message-ID: <512BC840.5030500@gmail.com>

Hi,

Perhaps PageSource( func ) is the function that is
relevant here.

The PageSource method, which accepts a function name,
will display its source code in a page-view:

gap> PageSource( MagmaElement );
Showing source in /Applications/GAP/gap4r5/lib/grptbl.gi (from line 162)

#############################################################################
##
#F  MagmaElement( <M>, <i> ) . . . . . . . . . .  <i>-th element of 
magma <M>
##
InstallGlobalFunction( MagmaElement, function( M, i )
     M:= AsSSortedList( M );
     if Length( M ) < i then
       return fail;
     else
       return M[i];
     fi;
end );


#############################################################################
##
#F  MagmaByMultiplicationTableCreator( <A>, <domconst> )
##
InstallGlobalFunction( MagmaByMultiplicationTableCreator,
     function( A, domconst )
     local F,      # the family of objects
           n,      # dimension of `A'
           range,  # the range `[ 1 .. n ]'
           elms,   # sorted list of elements
           M;      # the magma, result

     # Check that `A' is a valid multiplication table.
     if IsMatrix( A ) then
       n:= Length( A );
   -- <space> page, <n> next line, <b> back, <p> back line, <q> quit --

Sincerely, Sandeep.


Vipul Naik wrote:
> Hi,
>
> I'm not able to run ViewSource on GAP -- it does not recognize the command.
>
> I'm using GAP 4.5.6.
>
> Vipul
>
> * Quoting Alexander Konovalov who at 2013-02-24 20:38:44+0000 (Sun) wrote
>> On 23 Feb 2013, at 19:02, Cotton Seed<cotton at alum.mit.edu>  wrote:
>>
>>> Is there way to get the sorted index of a group element?  More
>>> specifically, let G be a group, and g an element of G.  Is there a function
>>> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
>>>
>>> Best,
>>> Cotton
>>
>> Dear Cotton,
>>
>> Let me first start with a hint how the source code of the MagmaElement
>> function may be explored to find an answer, and then suggest a more
>> efficient approach.
>>
>> First, looking at the code of MagmaElement function - this may be done by
>> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to
>> AsSSortedList:
>>
>> InstallGlobalFunction( MagmaElement, function( M, i )
>>     M:= AsSSortedList( M );
>>     if Length( M )<  i then
>>       return fail;
>>     else
>>       return M[i];
>>     fi;
>> end );
>>
>> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where
>> the latter contains all elements of M in strictly sorted order, w.r.t.
>> the canonical ordering defined on M (depending on the type of M).
>> Therefore, the index in which you're interested will be returned by
>>
>> Position( AsSSortedList( G ), g )
>>
>> For example,
>>
>> gap>  G:=SmallGroup(8,3);
>> <pc group of size 8 with 3 generators>
>> gap>  g:=Random(G);
>> f1*f3
>> gap>  s:=AsSSortedList(G);;
>> gap>  Position(s,g);
>> 6
>> gap>  MagmaElement(G,6);
>> f1*f3
>> gap>  MagmaElement(G,6)=g;
>> true
>>
>> Creating the list of all elements may not be very efficient, especially
>> when the group is very large. However, if the method for `Enumerator'
>> exists for such a group (see `?Enumerator), then there is another
>> approach. Enumerator(G) need not to store its elements explicitly,
>> but it knows how to determine the i-th element and the position of a
>> given object. For example, this works:
>>
>> gap>  S:=SymmetricGroup(50);
>> Sym( [ 1 .. 50 ] )
>> gap>  g:=Random(S);
>> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
>> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
>> gap>  enum:=Enumerator(S);
>> <enumerator of perm group>
>> gap>  pos:=Position(enum,g);
>> 19748951512546719853008099372809900742253637283670495935197327991
>> gap>  enum[pos]=g;
>> true
>>
>> while AsSSortedList(S) will run out of memory. There are methods for
>> enumerators of various types of algebraic structures defined in the
>> GAP library.
>>
>> Please note that the order in which MagmaElement and Enumerator will
>> sort elements of a domain sometimes may be different: the one for
>> MagmaElement is determined by the '\<' relation defined on the domain,
>> while the one for Enumerator depends on the algorithm used to enumerate
>> elements of a domain of some particular type. For example,
>>
>> gap>  F:=FreeGroup("a","b");
>> <free group on the generators [ a, b ]>
>> gap>  AssignGeneratorVariables(F);
>> #I  Assigned the global variables [ a, b ]
>> gap>  G:=F/[a^32,b^2,b^-1*a*b*a];
>> <fp group on the generators [ a, b ]>
>> gap>  First([1..Size(G)],i ->  not MagmaElement(G,i)=Enumerator(G)[i]);
>> 3
>> gap>  MagmaElement(G,3);
>> b
>> gap>  Enumerator(G)[3];
>> a^-1
>>
>> However, in most applications it is not the particular order that matters,
>> but the ability to determine the position of an element in the fixed
>> list of elements, and to retrieve the i-th element of that list.
>>
>> Hope this helps,
>> Alexander
>>
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From sandeepr.murthy at gmail.com  Mon Feb 25 20:38:21 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Mon, 25 Feb 2013 20:38:21 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
Message-ID: <512BCBBD.10200@gmail.com>

Hi,

If you wish to search for indices of group elements,
which are available via a sorted list using Elements( group ),
then, I think PositionSorted( sortedlist, elm ) would be
a faster way.  Here's an example for finding (1,2,3,4,5,6,7,8)
in SymmetricGroup( 8 ):

PositionSorted( Elements( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );
5914
gap> time;
31
Position( AsSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );
5914
gap> time;
386

Elements( group ) is sorted, and PositionSorted will use binary
search to find the element index, whereas Position can only use
linear search.

Sincerely, Sandeep.




Alexander Konovalov wrote:
> On 23 Feb 2013, at 19:02, Cotton Seed<cotton at alum.mit.edu>  wrote:
>
>> Is there way to get the sorted index of a group element?  More
>> specifically, let G be a group, and g an element of G.  Is there a function
>> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
>>
>> Best,
>> Cotton
>
>
> Dear Cotton,
>
> Let me first start with a hint how the source code of the MagmaElement
> function may be explored to find an answer, and then suggest a more
> efficient approach.
>
> First, looking at the code of MagmaElement function - this may be done by
> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to
> AsSSortedList:
>
> InstallGlobalFunction( MagmaElement, function( M, i )
>     M:= AsSSortedList( M );
>     if Length( M )<  i then
>       return fail;
>     else
>       return M[i];
>     fi;
> end );
>
> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where
> the latter contains all elements of M in strictly sorted order, w.r.t.
> the canonical ordering defined on M (depending on the type of M).
> Therefore, the index in which you're interested will be returned by
>
> Position( AsSSortedList( G ), g )
>
> For example,
>
> gap>  G:=SmallGroup(8,3);
> <pc group of size 8 with 3 generators>
> gap>  g:=Random(G);
> f1*f3
> gap>  s:=AsSSortedList(G);;
> gap>  Position(s,g);
> 6
> gap>  MagmaElement(G,6);
> f1*f3
> gap>  MagmaElement(G,6)=g;
> true
>
> Creating the list of all elements may not be very efficient, especially
> when the group is very large. However, if the method for `Enumerator'
> exists for such a group (see `?Enumerator), then there is another
> approach. Enumerator(G) need not to store its elements explicitly,
> but it knows how to determine the i-th element and the position of a
> given object. For example, this works:
>
> gap>  S:=SymmetricGroup(50);
> Sym( [ 1 .. 50 ] )
> gap>  g:=Random(S);
> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
> gap>  enum:=Enumerator(S);
> <enumerator of perm group>
> gap>  pos:=Position(enum,g);
> 19748951512546719853008099372809900742253637283670495935197327991
> gap>  enum[pos]=g;
> true
>
> while AsSSortedList(S) will run out of memory. There are methods for
> enumerators of various types of algebraic structures defined in the
> GAP library.
>
> Please note that the order in which MagmaElement and Enumerator will
> sort elements of a domain sometimes may be different: the one for
> MagmaElement is determined by the '\<' relation defined on the domain,
> while the one for Enumerator depends on the algorithm used to enumerate
> elements of a domain of some particular type. For example,
>
> gap>  F:=FreeGroup("a","b");
> <free group on the generators [ a, b ]>
> gap>  AssignGeneratorVariables(F);
> #I  Assigned the global variables [ a, b ]
> gap>  G:=F/[a^32,b^2,b^-1*a*b*a];
> <fp group on the generators [ a, b ]>
> gap>  First([1..Size(G)],i ->  not MagmaElement(G,i)=Enumerator(G)[i]);
> 3
> gap>  MagmaElement(G,3);
> b
> gap>  Enumerator(G)[3];
> a^-1
>
> However, in most applications it is not the particular order that matters,
> but the ability to determine the position of an element in the fixed
> list of elements, and to retrieve the i-th element of that list.
>
> Hope this helps,
> Alexander
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From alexk at mcs.st-andrews.ac.uk  Mon Feb 25 21:40:31 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 25 Feb 2013 21:40:31 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <512BCBBD.10200@gmail.com>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
	<512BCBBD.10200@gmail.com>
Message-ID: <31E9F968-AA93-4DDC-9177-6D104E592782@mcs.st-andrews.ac.uk>

Thanks for the remark about PositionSorted, Sandeep. However, I think in this example 
the difference is not coming from PositionSorted vs Position, but from AsSSortedList 
vs AsSortedList:

gap> PositionSorted( AsSSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );time;
5914
26
gap> PositionSorted( AsSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );time;
5914
371

gap> Position( AsSSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );time;
5914
25
gap> Position( AsSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );time;
5914
402

First, Elements is an outdated synonym for `AsSSortedList':

gap> Print(Elements);
function ( coll )
    Info( InfoPerformance, 2, "`Elements' is an outdated synonym for `AsSSortedList'" );
    Info( InfoPerformance, 2, "If sortedness is not required, `AsList' might be much faster!" );
    return AsSSortedList( coll );
end

Second, it is AsSortedList which takes most of the time in your example:

gap> AsSortedList( SymmetricGroup( 8 ) );;time;
362
gap> AsSSortedList( SymmetricGroup( 8 ) );;time;
24

The manual indeed says that "PositionSorted" uses binary search, whereas 
Position can in general use only linear search", however, in the case 
which we have now, Position is 'cleverer' that advised and it recognises 
that the argument is sorted. 

The remaining question is: why AsSortedList takes much longer than AsSSortedList?

The former calls SortedList which returns a new mutable and dense list:

gap> Print(ApplicableMethod(AsSortedList, [ SymmetricGroup( 8 ) ]));
function ( l )
    local  s;
    s := SortedList( l );
    MakeImmutable( s );
    return s;
end

Exploring the call stack further, you will also see calls to List and Sort,
and then finally Enumerator will be called to enumerate elements of the group.
Copying data etc. will take some time, while the latter method uses an 
immediate approach:

gap> Print(ApplicableMethod(AsSSortedList, [ SymmetricGroup( 8 ) ]));
function ( G )
    return ElementsStabChain( StabChainMutable( G ) );
end
gap> 

Best,
Alexander


On 25 Feb 2013, at 20:38, Sandeep Murthy <sandeepr.murthy at gmail.com> wrote:

> Hi,
> 
> If you wish to search for indices of group elements,
> which are available via a sorted list using Elements( group ),
> then, I think PositionSorted( sortedlist, elm ) would be
> a faster way.  Here's an example for finding (1,2,3,4,5,6,7,8)
> in SymmetricGroup( 8 ):
> 
> PositionSorted( Elements( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );
> 5914
> gap> time;
> 31
> Position( AsSortedList( SymmetricGroup( 8 ) ), (1,2,3,4,5,6,7,8) );
> 5914
> gap> time;
> 386
> 
> Elements( group ) is sorted, and PositionSorted will use binary
> search to find the element index, whereas Position can only use
> linear search.
> 
> Sincerely, Sandeep.
> 
> 
> 
> 
> Alexander Konovalov wrote:
>> On 23 Feb 2013, at 19:02, Cotton Seed<cotton at alum.mit.edu>  wrote:
>> 
>>> Is there way to get the sorted index of a group element?  More
>>> specifically, let G be a group, and g an element of G.  Is there a function
>>> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
>>> 
>>> Best,
>>> Cotton
>> 
>> 
>> Dear Cotton,
>> 
>> Let me first start with a hint how the source code of the MagmaElement
>> function may be explored to find an answer, and then suggest a more
>> efficient approach.
>> 
>> First, looking at the code of MagmaElement function - this may be done by
>> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to
>> AsSSortedList:
>> 
>> InstallGlobalFunction( MagmaElement, function( M, i )
>>    M:= AsSSortedList( M );
>>    if Length( M )<  i then
>>      return fail;
>>    else
>>      return M[i];
>>    fi;
>> end );
>> 
>> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where
>> the latter contains all elements of M in strictly sorted order, w.r.t.
>> the canonical ordering defined on M (depending on the type of M).
>> Therefore, the index in which you're interested will be returned by
>> 
>> Position( AsSSortedList( G ), g )
>> 
>> For example,
>> 
>> gap>  G:=SmallGroup(8,3);
>> <pc group of size 8 with 3 generators>
>> gap>  g:=Random(G);
>> f1*f3
>> gap>  s:=AsSSortedList(G);;
>> gap>  Position(s,g);
>> 6
>> gap>  MagmaElement(G,6);
>> f1*f3
>> gap>  MagmaElement(G,6)=g;
>> true
>> 
>> Creating the list of all elements may not be very efficient, especially
>> when the group is very large. However, if the method for `Enumerator'
>> exists for such a group (see `?Enumerator), then there is another
>> approach. Enumerator(G) need not to store its elements explicitly,
>> but it knows how to determine the i-th element and the position of a
>> given object. For example, this works:
>> 
>> gap>  S:=SymmetricGroup(50);
>> Sym( [ 1 .. 50 ] )
>> gap>  g:=Random(S);
>> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
>> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
>> gap>  enum:=Enumerator(S);
>> <enumerator of perm group>
>> gap>  pos:=Position(enum,g);
>> 19748951512546719853008099372809900742253637283670495935197327991
>> gap>  enum[pos]=g;
>> true
>> 
>> while AsSSortedList(S) will run out of memory. There are methods for
>> enumerators of various types of algebraic structures defined in the
>> GAP library.
>> 
>> Please note that the order in which MagmaElement and Enumerator will
>> sort elements of a domain sometimes may be different: the one for
>> MagmaElement is determined by the '\<' relation defined on the domain,
>> while the one for Enumerator depends on the algorithm used to enumerate
>> elements of a domain of some particular type. For example,
>> 
>> gap>  F:=FreeGroup("a","b");
>> <free group on the generators [ a, b ]>
>> gap>  AssignGeneratorVariables(F);
>> #I  Assigned the global variables [ a, b ]
>> gap>  G:=F/[a^32,b^2,b^-1*a*b*a];
>> <fp group on the generators [ a, b ]>
>> gap>  First([1..Size(G)],i ->  not MagmaElement(G,i)=Enumerator(G)[i]);
>> 3
>> gap>  MagmaElement(G,3);
>> b
>> gap>  Enumerator(G)[3];
>> a^-1
>> 
>> However, in most applications it is not the particular order that matters,
>> but the ability to determine the position of an element in the fixed
>> list of elements, and to retrieve the i-th element of that list.
>> 
>> Hope this helps,
>> Alexander
>> 
>> 
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum



From sandeepr.murthy at gmail.com  Mon Feb 25 21:42:17 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Mon, 25 Feb 2013 21:42:17 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <20130225212901.GA23932@math.uchicago.edu>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
	<20130225201630.GA20677@math.uchicago.edu>
	<512BC840.5030500@gmail.com>
	<DA07A735-161A-43E1-88C8-5E19754EEE56@mcs.st-andrews.ac.uk>
	<20130225212901.GA23932@math.uchicago.edu>
Message-ID: <512BDAB9.4030105@gmail.com>

Hi,

I don't think there is a built-in GAP function called ViewSource, it 
must be user-defined/compiled.

gap> FilenameFunc( ViewSource );
Error, Variable: 'ViewSource' must have a value
not in any function at line 28 of *stdin*

The kernel should be read-only, so I guess that is why PageSource does 
not work for kernel functions.

Sincerely, Sandeep.

Vipul Naik wrote:
> Thank you to both Sandeep Murthy and Alexander Konovalov. PageSource
> does not seem to work for many functions that GAP calls kernel
> functions (such as IsNormal). Does ViewSource work for these, or is
> there no way to view the source code for these?
>
> Vipul
>
> * Quoting Alexander Konovalov who at 2013-02-25 20:36:13+0000 (Mon) wrote
>> yes, thanks for correcting this. I actually have ViewSource defined
>> in my local gaprc file since pre-PageSource times (and actually opens
>> the file for editing, not for viewing). PageSource is the name to use
>> - sorry for giving a hint in the wrong direction :)
>>
>> Best wishes,
>> Alex
>>
>>
>> On 25 Feb 2013, at 20:23, Sandeep Murthy<sandeepr.murthy at gmail.com>  wrote:
>>
>>> Hi,
>>>
>>> Perhaps PageSource( func ) is the function that is
>>> relevant here.
>>>
>>> The PageSource method, which accepts a function name,
>>> will display its source code in a page-view:
>>>
>>> gap>  PageSource( MagmaElement );
>>> Showing source in /Applications/GAP/gap4r5/lib/grptbl.gi (from line 162)
>>>
>>> #############################################################################
>>> ##
>>> #F  MagmaElement(<M>,<i>  ) . . . . . . . . . .<i>-th element of magma<M>
>>> ##
>>> InstallGlobalFunction( MagmaElement, function( M, i )
>>>     M:= AsSSortedList( M );
>>>     if Length( M )<  i then
>>>       return fail;
>>>     else
>>>       return M[i];
>>>     fi;
>>> end );
>>>
>>>
>>> #############################################################################
>>> ##
>>> #F  MagmaByMultiplicationTableCreator(<A>,<domconst>  )
>>> ##
>>> InstallGlobalFunction( MagmaByMultiplicationTableCreator,
>>>     function( A, domconst )
>>>     local F,      # the family of objects
>>>           n,      # dimension of `A'
>>>           range,  # the range `[ 1 .. n ]'
>>>           elms,   # sorted list of elements
>>>           M;      # the magma, result
>>>
>>>     # Check that `A' is a valid multiplication table.
>>>     if IsMatrix( A ) then
>>>       n:= Length( A );
>>>   --<space>  page,<n>  next line,<b>  back,<p>  back line,<q>  quit --
>>>
>>> Sincerely, Sandeep.
>>>
>>>
>>> Vipul Naik wrote:
>>>> Hi,
>>>>
>>>> I'm not able to run ViewSource on GAP -- it does not recognize the command.
>>>>
>>>> I'm using GAP 4.5.6.
>>>>
>>>> Vipul
>>>>
>>>> * Quoting Alexander Konovalov who at 2013-02-24 20:38:44+0000 (Sun) wrote
>>>>> On 23 Feb 2013, at 19:02, Cotton Seed<cotton at alum.mit.edu>   wrote:
>>>>>
>>>>>> Is there way to get the sorted index of a group element?  More
>>>>>> specifically, let G be a group, and g an element of G.  Is there a function
>>>>>> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
>>>>>>
>>>>>> Best,
>>>>>> Cotton
>>>>> Dear Cotton,
>>>>>
>>>>> Let me first start with a hint how the source code of the MagmaElement
>>>>> function may be explored to find an answer, and then suggest a more
>>>>> efficient approach.
>>>>>
>>>>> First, looking at the code of MagmaElement function - this may be done by
>>>>> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to
>>>>> AsSSortedList:
>>>>>
>>>>> InstallGlobalFunction( MagmaElement, function( M, i )
>>>>>     M:= AsSSortedList( M );
>>>>>     if Length( M )<   i then
>>>>>       return fail;
>>>>>     else
>>>>>       return M[i];
>>>>>     fi;
>>>>> end );
>>>>>
>>>>> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where
>>>>> the latter contains all elements of M in strictly sorted order, w.r.t.
>>>>> the canonical ordering defined on M (depending on the type of M).
>>>>> Therefore, the index in which you're interested will be returned by
>>>>>
>>>>> Position( AsSSortedList( G ), g )
>>>>>
>>>>> For example,
>>>>>
>>>>> gap>   G:=SmallGroup(8,3);
>>>>> <pc group of size 8 with 3 generators>
>>>>> gap>   g:=Random(G);
>>>>> f1*f3
>>>>> gap>   s:=AsSSortedList(G);;
>>>>> gap>   Position(s,g);
>>>>> 6
>>>>> gap>   MagmaElement(G,6);
>>>>> f1*f3
>>>>> gap>   MagmaElement(G,6)=g;
>>>>> true
>>>>>
>>>>> Creating the list of all elements may not be very efficient, especially
>>>>> when the group is very large. However, if the method for `Enumerator'
>>>>> exists for such a group (see `?Enumerator), then there is another
>>>>> approach. Enumerator(G) need not to store its elements explicitly,
>>>>> but it knows how to determine the i-th element and the position of a
>>>>> given object. For example, this works:
>>>>>
>>>>> gap>   S:=SymmetricGroup(50);
>>>>> Sym( [ 1 .. 50 ] )
>>>>> gap>   g:=Random(S);
>>>>> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
>>>>> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
>>>>> gap>   enum:=Enumerator(S);
>>>>> <enumerator of perm group>
>>>>> gap>   pos:=Position(enum,g);
>>>>> 19748951512546719853008099372809900742253637283670495935197327991
>>>>> gap>   enum[pos]=g;
>>>>> true
>>>>>
>>>>> while AsSSortedList(S) will run out of memory. There are methods for
>>>>> enumerators of various types of algebraic structures defined in the
>>>>> GAP library.
>>>>>
>>>>> Please note that the order in which MagmaElement and Enumerator will
>>>>> sort elements of a domain sometimes may be different: the one for
>>>>> MagmaElement is determined by the '\<' relation defined on the domain,
>>>>> while the one for Enumerator depends on the algorithm used to enumerate
>>>>> elements of a domain of some particular type. For example,
>>>>>
>>>>> gap>   F:=FreeGroup("a","b");
>>>>> <free group on the generators [ a, b ]>
>>>>> gap>   AssignGeneratorVariables(F);
>>>>> #I  Assigned the global variables [ a, b ]
>>>>> gap>   G:=F/[a^32,b^2,b^-1*a*b*a];
>>>>> <fp group on the generators [ a, b ]>
>>>>> gap>   First([1..Size(G)],i ->   not MagmaElement(G,i)=Enumerator(G)[i]);
>>>>> 3
>>>>> gap>   MagmaElement(G,3);
>>>>> b
>>>>> gap>   Enumerator(G)[3];
>>>>> a^-1
>>>>>
>>>>> However, in most applications it is not the particular order that matters,
>>>>> but the ability to determine the position of an element in the fixed
>>>>> list of elements, and to retrieve the i-th element of that list.
>>>>>
>>>>> Hope this helps,
>>>>> Alexander
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Forum mailing list
>>>>> Forum at mail.gap-system.org
>>>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>> _______________________________________________
>>>> Forum mailing list
>>>> Forum at mail.gap-system.org
>>>> http://mail.gap-system.org/mailman/listinfo/forum


From alexk at mcs.st-andrews.ac.uk  Mon Feb 25 21:50:19 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 25 Feb 2013 21:50:19 +0000
Subject: [GAP Forum] sorted index of group element
In-Reply-To: <512BDAB9.4030105@gmail.com>
References: <CAEjWs7ofjFvP5cgaXG2Ac0OhiJne0R0N2KRDvJEFyUmUCH9RDA@mail.gmail.com>
	<06E94901-BCB5-43A8-A2F8-09A1260C0134@mcs.st-andrews.ac.uk>
	<20130225201630.GA20677@math.uchicago.edu>
	<512BC840.5030500@gmail.com>
	<DA07A735-161A-43E1-88C8-5E19754EEE56@mcs.st-andrews.ac.uk>
	<20130225212901.GA23932@math.uchicago.edu>
	<512BDAB9.4030105@gmail.com>
Message-ID: <05E14407-398B-45CA-81B6-491664E83FE6@mcs.st-andrews.ac.uk>

On 25 Feb 2013, at 21:42, Sandeep Murthy <sandeepr.murthy at gmail.com> wrote:

> Hi,
> 
> I don't think there is a built-in GAP function called ViewSource, it must be user-defined/compiled.

Yes, sorry, I gave the wrong name by mistake (I had it defined locally in my gaprc file with slightly 
different behaviour, since I was using it before PageSource was introduced in the released version of 
the system). Please use 'PageSource' instead.
> 
> gap> FilenameFunc( ViewSource );
> Error, Variable: 'ViewSource' must have a value
> not in any function at line 28 of *stdin*
> 
> The kernel should be read-only, so I guess that is why PageSource does not work for kernel functions.

The argument of PageSource must be a function, while IsNormal is an operation. 
This is how it works:

gap> IsNormal;                                                        
<Operation "IsNormal">
gap> ApplicableMethod(IsNormal, [ SymmetricGroup( 8 ), AlternatingGroup(8) ]);
function( super, sub ) ... end
gap> PageSource(last);
Showing source in /Users/alexk/gap4r6p2/lib/domain.gd (from line 429)
   APPEND_LIST_INTR( str, name );
   APPEND_LIST_INTR( str, "InParent" );
   InstallMethod( func,
       str,
       [ superreq, subreq ],
       function( super, sub )
       local value;
       if HasParent( sub ) and IsIdenticalObj( super, Parent( sub ) ) then
         value:= attr( sub );
       else
         value:= oper( super, sub );
       fi;
       return value;
       end );

   # Install the method for the attribute that calls the operation.
   str:= "method that calls the two-argument operation ";
   APPEND_LIST_INTR( str, name );
   APPEND_LIST_INTR( str, "Op" );
   InstallMethod( attr, str, [ subreq and HasParent ],
           D -> oper( Parent( D ), D ) );
end );


The manual have more examples:


 This  shows  the  file containing the source code of the function or method func in a pager (see
 Pager (2.4-1)). The display starts at a line shortly before the code of func.

 This  function  works if FilenameFunc(func) returns the name of a proper file. In that case this
 filename  and  the  position of the function definition are also printed. Otherwise the function
 indicates  that  the  source  is not available (for example this happens for functions which are
 implemented in the GAP C-kernel).

 Usage examples:
 met := ApplicableMethod(\^, [(1,2),2743527]); PageSource(met);
 PageSource(Combinations);
 ct:=CharacterTable(Group((1,2,3))); 
 met := ApplicableMethod(Size,[ct]); PageSource(met); 

HTH,
Alex



> 
> Vipul Naik wrote:
>> Thank you to both Sandeep Murthy and Alexander Konovalov. PageSource
>> does not seem to work for many functions that GAP calls kernel
>> functions (such as IsNormal). Does ViewSource work for these, or is
>> there no way to view the source code for these?
>> 
>> Vipul
>> 
>> * Quoting Alexander Konovalov who at 2013-02-25 20:36:13+0000 (Mon) wrote
>>> yes, thanks for correcting this. I actually have ViewSource defined
>>> in my local gaprc file since pre-PageSource times (and actually opens
>>> the file for editing, not for viewing). PageSource is the name to use
>>> - sorry for giving a hint in the wrong direction :)
>>> 
>>> Best wishes,
>>> Alex
>>> 
>>> 
>>> On 25 Feb 2013, at 20:23, Sandeep Murthy<sandeepr.murthy at gmail.com>  wrote:
>>> 
>>>> Hi,
>>>> 
>>>> Perhaps PageSource( func ) is the function that is
>>>> relevant here.
>>>> 
>>>> The PageSource method, which accepts a function name,
>>>> will display its source code in a page-view:
>>>> 
>>>> gap>  PageSource( MagmaElement );
>>>> Showing source in /Applications/GAP/gap4r5/lib/grptbl.gi (from line 162)
>>>> 
>>>> #############################################################################
>>>> ##
>>>> #F  MagmaElement(<M>,<i>  ) . . . . . . . . . .<i>-th element of magma<M>
>>>> ##
>>>> InstallGlobalFunction( MagmaElement, function( M, i )
>>>>    M:= AsSSortedList( M );
>>>>    if Length( M )<  i then
>>>>      return fail;
>>>>    else
>>>>      return M[i];
>>>>    fi;
>>>> end );
>>>> 
>>>> 
>>>> #############################################################################
>>>> ##
>>>> #F  MagmaByMultiplicationTableCreator(<A>,<domconst>  )
>>>> ##
>>>> InstallGlobalFunction( MagmaByMultiplicationTableCreator,
>>>>    function( A, domconst )
>>>>    local F,      # the family of objects
>>>>          n,      # dimension of `A'
>>>>          range,  # the range `[ 1 .. n ]'
>>>>          elms,   # sorted list of elements
>>>>          M;      # the magma, result
>>>> 
>>>>    # Check that `A' is a valid multiplication table.
>>>>    if IsMatrix( A ) then
>>>>      n:= Length( A );
>>>>  --<space>  page,<n>  next line,<b>  back,<p>  back line,<q>  quit --
>>>> 
>>>> Sincerely, Sandeep.
>>>> 
>>>> 
>>>> Vipul Naik wrote:
>>>>> Hi,
>>>>> 
>>>>> I'm not able to run ViewSource on GAP -- it does not recognize the command.
>>>>> 
>>>>> I'm using GAP 4.5.6.
>>>>> 
>>>>> Vipul
>>>>> 
>>>>> * Quoting Alexander Konovalov who at 2013-02-24 20:38:44+0000 (Sun) wrote
>>>>>> On 23 Feb 2013, at 19:02, Cotton Seed<cotton at alum.mit.edu>   wrote:
>>>>>> 
>>>>>>> Is there way to get the sorted index of a group element?  More
>>>>>>> specifically, let G be a group, and g an element of G.  Is there a function
>>>>>>> that will give me the index i so that MagmaElement(G,i) = g?  Thanks!
>>>>>>> 
>>>>>>> Best,
>>>>>>> Cotton
>>>>>> Dear Cotton,
>>>>>> 
>>>>>> Let me first start with a hint how the source code of the MagmaElement
>>>>>> function may be explored to find an answer, and then suggest a more
>>>>>> efficient approach.
>>>>>> 
>>>>>> First, looking at the code of MagmaElement function - this may be done by
>>>>>> typing `ViewSource(MagmaElement);' in GAP - you may spot the call to
>>>>>> AsSSortedList:
>>>>>> 
>>>>>> InstallGlobalFunction( MagmaElement, function( M, i )
>>>>>>    M:= AsSSortedList( M );
>>>>>>    if Length( M )<   i then
>>>>>>      return fail;
>>>>>>    else
>>>>>>      return M[i];
>>>>>>    fi;
>>>>>> end );
>>>>>> 
>>>>>> Thus, MagmaElement returns the i-th element of AsSSortedList(M), where
>>>>>> the latter contains all elements of M in strictly sorted order, w.r.t.
>>>>>> the canonical ordering defined on M (depending on the type of M).
>>>>>> Therefore, the index in which you're interested will be returned by
>>>>>> 
>>>>>> Position( AsSSortedList( G ), g )
>>>>>> 
>>>>>> For example,
>>>>>> 
>>>>>> gap>   G:=SmallGroup(8,3);
>>>>>> <pc group of size 8 with 3 generators>
>>>>>> gap>   g:=Random(G);
>>>>>> f1*f3
>>>>>> gap>   s:=AsSSortedList(G);;
>>>>>> gap>   Position(s,g);
>>>>>> 6
>>>>>> gap>   MagmaElement(G,6);
>>>>>> f1*f3
>>>>>> gap>   MagmaElement(G,6)=g;
>>>>>> true
>>>>>> 
>>>>>> Creating the list of all elements may not be very efficient, especially
>>>>>> when the group is very large. However, if the method for `Enumerator'
>>>>>> exists for such a group (see `?Enumerator), then there is another
>>>>>> approach. Enumerator(G) need not to store its elements explicitly,
>>>>>> but it knows how to determine the i-th element and the position of a
>>>>>> given object. For example, this works:
>>>>>> 
>>>>>> gap>   S:=SymmetricGroup(50);
>>>>>> Sym( [ 1 .. 50 ] )
>>>>>> gap>   g:=Random(S);
>>>>>> (1,40,16,24,8,21,19,39,20,12,28,6)(2,5,49,3,45,4,30,25,13,11,47,44,36,9,50,43,
>>>>>> 18,32)(7,46,22,15,35,41)(10,14,48,26,17)(23,42,33,29,37,38,27)
>>>>>> gap>   enum:=Enumerator(S);
>>>>>> <enumerator of perm group>
>>>>>> gap>   pos:=Position(enum,g);
>>>>>> 19748951512546719853008099372809900742253637283670495935197327991
>>>>>> gap>   enum[pos]=g;
>>>>>> true
>>>>>> 
>>>>>> while AsSSortedList(S) will run out of memory. There are methods for
>>>>>> enumerators of various types of algebraic structures defined in the
>>>>>> GAP library.
>>>>>> 
>>>>>> Please note that the order in which MagmaElement and Enumerator will
>>>>>> sort elements of a domain sometimes may be different: the one for
>>>>>> MagmaElement is determined by the '\<' relation defined on the domain,
>>>>>> while the one for Enumerator depends on the algorithm used to enumerate
>>>>>> elements of a domain of some particular type. For example,
>>>>>> 
>>>>>> gap>   F:=FreeGroup("a","b");
>>>>>> <free group on the generators [ a, b ]>
>>>>>> gap>   AssignGeneratorVariables(F);
>>>>>> #I  Assigned the global variables [ a, b ]
>>>>>> gap>   G:=F/[a^32,b^2,b^-1*a*b*a];
>>>>>> <fp group on the generators [ a, b ]>
>>>>>> gap>   First([1..Size(G)],i ->   not MagmaElement(G,i)=Enumerator(G)[i]);
>>>>>> 3
>>>>>> gap>   MagmaElement(G,3);
>>>>>> b
>>>>>> gap>   Enumerator(G)[3];
>>>>>> a^-1
>>>>>> 
>>>>>> However, in most applications it is not the particular order that matters,
>>>>>> but the ability to determine the position of an element in the fixed
>>>>>> list of elements, and to retrieve the i-th element of that list.
>>>>>> 
>>>>>> Hope this helps,
>>>>>> Alexander
>>>>>> 
>>>>>> 
>>>>>> _______________________________________________
>>>>>> Forum mailing list
>>>>>> Forum at mail.gap-system.org
>>>>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>>> _______________________________________________
>>>>> Forum mailing list
>>>>> Forum at mail.gap-system.org
>>>>> http://mail.gap-system.org/mailman/listinfo/forum



From fuat.erdem at metu.edu.tr  Mon Feb 25 18:56:15 2013
From: fuat.erdem at metu.edu.tr (Fuat Erdem)
Date: Mon, 25 Feb 2013 20:56:15 +0200
Subject: [GAP Forum] md5 sum needed
In-Reply-To: <FC62F680364248A5B18E325B5B06A737@carnia>
References: <FC62F680364248A5B18E325B5B06A737@carnia>
Message-ID: <20130225205615.106744dhr66o4o9b@horde.metu.edu.tr>

Dear Roberto,

I have double checked mine and they are as follows:

md5: 0c5d44f306f3013d1da7f22a0cc37398
sha1: 836a7de6d2ddbb4c4f1e67e17561576ea718a0bb

I would be pleased to know if they agree with yours.

Best regards,
Fuat.


Alinti Roberto R?dina <roberto.radina at tiscali.it>

> Dear forum,
> I need md5 or sha1 sums of  gap4r6p2_2013_02_02-01_00-win.zip  for a  
> check. It is the file for installing the last version of GAP.
> Can someone post it here? _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



____

Fuat Erdem
Department of Mathematics
Middle East Technical University, Ankara, Turkey
Office: Z-37
Phone: 0090 312 210 5386
URL: http://www.metu.edu.tr/~efuat/



From a.j.t.al-juburie at newcastle.ac.uk  Mon Feb 25 20:03:55 2013
From: a.j.t.al-juburie at newcastle.ac.uk (Abdulsatar Al-Juburie)
Date: Mon, 25 Feb 2013 20:03:55 +0000
Subject: [GAP Forum] Presentation
Message-ID: <5CA877F40086AF4BA25CA7791864174403B4F2@EXMBCT01.campus.ncl.ac.uk>

Dear Forum,

 I got by using GAP two  presentations for the automorphism of group of the free Abelian group of rank n. . However, I ask  if there is any way in GAP to let me know if these two presentations are isomorphic.
  
I would be appreciated if you could help me in this matter.

Best Regards,

Abdulsatar





From roberto.radina at tiscali.it  Tue Feb 26 13:30:22 2013
From: roberto.radina at tiscali.it (=?iso-8859-9?Q?Roberto_R=E0dina?=)
Date: Tue, 26 Feb 2013 14:30:22 +0100
Subject: [GAP Forum] md5 sum needed
References: <FC62F680364248A5B18E325B5B06A737@carnia>
	<20130225205615.106744dhr66o4o9b@horde.metu.edu.tr>
Message-ID: <5601D961A7C1483AB32E7D878345D561@carnia>

> md5: 0c5d44f306f3013d1da7f22a0cc37398
> sha1: 836a7de6d2ddbb4c4f1e67e17561576ea718a0bb
> 
> I would be pleased to know if they agree with yours.

yes, they (both) agree!



From hebert.perez at gmail.com  Tue Feb 26 15:14:36 2013
From: hebert.perez at gmail.com (=?ISO-8859-1?B?SGViZXJ0IFDpcmV6LVJvc+lz?=)
Date: Tue, 26 Feb 2013 16:14:36 +0100
Subject: [GAP Forum] Presentation
In-Reply-To: <5CA877F40086AF4BA25CA7791864174403B4F2@EXMBCT01.campus.ncl.ac.uk>
References: <5CA877F40086AF4BA25CA7791864174403B4F2@EXMBCT01.campus.ncl.ac.uk>
Message-ID: <CAOjorGNgT=_y8fWguT60AOtithDsUDvf7yT39A6SJi2D0UQKRg@mail.gmail.com>

Dear Abdulsatar,

I do not quite understand your question. I suppose that you want to
know whether the two groups specified by both presentations are
isomorphic. But you say that both presentations are of the same group,
namely the automorphism group of the free Abelian group of rank n. If
that is so, then obviously both groups are isomorphic, since they are
the same group !!

On the other hand, if you want to know, for two arbitrary
presentations P_1 and P_2, whether the corresponding groups G_1 and
G_2 are isomorphic, then it is impossible in general. This is one of
the three problems stated by Max Dehn in 1911, which turned out to be
unsolvable. The other two are the word problem and the conjugacy
problem. It is possible, however, to solve the problem for some
special  classes of presentations.

I hope this answers your questions.

Best regards,

Hebert Perez-Roses
The University of Lleida, Spain




2013/2/25 Abdulsatar Al-Juburie <a.j.t.al-juburie at newcastle.ac.uk>:
> Dear Forum,
>
>  I got by using GAP two  presentations for the automorphism of group of the free Abelian group of rank n. . However, I ask  if there is any way in GAP to let me know if these two presentations are isomorphic.
>
> I would be appreciated if you could help me in this matter.
>
> Best Regards,
>
> Abdulsatar
>
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From hulpke at math.colostate.edu  Tue Feb 26 15:46:39 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Tue, 26 Feb 2013 08:46:39 -0700
Subject: [GAP Forum] Presentation
In-Reply-To: <5CA877F40086AF4BA25CA7791864174403B4F2@EXMBCT01.campus.ncl.ac.uk>
References: <5CA877F40086AF4BA25CA7791864174403B4F2@EXMBCT01.campus.ncl.ac.uk>
Message-ID: <16CE0C07-9D5E-4EA8-95CB-F37552FD30C6@math.colostate.edu>



Dear Forum, Dear Abulsatar,

> I got by using GAP two  presentations for the automorphism of group of the free Abelian group of rank n. . However, I ask  if there is any way in GAP to let me know if these two presentations are isomorphic.

In the generic case of testing for such isomorphism the best computational approach I am aware of is:

@incollection {MR1200282,
    AUTHOR = {Holt, D. F. and Rees, Sarah},
     TITLE = {Testing for isomorphism between finitely presented groups},
 BOOKTITLE = {Groups, combinatorics \& geometry ({D}urham, 1990)},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {165},
     PAGES = {459--475},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {1992},
   MRCLASS = {20F05 (20-04)},
  MRNUMBER = {1200282 (94a:20051)},
MRREVIEWER = {Colin M. Campbell},
       DOI = {10.1017/CBO9780511629259.040},
       URL = {http://dx.doi.org/10.1017/CBO9780511629259.040},
}

(As you are in Newcastle I suppose you know this already.) This is not built into GAP as one turn-key routine, but some of the underlying functionality is there that could help building such a routine.

In your case however you have a particular group. I would try to find isomorphisms from both presentations to a representation as matrices in Z^{n x n} first. This will give you a guess for an isomorphism.

Then (assuming that the groups are G=<g1,..gn| rels1> and H=<h1,..hm|rels2> and phi:G->H is the guessed isomorphism)
form a new group 
X=<g1,..,gn,h1,...hn|rels1, rels2, g1=phi(g1),g2=phi(g2),...>
where phi(g1) is the word in the h1 that gives the image.

If phi indeed is a isomorphism, you can use Tietze transformations to eliminate either all g's or all h's from the presentation and end up with the presentations for H and G respectively. (It might be easier for one direction to use phi^-1 instead to define what the h's are in terms of the g's.)

Best,

   Alexander

-- Alexander Hulpke, Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke




From nik9kr at gmail.com  Wed Feb 27 13:55:39 2013
From: nik9kr at gmail.com (NIK NIK)
Date: Wed, 27 Feb 2013 17:55:39 +0400
Subject: [GAP Forum] mistake with Union
Message-ID: <CADEjdyd2EPBv1gii3MfuRb9LHL5GRFrdRD3BCsUkiPZR38feNA@mail.gmail.com>

 Dear forum

 I 've find mistake with Union.
++++++++++++++++++++++++++++++++++++++++++++++
gap> r := [ [ 2 ], [  ], [ 1, 3 ], [ 4 ] ];
[ [ 2 ], [  ], [ 1, 3 ], [ 4 ] ]
gap> Union( r{[]} );
[  ]
gap>st:= Union( r{[1,3]} );
[ 1 .. 3 ]
++++++++++++++++++++++++++++++++++++++++++++++

 But I need the all elements in list st:=[1,2,3].

This mistake makes many troubles in package "Automata".
++++++++++++++++++++++++++++++++++++++++++++++
gap> Display(rb1);
   |  1       2       3          4
-----------------------------------------
 a | [ 2 ]           [ 1, 3 ]   [ 4 ]
 b | [ 3 ]   [ 1 ]              [ 2, 4 ]
Initial states:  [ 1, 3 ]
Accepting state: [ 1 ]
gap> ddrb1:=NFAtoDFA(rb1);
#I  Determinized 4 to 5
< deterministic automaton on 2 letters with 5 states >
gap> Display(ddrb1);
   |  1  2  3  4  5
--------------------
 a |  2  2  1  2  5
 b |  3  4  5  3  5
Initial state:    [ 1 ]
Accepting states: [ 1, 2, 4 ]
+++++++++++++++++++++++++++++++++++++++++++++++


Thank you.
Nikolai Krainyukov


From mdelgado at fc.up.pt  Wed Feb 27 18:59:15 2013
From: mdelgado at fc.up.pt (Manuel Delgado)
Date: Wed, 27 Feb 2013 18:59:15 +0000
Subject: [GAP Forum] mistake with Union
In-Reply-To: <CADEjdyd2EPBv1gii3MfuRb9LHL5GRFrdRD3BCsUkiPZR38feNA@mail.gmail.com>
References: <CADEjdyd2EPBv1gii3MfuRb9LHL5GRFrdRD3BCsUkiPZR38feNA@mail.gmail.com>
Message-ID: <512E5783.7040908@fc.up.pt>

Dear Nikolai,

As the results in your message are those that I would expect, I am 
perhaps missing something. If this is the case, please let me know.

Unless I am mistaken, the "union" produces and displays the correct 
result. Note that
  gap> [1..3]=[1,2,3];
true

Assuming that the function MinimalizedAut works correctly, the automata 
rb1 and ddrb1 are equivalent:
gap> 
rb1=Automaton("nondet",4,2,[[[2],[],[1,3],[4]],[[3],[1],[],[2,4]]],[1,3],[1]);;
gap> min := MinimalizedAut(rb1);
< deterministic automaton on 2 letters with 4 states >
gap> Display(min);
    |  1  2  3  4
-----------------
  a |  2  4  3  4
  b |  3  1  3  2
Initial state:    [ 2 ]
Accepting states: [ 2, 4 ]
gap>
gap> ddrb1 := NFAtoDFA(rb1);
< deterministic automaton on 2 letters with 5 states >
gap> mind := MinimalizedAut(ddrb1);
< deterministic automaton on 2 letters with 4 states >
gap> Display(mind);
    |  1  2  3  4
-----------------
  a |  2  4  3  4
  b |  3  1  3  2
Initial state:    [ 2 ]
Accepting states: [ 2, 4 ]
gap>

The way the deterministic automaton is computed from the non 
deterministic one is perhaps different from the one you would expect, 
but, as far as I can remember, it is exactly as described in the 
automata package manual (which refers the power set construction and 
points to a report easily obtainable from the internet.)

Hope this helps.
Best,
Manuel Delgado

On 02/27/2013 01:55 PM, NIK NIK wrote:
>   Dear forum
>
>   I 've find mistake with Union.
> ++++++++++++++++++++++++++++++++++++++++++++++
> gap> r := [ [ 2 ], [  ], [ 1, 3 ], [ 4 ] ];
> [ [ 2 ], [  ], [ 1, 3 ], [ 4 ] ]
> gap> Union( r{[]} );
> [  ]
> gap>st:= Union( r{[1,3]} );
> [ 1 .. 3 ]
> ++++++++++++++++++++++++++++++++++++++++++++++
>
>   But I need the all elements in list st:=[1,2,3].
>
> This mistake makes many troubles in package "Automata".
> ++++++++++++++++++++++++++++++++++++++++++++++
> gap> Display(rb1);
>     |  1       2       3          4
> -----------------------------------------
>   a | [ 2 ]           [ 1, 3 ]   [ 4 ]
>   b | [ 3 ]   [ 1 ]              [ 2, 4 ]
> Initial states:  [ 1, 3 ]
> Accepting state: [ 1 ]
> gap> ddrb1:=NFAtoDFA(rb1);
> #I  Determinized 4 to 5
> < deterministic automaton on 2 letters with 5 states >
> gap> Display(ddrb1);
>     |  1  2  3  4  5
> --------------------
>   a |  2  2  1  2  5
>   b |  3  4  5  3  5
> Initial state:    [ 1 ]
> Accepting states: [ 1, 2, 4 ]
> +++++++++++++++++++++++++++++++++++++++++++++++
>
>
> Thank you.
> Nikolai Krainyukov
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From e.obrien at auckland.ac.nz  Fri Mar  1 00:11:47 2013
From: e.obrien at auckland.ac.nz (Eamonn O'Brien)
Date: Fri, 01 Mar 2013 13:11:47 +1300
Subject: [GAP Forum] Second announcement: Workshop at Braunschweig, May 21-24
Message-ID: <512FF243.3050601@auckland.ac.nz>

Dear Colleagues:

We will run a workshop entitled
"Questions, Algorithms, and Computations in Abstract Group Theory",
at the University of Braunschweig from May 21-24, 2013.

Our aim is to combine researchers from the areas of group theory,
computer science and algebraic geometry to obtain new advances
in the algorithmic theory of abstract groups.

More details about the workshop, including the list of speakers,
can be found at http://www.icm.tu-bs.de/ag_algebra/ws-qac

Best wishes.
Eamonn O'Brien


From roberto.radina at tiscali.it  Tue Mar 12 20:27:37 2013
From: roberto.radina at tiscali.it (=?iso-8859-1?Q?Roberto_R=E0dina?=)
Date: Tue, 12 Mar 2013 21:27:37 +0100
Subject: [GAP Forum] command line option -N
Message-ID: <D0E2E1A711AC4F9AAEC132C86AFAE642@carnia>

Dear forum,

the manual says:

"So if you have installed GAP yourself then you should think about creating
a workspace file immediately after you have started GAP with the command
line option -N,"

"Certain Boolean options (-b, -q, -e, -r, -A, -D, -M, -N, -T, -X, -Y) toggle
the current value"

but the point is: what is the effect of the -N option? My workspace was
created without it but it seems to work...





From alexk at mcs.st-andrews.ac.uk  Tue Mar 12 21:20:12 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Tue, 12 Mar 2013 21:20:12 +0000
Subject: [GAP Forum] command line option -N
In-Reply-To: <D0E2E1A711AC4F9AAEC132C86AFAE642@carnia>
References: <D0E2E1A711AC4F9AAEC132C86AFAE642@carnia>
Message-ID: <AFC4B1D4-84F7-4582-98FE-9C2139F90284@mcs.st-andrews.ac.uk>

Dear Roberto,

On 12 Mar 2013, at 20:27, Roberto R?dina <roberto.radina at tiscali.it> wrote:

> Dear forum,
> 
> the manual says:
> 
> "So if you have installed GAP yourself then you should think about creating
> a workspace file immediately after you have started GAP with the command
> line option -N,"
> 
> "Certain Boolean options (-b, -q, -e, -r, -A, -D, -M, -N, -T, -X, -Y) toggle
> the current value"
> 
> but the point is: what is the effect of the -N option? My workspace was
> created without it but it seems to work...

The -N option was used in GAP 4.4 to suppress the reading of any existing 
completion files. The mechanism of using completion files has been withdrawn
since GAP 4.5, so this option became undocumented. Thanks for pointing out
on these relic references to the -N option - we should clean them up.

Thus, I suppose that your workspace works fine. 

Best wishes,
Alexander

From gordon.royle at uwa.edu.au  Wed Mar 13 07:52:30 2013
From: gordon.royle at uwa.edu.au (Gordon Royle)
Date: Wed, 13 Mar 2013 15:52:30 +0800
Subject: [GAP Forum] Can I safely identify the moved points of PGL(n,
	2) with GF(2)^n\0?
Message-ID: <BE1DFC18-672C-4B12-8FBD-A93FDF1A41AB@uwa.edu.au>

If I use the groups

PGL(n,2)

in GAP, then is it guaranteed that the set permuted by this group can be identified in the obvious fashion with GF(2)^n \ 0?

What I mean is that it would be natural to assign the non-zero vectors in GF(2)^n\0 to integers in the range {1,2,?,2^n-1} simply by treating a 0/1 vector as the binary representation of an integer.

0000001 -> 1
0000010 -> 2
0000011 -> 3

and so on.

>From my experiments, GAP *appears* to behave consistently with this (for example, if I check the stabiliser of [x, y, x ^ y] where x ^ y is bitwise binary XOR, then it is always the correct thing).

But can I rely on it?




Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>














From neunhoef at mcs.st-and.ac.uk  Wed Mar 13 10:08:32 2013
From: neunhoef at mcs.st-and.ac.uk (Max Neunhoeffer)
Date: Wed, 13 Mar 2013 10:08:32 +0000
Subject: [GAP Forum] Can I safely identify the moved points of PGL(n,
 2) with GF(2)^n\0?
In-Reply-To: <BE1DFC18-672C-4B12-8FBD-A93FDF1A41AB@uwa.edu.au>
References: <BE1DFC18-672C-4B12-8FBD-A93FDF1A41AB@uwa.edu.au>
Message-ID: <20130313100832.GB32309@mcs.st-and.ac.uk>

Dear Gordon,

as far as I know the documentation does not guarantee this. However,
here is a way to guarantee some identification using the orb package
(here for n=8 by way of example):

gap> g := GL(IsMatrixGroup,8,2);
SL(8,2)
gap> v := ShallowCopy(Zero(GF(2)^8));
<a GF2 vector of length 8>
gap> v[1] := Z(2);
Z(2)^0
gap> o := Orb(g,v,OnLines,rec( storenumbers := true ));
<open orbit, 1 points>
gap> Enumerate(o);
<closed orbit, 255 points>
gap> permgens := ActionOnOrbit(o,GeneratorsOfGroup(g));;

It does not give you exactly the numbering you want but on the other hand

  o[i]

gives you quickly the i-th vector and

  Position(o,v)

for a vector v uses a hash table and thus gives you the number of a vector
in constant time.

Best regards,
  Max

On Wed, Mar 13, 2013 at 03:52:30PM +0800, Gordon Royle wrote:
> If I use the groups
> 
> PGL(n,2)
> 
> in GAP, then is it guaranteed that the set permuted by this group can be identified in the obvious fashion with GF(2)^n \ 0?
> 
> What I mean is that it would be natural to assign the non-zero vectors in GF(2)^n\0 to integers in the range {1,2,?,2^n-1} simply by treating a 0/1 vector as the binary representation of an integer.
> 
> 0000001 -> 1
> 0000010 -> 2
> 0000011 -> 3
> 
> and so on.
> 
> >>From my experiments, GAP *appears* to behave consistently with this (for example, if I check the stabiliser of [x, y, x ^ y] where x ^ y is bitwise binary XOR, then it is always the correct thing).
> 
> But can I rely on it?
> 
> 
> 
> 
> Professor Gordon Royle
> School of Mathematics and Statistics
> University of Western Australia
> Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

-- 
Max Neunhoeffer              http://www-groups.mcs.st-and.ac.uk/~neunhoef/
> > > > > > > > > > >  May the Source be with you! < < < < < < < < < < < < 
The University of St Andrews is a registered Scottish charity: No SC013532



From ciobotaru.mircea at gmail.com  Wed Mar 13 18:42:12 2013
From: ciobotaru.mircea at gmail.com (Ciobotaru Mircea)
Date: Wed, 13 Mar 2013 20:42:12 +0200
Subject: [GAP Forum] gap in ubuntu
Message-ID: <CALHpxBDBPnaXqBJABBTeh0LhE3Hd3mnu-VA71tmN11_YfsJd7A@mail.gmail.com>

whith Gdebi ,the lists librari from gap not work!!  whatis problems???

-- 
   web : http://picasaweb.google.com/ciobotaru.mircea
   web :http://SEMINEU.sunphoto.ro <http://semineu.sunphoto.ro/>
   web :http;//piatracubica.sunphoto.ro
facebook : Piatra Cubica Cluj
SKYPE: bazalt104
YAHOO:bazalt104

celular +40  744 804 754      fix 0264 411 536









]

From A.Egri-Nagy at herts.ac.uk  Wed Mar 13 22:46:56 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Thu, 14 Mar 2013 09:46:56 +1100
Subject: [GAP Forum] gap in ubuntu
In-Reply-To: <CALHpxBDBPnaXqBJABBTeh0LhE3Hd3mnu-VA71tmN11_YfsJd7A@mail.gmail.com>
References: <CALHpxBDBPnaXqBJABBTeh0LhE3Hd3mnu-VA71tmN11_YfsJd7A@mail.gmail.com>
Message-ID: <CAP=h6j2LXY2_8zwB0ENaQ09UpP4pVHhRvV44DKytS_0rnpbP2g@mail.gmail.com>

Dear Ciobotaru,

Ubuntu repositories contain an old version of GAP. It is lot better to
stick with the recommended installation method: download the archive and
compile GAP from sources. http://www.gap-system.org/Download/index.html

I hope this helps...

best wishes,
Attila

On Thu, Mar 14, 2013 at 5:42 AM, Ciobotaru Mircea <
ciobotaru.mircea at gmail.com> wrote:

> whith Gdebi ,the lists librari from gap not work!!  whatis problems???
>
> --
>    web : http://picasaweb.google.com/ciobotaru.mircea
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>    web :http;//piatracubica.sunphoto.ro
> facebook : Piatra Cubica Cluj
> SKYPE: bazalt104
> YAHOO:bazalt104
>
> celular +40 744 804 754      fix 0264 411 536
>
>
>
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> ]
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From sarwarvu at gmail.com  Fri Mar 15 12:04:01 2013
From: sarwarvu at gmail.com (sarwarvu at gmail.com)
Date: Fri, 15 Mar 2013 12:04:01 +0000
Subject: [GAP Forum] sarwarvu@gmail.com wants to follow you. Accept?
Message-ID: <0.0.2DC.A48.1CE21752E77D118.1E2F@mail5.infoaxe.net>

Hi,

sarwarvu at gmail.com wants to follow you.

****** Is sarwarvu at gmail.com you friend? ******
If Yes please follow the link below:
http://invites.infoaxe.net/signup_e.html?fullname=&email=forum at mail.gap-system.org&invitername=Muhammad&inviterid=15030613&userid=0&token=0&emailmasterid=72f2a626-600c-420b-92c9-8b98b03fd80e&uie=0&src=txt_yes

If No please follow the link below:
http://invites.infoaxe.net/signup_e_no.html?fullname=&email=forum at mail.gap-system.org&invitername=Muhammad&inviterid=15030613&userid=0&token=0&emailmasterid=72f2a626-600c-420b-92c9-8b98b03fd80e&uie=0&src=txt_no


Follow the link below to unsubscribe from all emails from Flipora, 440 N.Wolfe Rd MS #153, Sunnyvale, CA. 94085
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From kroeker at uni-math.gwdg.de  Mon Mar 18 13:36:08 2013
From: kroeker at uni-math.gwdg.de (=?utf-8?B?Ikpha29iIEtyw7ZrZXIi?=)
Date: Mon, 18 Mar 2013 14:36:08 +0100
Subject: [GAP Forum] Spam follow request from info@infoaxe.net?
Message-ID: <d4ff5d93f50e5dfb7df654ae0f252ddb.squirrel@webmail.uni-math.gwdg.de>

Hello,


it seems  info at infoaxe.net sends follower requests to the gap forum users
(at least to me). Please be alerted!




Jakob




From jjm at mcs.st-and.ac.uk  Mon Mar 18 14:36:13 2013
From: jjm at mcs.st-and.ac.uk (John McDermott)
Date: Mon, 18 Mar 2013 14:36:13 +0000
Subject: [GAP Forum] Spam follow request from info@infoaxe.net?
In-Reply-To: <d4ff5d93f50e5dfb7df654ae0f252ddb.squirrel@webmail.uni-math.gwdg.de>
References: <d4ff5d93f50e5dfb7df654ae0f252ddb.squirrel@webmail.uni-math.gwdg.de>
Message-ID: <869176F3-4631-419D-9555-BFC5DEE1D3E6@mcs.st-andrews.ac.uk>

Dear Jakob, dear Forum,

On 18 Mar 2013, at 13:36, Jakob Kr?ker wrote:

> Hello,
> 
> 
> it seems  info at infoaxe.net sends follower requests to the gap forum users
> (at least to me). Please be alerted!

Yes, this mail was sent to the entire Forum. I apologise for the spam, which got through because it came from a registered user's address. That user has been placed on moderation and we have added a filter which we hope will catch other abuses from this infoaxe domain.

Best wishes,
John



> 
> 
> 
> Jakob
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

--
John McDermott
Scientific Officer
Centre for Interdisciplinary Research in Computational Algebra
School of Computer Science
University of St Andrews

From msorouhesh at gmail.com  Tue Mar 19 17:13:32 2013
From: msorouhesh at gmail.com (Mohammad Reza Sorouhesh)
Date: Tue, 19 Mar 2013 21:43:32 +0430
Subject: [GAP Forum] A Subgroup of S_4 and isomorphic with Z_2 x Z_2
Message-ID: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>

Dear forum,

May I ask you how can I have the subgroup of S_4 which is isomorphic with
Z_2 X Z_2. I know that the Cayley's Theorem guaranties this event.

Best Wishes

M.R.Sorouhesh

From williamdemeo at gmail.com  Tue Mar 19 19:26:52 2013
From: williamdemeo at gmail.com (William DeMeo)
Date: Tue, 19 Mar 2013 15:26:52 -0400
Subject: [GAP Forum] A Subgroup of S_4 and isomorphic with Z_2 x Z_2
In-Reply-To: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>
References: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>
Message-ID: <CAHO_k7RTPd7Co=fwfcjgeK5doRVLcGTVmdteAou8AycsafN51g@mail.gmail.com>

There's probably a nicer way, but you could do

gap> g:=SymmetricGroup(4);
gap> ccsg:=ConjugacyClassesSubgroups(g);
gap> V:=Representative(ccsg[5]);
gap> StructureDescription(V);
"C2 x C2"

Cheers,
William


--
William DeMeo
Department of Mathematics
University of South Carolina
http://williamdemeo.wordpress.com
mobile:808-298-4874 office:803-777-7510




On Tue, Mar 19, 2013 at 1:13 PM, Mohammad Reza Sorouhesh
<msorouhesh at gmail.com> wrote:
> Dear forum,
>
> May I ask you how can I have the subgroup of S_4 which is isomorphic with
> Z_2 X Z_2. I know that the Cayley's Theorem guaranties this event.
>
> Best Wishes
>
> M.R.Sorouhesh
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From Bill.Allombert at math.u-bordeaux1.fr  Tue Mar 19 19:44:28 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Tue, 19 Mar 2013 20:44:28 +0100
Subject: [GAP Forum] A Subgroup of S_4 and isomorphic with Z_2 x Z_2
In-Reply-To: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>
References: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>
Message-ID: <20130319194428.GA29129@yellowpig>

On Tue, Mar 19, 2013 at 09:43:32PM +0430, Mohammad Reza Sorouhesh wrote:
> Dear forum,
> 
> May I ask you how can I have the subgroup of S_4 which is isomorphic with
> Z_2 X Z_2. I know that the Cayley's Theorem guaranties this event.

Cayley theorem give you an explicit map from Z_2 X Z_2 to S_4, you just need
to compute its image. This is quite easy to do by hand.

Cheers,
Bill.


From mckay at encs.concordia.ca  Tue Mar 19 23:57:30 2013
From: mckay at encs.concordia.ca (John McKay)
Date: Tue, 19 Mar 2013 19:57:30 -0400 (EDT)
Subject: [GAP Forum] A Subgroup of S_4 and isomorphic with Z_2 x Z_2
In-Reply-To: <CAHO_k7RTPd7Co=fwfcjgeK5doRVLcGTVmdteAou8AycsafN51g@mail.gmail.com>
References: <CAJn1Z0OyCg6Jt7W-BNLA=pxuTScuA2eRR9_0Jk5nAeQgAWOx3A@mail.gmail.com>
	<CAHO_k7RTPd7Co=fwfcjgeK5doRVLcGTVmdteAou8AycsafN51g@mail.gmail.com>
Message-ID: <Pine.LNX.4.58.1303191951330.31472@focus.encs.concordia.ca>


No-one has mentioned that here are two classes of C2 x C2 in S4.

They are: transiive V4 = <I, (1 2)(3 4), (1 4)(2 3), (1 3)(2 4)>

wich is a normal subgroup of S4, and

intransitive V4 = <I, (1 2)(3)(4), (1)(2)(3 4), (1 2)(3 4)>

which is not.

[Remark: Is Klein's V4 transitive, intransitive or abstract?]

John McKay

===


On Tue, 19 Mar 2013, William DeMeo wrote:

> There's probably a nicer way, but you could do
>
> gap> g:=SymmetricGroup(4);
> gap> ccsg:=ConjugacyClassesSubgroups(g);
> gap> V:=Representative(ccsg[5]);
> gap> StructureDescription(V);
> "C2 x C2"
>
> Cheers,
> William
>
>
> --
> William DeMeo
> Department of Mathematics
> University of South Carolina
> http://williamdemeo.wordpress.com
> mobile:808-298-4874 office:803-777-7510
>
>
>
>
> On Tue, Mar 19, 2013 at 1:13 PM, Mohammad Reza Sorouhesh
> <msorouhesh at gmail.com> wrote:
> > Dear forum,
> >
> > May I ask you how can I have the subgroup of S_4 which is isomorphic with
> > Z_2 X Z_2. I know that the Cayley's Theorem guaranties this event.
> >
> > Best Wishes
> >
> > M.R.Sorouhesh
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>


From joachim.neubueser at t-online.de  Wed Mar 20 16:18:32 2013
From: joachim.neubueser at t-online.de (=?ISO-8859-15?Q?Joachim_Neub=FCser?=)
Date: Wed, 20 Mar 2013 17:18:32 +0100
Subject: [GAP Forum] suggestion re S4 etc
Message-ID: <5149E158.5080302@t-online.de>

Dear Forum members,

The recent discussion of the question about subgroups of the symmetric 
group S4 that are  isomorphic to the direct product of two cyclic groups of
oder 2 prompts me  to remind that for a detailed understanding of the 
subgroup structure of smaller groups GAP provides the package XGAP which 
allows a graphical depiction of the subgroup lattice or parts thereof 
and the switching from the graphical description to further group 
theoretical investigation of the subgroups displayed. The XGAP manual 
gives several examples of the use of XGAP even in cases where the 
complete subgroup lattice is far too big to be displayed.

In the case of S4 you can nicely see  what John McKay pointed out and in 
fact can get a good understanding of how this all works.

Have fun with XGAP!   Joachim Neub?ser



From alexk at mcs.st-andrews.ac.uk  Thu Mar 21 13:43:57 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 21 Mar 2013 13:43:57 +0000
Subject: [GAP Forum] GAP 4.6.3 release announcement
Message-ID: <92A5F352-4C80-4A6B-88C3-98B617E1C32D@mcs.st-andrews.ac.uk>

Dear GAP Forum,

We have just released the next minor release, GAP 4.6.3, which is now
available for download from the GAP website

	http://www.gap-system.org

and eventually will be also available via alternative GAP distributions 
listed at

	http://www.gap-system.org/Download/#alternatives
	
You may access the overview of changes in GAP 4.6.3 by entering 
'?Changes between GAP 4.5 and GAP 4.6' in GAP 4.6.3 and scrolling 
till the end of the chapter, or view it online at

http://www.gap-system.org/Manuals/doc/changes/chap2.html#X7C2A78667F08A971

In addition to the improved functionality and fixed bugs in the core GAP 
system, GAP 4.6.3 distribution includes the new package SpynSim by L. Maas, 
which contains Brauer tables of Schur covers of symmetric and alternating 
groups and provides some related functionalities. Other packages that are
updated since the previous GAP 4.6.2 release are listed below:

================================================
Package name          | Version     | Date      
------------------------------------------------ 
CRISP                 | 1.3.6       | 13/03/2013
CTblLib               | 1.2.2       | 07/03/2013
Float                 | 0.5.9       | 17/03/2013
Gauss                 | 2013.03.07  | 07/03/2013
gpd                   | 1.19        | 11/03/2013
GradedModules         | 2013.02.07  | 07/02/2013
GradedRingForHomalg   | 2013.08.07  | 07/08/2013
HAP                   | 1.10.10.2   | 05/03/2013
HomalgToCAS           | 2013.02.22  | 22/02/2013
MatricesForHomalg     | 2013.02.24  | 24/02/2013
Modules               | 2013.02.10  | 10/02/2013
Polycyclic            | 2.11        | 07/03/2013
PolymakeInterface     | 2013.03.06  | 06/03/2013
RingsForHomalg        | 2013.02.25  | 25/02/2013
================================================

We encourage all users to upgrade to GAP 4.6.3. If you need any help 
or would like to report any problems, please do not hesitate to contact 
us at support at gap-system.org.

Please note that we are regularly updating the GAP distribution to 
include new versions of GAP packages, but we may not announce each 
of them to the Forum. We intend to use the Forum to announce updates 
of the core GAP system and only of some packages which may fix serious 
issues or have major influence on GAP. 

Wishing you fun and success using GAP,

The GAP Group


From alexk at mcs.st-andrews.ac.uk  Thu Mar 21 14:25:03 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 21 Mar 2013 14:25:03 +0000
Subject: [GAP Forum] irreducible representations of the dihedral group
	D10 over GF(4)
In-Reply-To: <CAENqgLYy4vhk1i593Gw1iO+V9iFj9xp8fhbOZhjdRsC0MU9buw@mail.gmail.com>
References: <CAENqgLYy4vhk1i593Gw1iO+V9iFj9xp8fhbOZhjdRsC0MU9buw@mail.gmail.com>
Message-ID: <C4607127-F503-4B67-93E0-1CA678E6C123@mcs.st-andrews.ac.uk>


On 12 Jul 2012, at 17:58, Neha Makhijani <nehamakhijani at gmail.com> wrote:

> Can somebody please clarify as to why I am not able to get the irreducible
> representations of the dihedral group over GF(4)??
> 
> IrreducibleRepresentations(DihedralGroup(10),GF(2^2));
> List Element: <position> must be a positive integer (not a boolean)
> 
> Thanks!
> 
> Neha

Dear Neha,

Sorry it took longer than we expected to fix this. Just released GAP 4.6.3 
provides the default method for AbsoluteIrreducibleModules as a temporary 
workaround for the problem which may cause returning wrong results or 
producing an error when being called for a non-prime field. As a result,
your example now works:

gap> IrreducibleRepresentations(DihedralGroup(10),GF(2^2));
[ [ f1, f2 ] -> [ [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ] ], 
  [ f1, f2 ] -> [ [ [ Z(2^2), Z(2)^0 ], [ Z(2^2), Z(2^2) ] ], 
      [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2^2) ] ] ], 
  [ f1, f2 ] -> [ [ [ Z(2^2)^2, Z(2^2)^2 ], [ Z(2)^0, Z(2^2)^2 ] ], 
      [ [ Z(2^2)^2, Z(2)^0 ], [ Z(2)^0, 0*Z(2) ] ] ] ]

Best wishes,
Alexander



From alexk at mcs.st-andrews.ac.uk  Thu Mar 21 14:27:30 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 21 Mar 2013 14:27:30 +0000
Subject: [GAP Forum] AbsoluteIrreducibleModules error
In-Reply-To: <CAAwatYW=U+rtbj9G7YmAZZZQw6QMZ=Bk3pyZpHMHFck3tSEOAQ@mail.gmail.com>
References: <CAAwatYW=U+rtbj9G7YmAZZZQw6QMZ=Bk3pyZpHMHFck3tSEOAQ@mail.gmail.com>
Message-ID: <47F70B2C-18CF-43C9-B89C-4C70104C632F@mcs.st-andrews.ac.uk>

Dear Anvita,

Thank you for reporting this bug. The same fix which I've
just mentioned in the previous posting to the forum also fixes
this problem.

Best wishes,
Alexander


On 11 Dec 2012, at 07:03, Anvita <anvita21 at gmail.com> wrote:

> Dear Forum,
> 
> According to the Manual, the command AbsoluteIrreducibleModules(G, F, dim)
> returns a list of all absolutely irreducible modules of G over the
> field F in dimension dim.
> However, it seems to produce an error if the field F is not prime.
> 
> C:=CyclicGroup(3);
> AbsoluteIrreducibleModules(C,GF(4),1);
> 
> Error, List Element: <list>[1] must have an assigned value in
> ...
> 
> Certainly, the modules in this example are easy to find by hand, but I
> first came about
> this error when trying to compute a more complicated and meaningful example.
> 
> Thank you,
> Anvita
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From alexk at mcs.st-andrews.ac.uk  Thu Mar 21 14:29:40 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 21 Mar 2013 14:29:40 +0000
Subject: [GAP Forum] Irreducible representation of dihedral group D20
	over GF(8)
In-Reply-To: <CAENqgLZ7EfKpLKrm5wN=r01E+gVxkgNAqQjhg5ATF7n+_yVLrA@mail.gmail.com>
References: <CAENqgLZ7EfKpLKrm5wN=r01E+gVxkgNAqQjhg5ATF7n+_yVLrA@mail.gmail.com>
Message-ID: <D61D3EB1-AF86-4F44-A9D9-C341DAFEECC0@mcs.st-andrews.ac.uk>

P.S. This computation now works too in GAP 4.6.3 and Image(phi2,b)^2
returns an identity matrix. Thanks for reporting this bug!

Best wishes,
Alexander


On 10 Dec 2012, at 22:04, Neha Wadhwani <nehamakhijani at gmail.com> wrote:

> Hi
> 
> I am not able to understand if the following is actually a well defined
> homomorphism!
> 
> *G:=DihedralGroup(20);*
> <pc group of size 20 with 3 generators>
> 
> *b:=G.1*G.2;*
> f1*f2
> 
> *b^2;*
> <identity> of ...
> 
> *phi:=IrreducibleRepresentations(G,GF(8));*
> [ Pcgs([ f1, f2, f3 ]) -> [ [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ]
> ],
>  Pcgs([ f1, f2, f3 ]) ->
>    [ [ [ Z(2)^0, 0*Z(2), Z(2^3), Z(2)^0 ], [ 0*Z(2), Z(2)^0, Z(2^3)^6,
>               Z(2^3)^3 ], [ 0*Z(2), 0*Z(2), Z(2^3), Z(2^3)^3 ],
>          [ 0*Z(2), 0*Z(2), Z(2^3)^2, Z(2)^0 ] ],
>      [ [ Z(2^3)^6, Z(2^3)^5, Z(2^3)^6, Z(2^3) ],
>          [ Z(2^3)^4, Z(2^3), Z(2)^0, Z(2^3)^5 ],
>          [ Z(2^3)^2, Z(2^3)^6, Z(2^3)^3, Z(2^3)^4 ],
>          [ Z(2^3)^5, Z(2)^0, Z(2^3)^3, Z(2^3)^6 ] ],
>      [ [ Z(2^3)^2, Z(2^3)^4, Z(2^3), 0*Z(2) ],
>          [ Z(2^3)^3, Z(2^3), 0*Z(2), Z(2^3) ],
>          [ Z(2^3), Z(2^3), Z(2^3)^3, Z(2^3)^5 ],
>          [ Z(2)^0, 0*Z(2), Z(2^3)^4, Z(2^3)^2 ] ] ] ]
> 
> *phi2:=phi[2];;*
> *
> *
> *Image(phi2,b)^2;*
> [ [ Z(2^3)^6, Z(2^3)^3, 0*Z(2), 0*Z(2) ],
>  [ Z(2^3)^2, Z(2^3)^4, 0*Z(2), 0*Z(2) ],
>  [ Z(2^3)^4, Z(2^3)^3, Z(2^3), Z(2^3)^6 ],
>  [ Z(2^3)^2, Z(2^3)^6, Z(2^3)^5, Z(2^3)^5 ] ]
> *which is not an identity matrix..*
> *
> *
> *Please let me know if I am going wrong....*
> *
> *
> *Thanks!*
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From alexk at mcs.st-andrews.ac.uk  Fri Mar 22 08:36:47 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 22 Mar 2013 08:36:47 +0000
Subject: [GAP Forum] International Workshop "Parallel programming in GAP"
Message-ID: <569480AB-7EEB-46EB-A2D5-ED0C7E0EE5A4@mcs.st-andrews.ac.uk>

International Workshop "Parallel programming in GAP"

August 18th-24th, 2013, University of St Andrews, Scotland

http://www.gap-system.org/hpcgap2013/

The workshop is organised by the Centre of Interdisciplinary 
Research in Computational Algebra of the University of St Andrews.
It is supported by the EPSRC project "HPC-GAP: High Performance 
Computational Algebra and Discrete Mathematics":

	http://www-circa.mcs.st-and.ac.uk/hpcgap.php

In this project we are reengineering the GAP system to take 
advantage of computer architectures suitable for parallel
computations. The workshop is organised to present the results 
of the project to the GAP community, and we invite everyone who
is interested in parallel programming in GAP. Developers of GAP 
and authors of GAP packages are particularly welcome, since your
contribution will be important to eventually transform the HPC-GAP 
version of the system into the next mainstream release.

The workshop will comprise of lectures and tutorials given by 
the participants of the HPC-GAP project, and case studies sessions
where we intend to look at some particular GAP packages and 
estimate main tasks needed to adapt them to HPC-GAP. We plan 
to allow enough time to work in small groups and have informal
discussions about HPC-GAP and GAP development in general.

Schedule:

- August 18th (Sunday): Arrival day
- August 19th-23th (Monday-Friday): Workshop
- August 24th (Saturday): Departure day

Registration and accommodation:

The organisers will provide a limited number of B&B places in McIntosh Hall 
( http://www.st-andrews.ac.uk/accommodation/ug/residences/mcintosh/ ). These
will be provided free of charge and will be allocated on a first come - first 
served basis, so early registration is advised. If there will be larger 
demand for accommodation, we will help you to find another place to stay and 
will partially contribute towards the costs of your accommodation. We regret 
that there is no support available for daily expenses and travel.

To register, please send your contact details to organisers by email to

	hpcgap2013 at gap-system.org 

Deadlines:

- for the full registration: July 15th 2013
- for the non-residential registration: August 5th 2013

Organisers:
- Steve Linton
- Reimer Behrends
- Vladimir Janjic
- Alexander Konovalov
- John McDermott
- Angela Miguel
- Max Neunh?ffer

---

Note that other events in St Andrews in 2013 include:
* Groups St Andrews 2013:   3rd-11th August
 http://www.groupsstandrews.org/2013/

* Computational Group Theory (LMS/EPSRC Short Instructional Course): 29th July-2nd August
 http://www-circa.mcs.st-and.ac.uk/cgt2013/



From robert.bailey at ryerson.ca  Fri Mar 22 18:24:10 2013
From: robert.bailey at ryerson.ca (Robert Bailey)
Date: Fri, 22 Mar 2013 14:24:10 -0400
Subject: [GAP Forum] Reading strongly regular graphs into GAP
Message-ID: <1363976650.1613.159.camel@mathadmin-desktop>

Dear Forum,

This is perhaps not strictly a GAP question, but anyway....

I've been working on some computations in GAP (using the GRAPE and other
packages), testing certain properties of distance-regular and strongly
regular graphs.  (I can go into more detail if necessary--but the
SetOrbit package of Pech and Reichard has been especially useful.)

There is an online catalogue of strongly regular graphs on Ted Spence's
webpage:
http://www.maths.gla.ac.uk/~es/srgraphs.php

The graphs are given by their adjacency matrices; however, as given
these matrices are not immediately readable by GAP.  Does anyone know of
an easy way to convert them into the right format (i.e. adding the
commas and brackets)?  For cases where there are a small number of
graphs, I've been able to do search/replace in a text editor to add the
commas, then add the brackets manually---but this isn't really feasible
when there are 32,548 matrices of size 36x36.

Thanks,
Robert Bailey.

-- 
Dr. Robert Bailey
Department of Mathematics
Ryerson University
350 Victoria St.
Toronto, Ontario M5B 2K3
Canada

Office: EPH 442B
Telephone: +1 416-979-5000 x2874
Web: www.math.ryerson.ca/~rbailey



From mathieu.dutour at gmail.com  Fri Mar 22 18:53:37 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Fri, 22 Mar 2013 19:53:37 +0100
Subject: [GAP Forum] Reading strongly regular graphs into GAP
In-Reply-To: <1363976650.1613.159.camel@mathadmin-desktop>
References: <1363976650.1613.159.camel@mathadmin-desktop>
Message-ID: <CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>

The basic strategy in that case is that you write a perl
script that reads as input the file from Spence web page
and then write as output in a format that GAP can read.

You can of course use Python or any other language that
has good text capabilities.

  Mathieu


On Fri, Mar 22, 2013 at 7:24 PM, Robert Bailey <robert.bailey at ryerson.ca>wrote:

> Dear Forum,
>
> This is perhaps not strictly a GAP question, but anyway....
>
> I've been working on some computations in GAP (using the GRAPE and other
> packages), testing certain properties of distance-regular and strongly
> regular graphs.  (I can go into more detail if necessary--but the
> SetOrbit package of Pech and Reichard has been especially useful.)
>
> There is an online catalogue of strongly regular graphs on Ted Spence's
> webpage:
> http://www.maths.gla.ac.uk/~es/srgraphs.php
>
> The graphs are given by their adjacency matrices; however, as given
> these matrices are not immediately readable by GAP.  Does anyone know of
> an easy way to convert them into the right format (i.e. adding the
> commas and brackets)?  For cases where there are a small number of
> graphs, I've been able to do search/replace in a text editor to add the
> commas, then add the brackets manually---but this isn't really feasible
> when there are 32,548 matrices of size 36x36.
>
> Thanks,
> Robert Bailey.
>
> --
> Dr. Robert Bailey
> Department of Mathematics
> Ryerson University
> 350 Victoria St.
> Toronto, Ontario M5B 2K3
> Canada
>
> Office: EPH 442B
> Telephone: +1 416-979-5000 x2874
> Web: www.math.ryerson.ca/~rbailey
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From hulpke at math.colostate.edu  Fri Mar 22 19:13:37 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri, 22 Mar 2013 13:13:37 -0600
Subject: [GAP Forum] Reading strongly regular graphs into GAP
In-Reply-To: <1363976650.1613.159.camel@mathadmin-desktop>
References: <1363976650.1613.159.camel@mathadmin-desktop>
Message-ID: <11C76D8B-7228-4E14-AB83-BCDFFD11AD6C@math.colostate.edu>



Dear Forum, Dear Robert Bailey,

> This is perhaps not strictly a GAP question, but anyway....
> 
> I've been working on some computations in GAP (using the GRAPE and other
> packages), testing certain properties of distance-regular and strongly
> [...]
> 
> The graphs are given by their adjacency matrices; however, as given
> these matrices are not immediately readable by GAP.  Does anyone know of
> an easy way to convert them into the right format

As Mathieu Dutour already wrote, the classical method is to coax your favorite P-named language (Perl, Python) to parse these matrices so that you get a valid GAP input file.
However you can also read in the file line by line to GAP and write a small routine to parse the data. Personally (with the bias that I know GAP far better than Perl or Python) I find this easier.
For example the appended program can be used to read in the lists of adjacency matrices as given on this web page, the function call

a:=ReadMatrixList("PathTofilename");;

returns a list of the adjacency matrices over Q. (You can probably take it from there.)

At the moment the function assumes single digits but it should be easy to adapt to more complicated formats.

(This function ought to work also under Windows, but as usual you need to be careful how to specify the path.)

I hope this is of help,

   Alexander Hulpke

# the promised function
ReadMatrixList:=function(file)
local l,f,m,row;
  l:=[];
  f:=InputTextFile(file);
  m:=fail;
  while not IsEndOfStream(f) do
    row:=ReadLine(f);
    if row<>fail then
      row:=Chomp(row); # remove CR,LF
      row:=Filtered(row,x->x<>' '); # remove blanks
      if Length(row)=0 then
        # new matrix
        if m<>fail and Length(m)>0 then Add(l,m);fi;
        m:=[];
      elif IsSubset(DIGITS,row) then
        # new row
        row:=List(row,x->Int([x]));
        Add(m,row);
      else
        Print("#I ",row,"\n"); # non parsed row
      fi;
    fi;
  od;
  CloseStream(f);
  if m<>fail and Length(m)>0 then Add(l,m);fi;
  return l;
end;

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke




From robert.bailey at ryerson.ca  Fri Mar 22 19:15:43 2013
From: robert.bailey at ryerson.ca (Robert Bailey)
Date: Fri, 22 Mar 2013 15:15:43 -0400
Subject: [GAP Forum] Reading strongly regular graphs into GAP
In-Reply-To: <CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>
References: <1363976650.1613.159.camel@mathadmin-desktop>
	<CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>
Message-ID: <fb99b4f46e59a.514c759f@ryerson.ca>

Thanks for the reply.  I suspected that this might be the answer--the problem is I have no knowledge of perl or Python or such languages.

What I was hoping was that someone might have a suitable piece of code lying around already.....

Thanks again,
Robert.

----- Original Message -----
From: Mathieu Dutour <mathieu.dutour at gmail.com>
Date: Friday, March 22, 2013 2:53 pm
Subject: Re: [GAP Forum] Reading strongly regular graphs into GAP
To: Robert Bailey <robert.bailey at ryerson.ca>
Cc: GAP forum <forum at gap-system.org>


> The basic strategy in that case is that you write a perl
>  script that reads as input the file from Spence web page
>  and then write as output in a format that GAP can read.
>  
>  You can of course use Python or any other language that
>  has good text capabilities.
>  
>    Mathieu
>  
>  
>  On Fri, Mar 22, 2013 at 7:24 PM, Robert Bailey <robert.bailey at ryerson.ca>wrote:
>  
>  > Dear Forum,
>  >
>  > This is perhaps not strictly a GAP question, but anyway....
>  >
>  > I've been working on some computations in GAP (using the GRAPE and 
> other
>  > packages), testing certain properties of distance-regular and strongly
>  > regular graphs.  (I can go into more detail if necessary--but the
>  > SetOrbit package of Pech and Reichard has been especially useful.)
>  >
>  > There is an online catalogue of strongly regular graphs on Ted Spence's
>  > webpage:
>  > http://www.maths.gla.ac.uk/~es/srgraphs.php
>  >
>  > The graphs are given by their adjacency matrices; however, as given
>  > these matrices are not immediately readable by GAP.  Does anyone 
> know of
>  > an easy way to convert them into the right format (i.e. adding the
>  > commas and brackets)?  For cases where there are a small number of
>  > graphs, I've been able to do search/replace in a text editor to add 
> the
>  > commas, then add the brackets manually---but this isn't really feasible
>  > when there are 32,548 matrices of size 36x36.
>  >
>  > Thanks,
>  > Robert Bailey.
>  >
>  > --
>  > Dr. Robert Bailey
>  > Department of Mathematics
>  > Ryerson University
>  > 350 Victoria St.
>  > Toronto, Ontario M5B 2K3
>  > Canada
>  >
>  > Office: EPH 442B
>  > Telephone: +1 416-979-5000 x2874
>  > Web: www.math.ryerson.ca/~rbailey
>  >
>  >
>  > _______________________________________________
>  > Forum mailing list
>  > Forum at mail.gap-system.org
>  > http://mail.gap-system.org/mailman/listinfo/forum
>  >
>  


From robert.bailey at ryerson.ca  Fri Mar 22 19:19:39 2013
From: robert.bailey at ryerson.ca (Robert Bailey)
Date: Fri, 22 Mar 2013 15:19:39 -0400
Subject: [GAP Forum] Reading strongly regular graphs into GAP
In-Reply-To: <fb99b4f46e59a.514c759f@ryerson.ca>
References: <1363976650.1613.159.camel@mathadmin-desktop>
	<CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>
	<fb99b4f46e59a.514c759f@ryerson.ca>
Message-ID: <fbb691a769361.514c768b@ryerson.ca>

>  What I was hoping was that someone might have a suitable piece of 
> code lying around already.....
>
.....like the one Alexander Hulpke just provided.  Apologies for the cross-posting.
  
> --
> Dr. Robert Bailey
> Department of Mathematics
> Ryerson University
> 350 Victoria St.
> Toronto, Ontario M5B 2K3
> Canada
>
> Office: EPH 442B
> Telephone: +1 416-979-5000 x2874
> Web: www.math.ryerson.ca/~rbailey
>


From max at quendi.de  Fri Mar 22 19:25:43 2013
From: max at quendi.de (Max Horn)
Date: Fri, 22 Mar 2013 20:25:43 +0100
Subject: [GAP Forum] Reading strongly regular graphs into GAP
In-Reply-To: <CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>
References: <1363976650.1613.159.camel@mathadmin-desktop>
	<CADm_tePQa=QY8zor7-JtSximiC3fxz42aqCPebCF5FcsVT40Cw@mail.gmail.com>
Message-ID: <E804334C-EAE4-4353-90D5-119D6A8C8554@quendi.de>


On 22.03.2013, at 19:53, Mathieu Dutour wrote:

> The basic strategy in that case is that you write a perl
> script that reads as input the file from Spence web page
> and then write as output in a format that GAP can read.
> 
> You can of course use Python or any other language that
> has good text capabilities.

Actually, it would be rather easy to read the files with GAP itself, there is no need to involve Perl or Python. The adjacency matrices just consist of a 

Indeed, if you wanted to be really fancy, you could even write a GAP program which downloads those files directly from the website (e.g. using the IO packages). Although that would probably overkill for this purpose ;-).

Here is an example for parsing one of the files (the one named 64-18-2-6):

adj_mats := [];
stream := InputTextFile("64-18-2-6");

# Read first line, containing data like
#   dim = 64, degree = 18, lambda = 2, mu = 6
# We could parse it, but to keep things simple, let's just skip it and the empty
# line after it.
ReadLine(stream);
ReadLine(stream);

# Now start parsing
while not IsEndOfStream(stream) do
    # Read in next matrix
    adj := [];
    while not IsEndOfStream(stream) do
        line := Chomp(ReadLine(stream));
        if line = fail or IsEmpty(line) then
            if not IsEmpty(adj) then
                Add(adj_mats, adj);
            fi;
            break;
        fi;
        
        if not ForAll(line, x -> x in "01") then
            break; # "garbage", e.g. a line with text
        fi;
        
        Add(adj, List(line, x -> Position("01", x)-1));
    od;
od;

CloseStream(stream);




Cheers,
Max

From ljj198123 at 126.com  Sun Mar 24 06:43:18 2013
From: ljj198123 at 126.com (=?GBK?B?wfW9qL78?=)
Date: Sun, 24 Mar 2013 14:43:18 +0800 (CST)
Subject: [GAP Forum] About maximal normal p'-subgroup
In-Reply-To: <5348288.192691249020540921.JavaMail.coremail@bj126app59.126.com>
References: <5348288.192691249020540921.JavaMail.coremail@bj126app59.126.com>
Message-ID: <cf89971.9d89.13d9b230b8f.Coremail.ljj198123@126.com>



Dear forum,
 
Let G be a finite group. I would like to know how we can compute the maximal normal p'-subgroup of G in gap.
 Is there a method to get it?
   Best wishes
  Jianjun Liu

From resteban at mat.upv.es  Sun Mar 24 13:38:39 2013
From: resteban at mat.upv.es (Ramon Esteban-Romero)
Date: Sun, 24 Mar 2013 14:38:39 +0100
Subject: [GAP Forum] About maximal normal p'-subgroup
In-Reply-To: <cf89971.9d89.13d9b230b8f.Coremail.ljj198123@126.com>
References: <5348288.192691249020540921.JavaMail.coremail@bj126app59.126.com>
	<cf89971.9d89.13d9b230b8f.Coremail.ljj198123@126.com>
Message-ID: <514F01DF.4020102@mat.upv.es>

Dear forum, dear Jianjun,

One possibility, if there are methods to compute Sylow p-complements
(for instance, in soluble groups), is to compute the core of one of
these p-complements or Hall p'-subgroups:
  Core(g, SylowComplement(g,p));

Best wishes,
-- 
Ramon

Al 24/03/13 07:43, En/na ??? ha escrit:
> 
> 
> Dear forum,
>  
> Let G be a finite group. I would like to know how we can compute the maximal normal p'-subgroup of G in gap.
>  Is there a method to get it?
>    Best wishes
>   Jianjun Liu
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From Bill.Allombert at math.u-bordeaux1.fr  Mon Mar 25 18:23:34 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Mon, 25 Mar 2013 19:23:34 +0100
Subject: [GAP Forum] building new group law from old one
Message-ID: <20130325182334.GL23868@yellowpig>

Dear GAP forum,

Let (G,.) a group such that [G,[G,G]] = 0.
I like to define a new group law * such that
a*b = ab[a,b]. It can be proven that (G,*) is also a group.

What is the nicest way to define (G,*) in GAP ?
(I like to check whether (G,.) and (G,*) are isomorphic).

Cheers,
Bill.


From alexk at mcs.st-andrews.ac.uk  Mon Mar 25 22:46:15 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 25 Mar 2013 22:46:15 +0000
Subject: [GAP Forum] building new group law from old one
In-Reply-To: <20130325182334.GL23868@yellowpig>
References: <20130325182334.GL23868@yellowpig>
Message-ID: <B5A3D774-8767-4759-A660-C7E7AEA759BC@mcs.st-andrews.ac.uk>

Dear Bill, dear Forum,

On 25 Mar 2013, at 18:23, Bill Allombert <Bill.Allombert at math.u-bordeaux1.fr> wrote:

> Dear GAP forum,
> 
> Let (G,.) a group such that [G,[G,G]] = 0.
> I like to define a new group law * such that
> a*b = ab[a,b]. It can be proven that (G,*) is also a group.
> 
> What is the nicest way to define (G,*) in GAP ?
> (I like to check whether (G,.) and (G,*) are isomorphic).
> 
> Cheers,
> Bill.

What about using ArithmeticElementCreator (see ?ArithmeticElementCreator).
For example, specify operations as follows:

gap> law:=rec(
> ElementName:="MyLaw",
> One:= a -> One(a),
> Multiplication:=function(a,b) return a*b*(a^-1*b^-1*a*b);end,
> Inverse:= a -> a^-1,
> MathInfo:=IsMultiplicativeElementWithInverse);;

gap> wrap:=ArithmeticElementCreator(law);
function( x ) ... end

Then create a group:

gap> G:=DihedralGroup(8);
<pc group of size 8 with 3 generators>
gap> g:=AsList(G);
[ <identity> of ..., f1, f2, f3, f1*f2, f1*f3, f2*f3, f1*f2*f3 ]

Now let's wrap all elements of G into new multiplicative elements 
and generate a group using all of them (don't know if I can take
the same generators; in larger example one can try to do successive
closures, if need be):

gap> t:=List(g,wrap);
[ <identity> of ..., f1, f2, f3, f1*f2, f1*f3, f2*f3, f1*f2*f3 ]
gap> H:=Group(t);
#I  default `IsGeneratorsOfMagmaWithInverses' method returns `true' for [ <identity> of ..., f1, f2, f3, f1*f2, f1*f3, f2*f3, f1*f2*f3 ]
<group with 8 generators>

The warning may be ignored. Now we see that in this example H is isomorphic to G:

gap> IdGroup(H);
[ 8, 3 ]

If your groups are very large, maybe a more low level approach would be needed, 
and isomorphism check will be tricker, but hope that the example above may help.

Best wishes,
Alexander




From L.H.Soicher at qmul.ac.uk  Wed Apr  3 12:01:15 2013
From: L.H.Soicher at qmul.ac.uk (Leonard Soicher)
Date: Wed, 3 Apr 2013 12:01:15 +0100
Subject: [GAP Forum] Combinatorics, Algebra, and More. Second announcement.
Message-ID: <20130403110115.GA21110@maths.qmul.ac.uk>

Dear GAP-Forum,

I hope that many of you know Peter Cameron and his many contributions
to combinatorics and group theory, including computation, and would be 
interested in this conference in his honour. 

Best wishes,
Leonard 

Second announcement:

Combinatorics, Algebra, and More: 
a Conference in Celebration of Peter Cameron
8-10 July 2013 (arrival 7 July, departure 11 July)
Queen Mary, University of London, UK

See  http://www.maths.qmul.ac.uk/~camconf/

for more information and from where you can register, book on-site
accommodation, and reserve a place at the conference dinner.

* Early-bird reduced rate registration fees end after Thursday April 4th.

* Reduced rates for all PhD students.

* PhD students based in the UK without official funding for
conference attendance should email the conference organisers
(camconf at maths.qmul.ac.uk) to request funding for travel and
accommodation.

* Please forward this announcement to anyone you think may be interested.

* Thank you if you have already registered! 



From pjc at mcs.st-and.ac.uk  Mon Apr  1 12:35:04 2013
From: pjc at mcs.st-and.ac.uk (Peter Cameron)
Date: Mon, 1 Apr 2013 12:35:04 +0100
Subject: [GAP Forum] O'Nan--Scott type
Message-ID: <20130401113504.GA28928@chrystal.mcs.st-andrews.ac.uk>

Dear Forum,

I have a question about the O'Nan--Scott type of a primitive group; I would
appreciate advice. I hope the forum i s the right place to ask this.

The GAP function ONanScottType classifies primitive permutation groups into
eight types, of which the first is "affine".

My view of the O'Nan--Sccott theorem is a bit different. It is, first, a
reduction for primitive groups, rather like the reduction from transitive to
primitive. Call a primitive group G on Omega "non-basic" if it preserves a
Cartesian product structure on Omega, i.e. an identification of Omega with
A^B for some sets A,B such that G is identified with a subgroup of
Sym(A) wr Sym(B) with the product action. Now a non-basic group is of wreath
product or twisted wreath product type, and a basic group of affine, diagonal
or almost simple type.

Except for a small problem.

For example, the group PrimitiveGroup(25,5), the wreath product of D(10) with
Sym(2), has ONanScottType(PrimitiveGroup(25,5))="1" (i.e. affine), even
though this group is not basic.

For applications to synchronization and other things, I need to be able to
identify the non-basic groups, and ONanScottType won't do this for affine
groups. I would like a function IsBasic, similar to IsPrimitive.

It seems to me that there are several possibilities:

1. Perhaps this problem is already solved by some GAP code, or can be easily
solved by existing technology.

2. Maybe I could take some of the code for ONanScottType and adapt it.

3. If G is affine then it has the form p^n:H, where H is an irreducible linear
group; G is basic if and only if H is primitive (i.e. not in Aschbacher class
2). I could construct the linear group and use matrix group code to test this.

4. Maybe I should just write a bare-hands program to do this.

Any thoughts?

Peter.




From glebsky at cactus.iico.uaslp.mx  Mon Apr  8 19:11:47 2013
From: glebsky at cactus.iico.uaslp.mx (glebsky at cactus.iico.uaslp.mx)
Date: Mon, 8 Apr 2013 13:11:47 -0500 (CDT)
Subject: [GAP Forum] something wrong with  NewmanInfinityCriterion?
Message-ID: <46080.201.141.124.241.1365444707.squirrel@cactus.iico.uaslp.mx>

Well.. It is known that the groups
M(a,b,c)=<x,y,z | x^y=x^a, y^z=y^b, z^x=z^b> are finite (see for example
D.L. Johnson Presentations of groups, Ch.7, exercise 16).
(Here a,b,c are natural numbers, x^y=y^(-1)*x*y.)

But running
GAP (inside SAGE) I have got:

sage: f:=FreeGroup("a","b","c");
sage:
G:=f/[f.2^-1*f.1*f.2*f.1^-4,f.3^-1*f.2*f.3*f.2^-4,f.1^-1*f.3*f.1*f.3^-4];
<free group on the generators [ a, b, c ]>
<fp group on the generators [ a, b, c ]>
sage: AbelianInvariants(G);
[ 3, 3, 3 ]
sage: NewmanInfinityCriterion(G,3)
true

Looks wrong?  As far as I understand, passing  NewmanInfinityCriterion(G,3)
meens that G has arbitrary large homomorphic images in 3-groups. It seems
to contradict with the following (G is the same as above):

sage: G3:=PQuotient(G,3);
sage: h3:=EpimorphismQuotientSystem(G3);
<3-quotient system of 3-class 4 with 9 generators>
[ a, b, c ] -> [ a1, a2, a3 ]
sage: G3:=Image(h3)
<pc group of size 19683 with 9 generators>

I am new user of the GAP. I starting to play with a GAP inside SAGE, 4.4.2,

                                                        Lev.


From hulpke at math.colostate.edu  Mon Apr  8 19:43:19 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Mon, 8 Apr 2013 12:43:19 -0600
Subject: [GAP Forum] something wrong with  NewmanInfinityCriterion?
In-Reply-To: <46080.201.141.124.241.1365444707.squirrel@cactus.iico.uaslp.mx>
References: <46080.201.141.124.241.1365444707.squirrel@cactus.iico.uaslp.mx>
Message-ID: <9DDE6ECD-A560-4CB4-825C-90AB7D0A11F3@math.colostate.edu>



Dear Lev Glebsky,

Thank you very much for this bug report. It was prompted by a misprint in a book and will be fixed in the next release of GAP.

Regards,

   Alexander Hulpke


On Apr 8, 2013, at 4/8/13 12:11, glebsky at cactus.iico.uaslp.mx wrote:

> Well.. It is known that the groups
> M(a,b,c)=<x,y,z | x^y=x^a, y^z=y^b, z^x=z^b> are finite (see for example
> D.L. Johnson Presentations of groups, Ch.7, exercise 16).
> (Here a,b,c are natural numbers, x^y=y^(-1)*x*y.)
> 
> But running
> GAP (inside SAGE) I have got:
> 
> sage: f:=FreeGroup("a","b","c");
> sage:
> G:=f/[f.2^-1*f.1*f.2*f.1^-4,f.3^-1*f.2*f.3*f.2^-4,f.1^-1*f.3*f.1*f.3^-4];
> <free group on the generators [ a, b, c ]>
> <fp group on the generators [ a, b, c ]>
> sage: AbelianInvariants(G);
> [ 3, 3, 3 ]
> sage: NewmanInfinityCriterion(G,3)
> true
> 
> Looks wrong?  As far as I understand, passing  NewmanInfinityCriterion(G,3)
> meens that G has arbitrary large homomorphic images in 3-groups. It seems
> to contradict with the following (G is the same as above):
> 
> sage: G3:=PQuotient(G,3);
> sage: h3:=EpimorphismQuotientSystem(G3);
> <3-quotient system of 3-class 4 with 9 generators>
> [ a, b, c ] -> [ a1, a2, a3 ]
> sage: G3:=Image(h3)
> <pc group of size 19683 with 9 generators>
> 
> I am new user of the GAP. I starting to play with a GAP inside SAGE, 4.4.2,
> 
>                                                        Lev.
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From Bill.Allombert at math.u-bordeaux1.fr  Mon Apr  8 19:47:08 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Mon, 8 Apr 2013 20:47:08 +0200
Subject: [GAP Forum] something wrong with  NewmanInfinityCriterion?
In-Reply-To: <46080.201.141.124.241.1365444707.squirrel@cactus.iico.uaslp.mx>
References: <46080.201.141.124.241.1365444707.squirrel@cactus.iico.uaslp.mx>
Message-ID: <20130408184708.GA31366@yellowpig>

On Mon, Apr 08, 2013 at 01:11:47PM -0500, glebsky at cactus.iico.uaslp.mx wrote:
> Well.. It is known that the groups
> M(a,b,c)=<x,y,z | x^y=x^a, y^z=y^b, z^x=z^b> are finite (see for example
> D.L. Johnson Presentations of groups, Ch.7, exercise 16).
> (Here a,b,c are natural numbers, x^y=y^(-1)*x*y.)

At least M(1,1,1) is infinite.

Cheers,
Bill.


From marek at mitros.org  Wed Apr 10 10:42:05 2013
From: marek at mitros.org (Marek Mitros)
Date: Wed, 10 Apr 2013 11:42:05 +0200
Subject: [GAP Forum] 3-transposition groups
Message-ID: <CAOng4KieuvPMiAtmxe4cR3iaMuT7UpqfMPnROc8wJ=QSz+u_mg@mail.gmail.com>

Dear Forum,

I have read in wikipedia that there are following 3-transposition groups.
See below quote from wikipedia article on "3-transposition groups". I have
no problem to obtain in GAP groups SO(1,n,2), Omega(1,n,2), PSU(n,2),
Sp(n,2). I can also define Fischer groups Fi22, Fi23, Fi24 using Atlas
package. I have only trouble with O+-(2n,3) case. E.g. neither SO(1,6,3)
nor Omega (1,6,3) is 3-transposition group. What is the way to define the
3-transposition group defined under case  O?, ?(*n*, 3) below.


Regards,
Marek

----------------------------------


Suppose that *G* is a group that is generated by conjugacy class of
3-transpositions and such that the 2 and 3
cores<http://en.wikipedia.org/wiki/P-core>
*O*2(*G*) and *O*3(*G*) are both contained in the center *Z*(*G*) of
*G*and the derived group of
*G* is perfect. Then Fischer
(1971<http://en.wikipedia.org/wiki/3-transposition_group#CITEREFFischer1971>)
proved that up to isomorphism *G*/*Z*(*G*) is one of the following groups
and *D* is the image of the given conjugacy class:

   - *G*/*Z*(*G*) is a symmetric group *Sn*, and *D* is the class of
   transpositions.
   - *G*/*Z*(*G*) is a symplectic group Sp(2*n*, 2) over the field of order
   2, and *D* is the class of transvections
   - *G*/*Z*(*G*) is a projective special unitary group PSU(*n*, 2),
and *D*is the class of transvections
   - *G*/*Z*(*G*) is an orthogonal group O?(2*n*, 2), and *D* is the class
   of transvections
   - *G*/*Z*(*G*) is an index 2 subgroup O?, ?(*n*, 3) of the orthogonal
   group O?(*n*, 3) generated by the class *D* of reflections of norm ?
   vectors, where ? and ? can be 1 or -1.
   - *G*/*Z*(*G*) is one of the three Fischer
groups<http://en.wikipedia.org/wiki/Fischer_group>Fi
   22, Fi23, Fi24.

If the condition that the derived group of *G* is perfect is dropped there
are two extra cases:

   - *G*/*Z*(*G*) is one of two groups containing on orthogonal group O+(8,
   2) or O-(8, 3) with index 3.

From sam at Math.RWTH-Aachen.De  Wed Apr 10 12:52:06 2013
From: sam at Math.RWTH-Aachen.De (Thomas Breuer)
Date: Wed, 10 Apr 2013 13:52:06 +0200
Subject: [GAP Forum] 3-transposition groups
In-Reply-To: <CAOng4KieuvPMiAtmxe4cR3iaMuT7UpqfMPnROc8wJ=QSz+u_mg@mail.gmail.com>
References: <CAOng4KieuvPMiAtmxe4cR3iaMuT7UpqfMPnROc8wJ=QSz+u_mg@mail.gmail.com>
Message-ID: <20130410115206.GA25943@gemma.math.rwth-aachen.de>

Dear Marek,

the group GO(+1,6,3) has the structure 2 x PGO(+1,6,3).
The group in question is PGO(+1,6,3), which is called L4(3).2_2
in the ATLAS of Finite Groups.
In GAP, you can construct the group for example as the permutation
group obtained from the projective action of GO(+1,6,3),
or as `PrimitiveGroup( 117, 3 )'.

The group GO(-1,6,3) has the structure 2.U_4(3).(2^2)_{122},
using ATLAS notation.
The group in question is U_4(3).2_2.
In GAP, it can be obtained for example as `PrimitiveGroup( 126, 8 )'.

All the best,
Thomas


On Wed, Apr 10, 2013 at 11:42:05AM +0200, Marek Mitros wrote:
> Dear Forum,
> 
> I have read in wikipedia that there are following 3-transposition groups.
> See below quote from wikipedia article on "3-transposition groups". I have
> no problem to obtain in GAP groups SO(1,n,2), Omega(1,n,2), PSU(n,2),
> Sp(n,2). I can also define Fischer groups Fi22, Fi23, Fi24 using Atlas
> package. I have only trouble with O+-(2n,3) case. E.g. neither SO(1,6,3)
> nor Omega (1,6,3) is 3-transposition group. What is the way to define the
> 3-transposition group defined under case  O?, ?(*n*, 3) below.
> 
> 
> Regards,
> Marek
> 
> ----------------------------------
> 
> 
> Suppose that *G* is a group that is generated by conjugacy class of
> 3-transpositions and such that the 2 and 3
> cores<http://en.wikipedia.org/wiki/P-core>
> *O*2(*G*) and *O*3(*G*) are both contained in the center *Z*(*G*) of
> *G*and the derived group of
> *G* is perfect. Then Fischer
> (1971<http://en.wikipedia.org/wiki/3-transposition_group#CITEREFFischer1971>)
> proved that up to isomorphism *G*/*Z*(*G*) is one of the following groups
> and *D* is the image of the given conjugacy class:
> 
>    - *G*/*Z*(*G*) is a symmetric group *Sn*, and *D* is the class of
>    transpositions.
>    - *G*/*Z*(*G*) is a symplectic group Sp(2*n*, 2) over the field of order
>    2, and *D* is the class of transvections
>    - *G*/*Z*(*G*) is a projective special unitary group PSU(*n*, 2),
> and *D*is the class of transvections
>    - *G*/*Z*(*G*) is an orthogonal group O?(2*n*, 2), and *D* is the class
>    of transvections
>    - *G*/*Z*(*G*) is an index 2 subgroup O?, ?(*n*, 3) of the orthogonal
>    group O?(*n*, 3) generated by the class *D* of reflections of norm ?
>    vectors, where ? and ? can be 1 or -1.
>    - *G*/*Z*(*G*) is one of the three Fischer
> groups<http://en.wikipedia.org/wiki/Fischer_group>Fi
>    22, Fi23, Fi24.
> 
> If the condition that the derived group of *G* is perfect is dropped there
> are two extra cases:
> 
>    - *G*/*Z*(*G*) is one of two groups containing on orthogonal group O+(8,
>    2) or O-(8, 3) with index 3.



From member at linkedin.com  Fri Apr 12 03:26:48 2013
From: member at linkedin.com (Alireza Abdollahi via LinkedIn)
Date: Fri, 12 Apr 2013 02:26:48 +0000 (UTC)
Subject: [GAP Forum] Invitation to connect on LinkedIn
Message-ID: <1762105033.5760490.1365733608513.JavaMail.app@ela4-app0134.prod>

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From member at linkedin.com  Fri Apr 12 03:27:11 2013
From: member at linkedin.com (Alireza Abdollahi via LinkedIn)
Date: Fri, 12 Apr 2013 02:27:11 +0000 (UTC)
Subject: [GAP Forum] Invitation to connect on LinkedIn
Message-ID: <21337448.11648058.1365733631243.JavaMail.app@ela4-app0128.prod>

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From graham.ellis at nuigalway.ie  Mon Apr 15 17:51:38 2013
From: graham.ellis at nuigalway.ie (Ellis, Grahamj)
Date: Mon, 15 Apr 2013 17:51:38 +0100
Subject: [GAP Forum] 2-year lectureship at Galway
References: <CAOng4KieuvPMiAtmxe4cR3iaMuT7UpqfMPnROc8wJ=QSz+u_mg@mail.gmail.com>
	<20130410115206.GA25943@gemma.math.rwth-aachen.de>
Message-ID: <47C2E007B3E98F4E8BBC7997F007CE13107718CC@EVS1.ac.nuigalway.ie>

Applications are invited for appointment as a Lecturer Fixed Term in Mathematics at NUI Galway for the period 1st September 2013 to 31st August 2015.

We are looking for someone with interests in an area of algebra, geometry or topology.

The application form can be found here:

http://www.nuigalway.ie/media/nuigalwayie/content/files/hr/lecturer-fixed-term-mathematics.doc

If you'd like further details on the duties of the post please do contact me.


Graham

e-mail: graham.ellis at nuigalway.ie
tel: +353 91 493011

School of Mathematics, Statistics and Applied Mathematics
National University of Ireland, Galway
http://hamilton.nuigalway.ie


From luizrobertomeier at gmail.com  Thu Apr 18 12:25:07 2013
From: luizrobertomeier at gmail.com (Luiz Meier)
Date: Thu, 18 Apr 2013 08:25:07 -0300
Subject: [GAP Forum] Basic help on output (MultiplicationTable)
Message-ID: <CALxKSnwZASZAxD_unvL3yivC7U+-FU1Jk0e22fgyNiPyeEvGCQ@mail.gmail.com>

Hello people,

I'm reading and testing the book:

Abstract Algebra - An Interactive Approach (Mathematica and GAP) Paulsen
(CRC) ISBN:

I'm using GAP 4.5.7 inside SAGE 5.8 (in Fedora 17 64bits) also in
VirtualBox (Win 7 64bits).

OBS.: The book uses the command MultTable (when it was changed to
MultiplicationTable command?)

Question:

When I use the command (just to test): gap> MultiplicationTable([0..9]) in
the book I read:

+|0 1 2 3 4 5 6 7 8 9
-+----------------------------
0|0 1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9 0
2|2 3 4 5 6 7 8 9 0 1
3|3 4 5 6 7 8 9 0 1 2
4|4 5 6 7 8 9 0 1 2 3
5|5 6 7 8 9 0 1 2 3 4
6|6 7 8 9 0 1 2 3 4 5
7|7 8 9 0 1 2 3 4 5 6
8|8 9 0 1 2 3 4 5 6 7
9|9 0 1 2 3 4 5 6 7 8


But instead of it, I get:

[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ],
  [ 1, 3, 5, 7, 9, fail, fail, fail, fail, fail ],
  [ 1, 4, 7, 10, fail, fail, fail, fail, fail, fail ],
  [ 1, 5, 9, fail, fail, fail, fail, fail, fail, fail ],
  [ 1, 6, fail, fail, fail, fail, fail, fail, fail, fail ],
  [ 1, 7, fail, fail, fail, fail, fail, fail, fail, fail ],
  [ 1, 8, fail, fail, fail, fail, fail, fail, fail, fail ],
  [ 1, 9, fail, fail, fail, fail, fail, fail, fail, fail ],
  [ 1, 10, fail, fail, fail, fail, fail, fail, fail, fail ] ]

What am I doing wrong? Where can I found informations about such simple
things to avoid to bore you all? Thank you all in advance.

-- 
*Luiz Roberto Meier*
--

From generalrao at hotmail.com  Sat Apr 20 15:18:04 2013
From: generalrao at hotmail.com (=?gb2312?B?yMS54w==?=)
Date: Sat, 20 Apr 2013 22:18:04 +0800
Subject: [GAP Forum] Command for listing the generators of a given group
Message-ID: <BAY172-W216BD4D211ACC586D02761C5C90@phx.gbl>

Dear forum,

I am having trouble in finding the command for displaying the generators of a given group. Any help would be appreciated.

Regards,
Grant
 		 	   		  

From sandeepr.murthy at gmail.com  Sat Apr 20 15:26:25 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Sat, 20 Apr 2013 15:26:25 +0100
Subject: [GAP Forum] Command for listing the generators of a given group
In-Reply-To: <BAY172-W216BD4D211ACC586D02761C5C90@phx.gbl>
References: <BAY172-W216BD4D211ACC586D02761C5C90@phx.gbl>
Message-ID: <B737F819-E705-47A4-A330-17FF388571C6@gmail.com>

Hi

The command

GeneratorsOfGroup( G )

return a list of generators of a group G.

Sandeep

On 20 Apr 2013, at 15:18, ?? <generalrao at hotmail.com> wrote:

> Dear forum,
> 
> I am having trouble in finding the command for displaying the generators of a given group. Any help would be appreciated.
> 
> Regards,
> Grant
>                         
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From e.obrien at auckland.ac.nz  Thu Apr 25 00:21:46 2013
From: e.obrien at auckland.ac.nz (Eamonn O'Brien)
Date: Thu, 25 Apr 2013 11:21:46 +1200
Subject: [GAP Forum] using nq package in GAP
Message-ID: <5178690A.7050601@auckland.ac.nz>

Dear Forum:

I am attempting to use the "nq"package as part of
  GAP, Version 4.6.2 of 02-Feb-2013under Linux.

It is installed in directory /usr/local/gap/pkg/nq-2.2

The package is compiled and the executable is available.
forder% dir bin/x86_64-unknown-linux-gnu-gcc/nq

But RequirePackage ("nq") fails.

The following seems to be the culprit.

gap>     path := DirectoriesPackagePrograms( "nq" );
[ 
dir("/usr/local/gap4r6/pkg/nq-2.4/bin/x86_64-unknown-linux-gnu-gcc-default64\
/") ]

Why nq-2.4? The directory is nq-2.2?

Any suggestions are welcome.

Thanks.
Eamonn

From alexk at mcs.st-and.ac.uk  Thu Apr 25 00:42:00 2013
From: alexk at mcs.st-and.ac.uk (Alexander Konovalov)
Date: Thu, 25 Apr 2013 00:42:00 +0100
Subject: [GAP Forum] using nq package in GAP
In-Reply-To: <5178690A.7050601@auckland.ac.nz>
References: <5178690A.7050601@auckland.ac.nz>
Message-ID: <F68D4689-0419-417E-ACA5-CAF5C9419747@mcs.st-andrews.ac.uk>

Dear Eamonn,

nq-2.4 is dated January 12th 2012 and is included in GAP 4.6.2 distribution - please 
see an overview listing all versions of packages that were included here:

	http://www.gap-system.org/Releases/4.6.2.html#gap4r6p2_2013_02_02-01_00

One path below has directory 'gap' while the other one - 'gap4r6', maybe that is a problem
and gap4r6/pkg/nq-2.4 is not compiled?

Best wishes,
Alexander


On 25 Apr 2013, at 00:21, Eamonn O'Brien wrote:

> Dear Forum:
> 
> I am attempting to use the "nq"package as part of
> GAP, Version 4.6.2 of 02-Feb-2013under Linux.
> 
> It is installed in directory /usr/local/gap/pkg/nq-2.2
> 
> The package is compiled and the executable is available.
> forder% dir bin/x86_64-unknown-linux-gnu-gcc/nq
> 
> But RequirePackage ("nq") fails.
> 
> The following seems to be the culprit.
> 
> gap>     path := DirectoriesPackagePrograms( "nq" );
> [ dir("/usr/local/gap4r6/pkg/nq-2.4/bin/x86_64-unknown-linux-gnu-gcc-default64\
> /") ]
> 
> Why nq-2.4? The directory is nq-2.2?
> 
> Any suggestions are welcome.
> 
> Thanks.
> Eamonn
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From fvanhove at cage.UGent.be  Fri Apr 26 07:34:38 2013
From: fvanhove at cage.UGent.be (Frederic Vanhove)
Date: Fri, 26 Apr 2013 08:34:38 +0200
Subject: [GAP Forum] GRAPE: maximal cliques of given size?
Message-ID: <517A1FFE.2010908@cage.UGent.be>

Dear members of the forum,

I have a question on cliques in GAP, and on the package GRAPE in particular.
I would like to obtain all maximal cliques (up to isomorphism) of a 
given size k in a graph.

CompleteSubgraphsOfGivenSize(graph,k,true);
will give me representatives (maybe isomorphic ones) of cliques of size k

Cliques(graph, -1,2);
will give me representatives (maybe isomorphic ones) of maximal cliques 
of any size

But is there any (efficient) way to obtain the maximal cliques of one 
fixed size k (I am hoping this would be faster than Cliques(graph,-1,2))

Thanks,
Kind regards,
Fr?d?ric








From member at linkedin.com  Fri Apr 26 08:56:30 2013
From: member at linkedin.com (Vo Tam Van)
Date: Fri, 26 Apr 2013 07:56:30 +0000 (UTC)
Subject: [GAP Forum] Invitation to connect on LinkedIn
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From: member at linkedin.com (Vo Tam Van)
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Subject: [GAP Forum] Invitation to connect on LinkedIn
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From L.H.Soicher at qmul.ac.uk  Fri Apr 26 09:29:36 2013
From: L.H.Soicher at qmul.ac.uk (Leonard Soicher)
Date: Fri, 26 Apr 2013 09:29:36 +0100
Subject: [GAP Forum] GRAPE: maximal cliques of given size?
In-Reply-To: <517A1FFE.2010908@cage.UGent.be>
References: <517A1FFE.2010908@cage.UGent.be>
Message-ID: <20130426082936.GA6943@maths.qmul.ac.uk>

Dear Fr?d?ric, Dear GAP-Forum,

First, make sure you have the latest version of GRAPE (4.6), and read the
documentation for the very flexible function CompleteSubgraphsOfGivenSize
(you should also review the documentation for CompleteSubgraphs
(a.k.a. Cliques)).

In particular:

        CompleteSubgraphsOfGivenSize( gamma, k, 2, true ); 

will return a set of  gamma.group  orbit-representatives of the maximal
cliques of size  k  of the simple graph  gamma.  If you want to classify
the maximal cliques of size  k  up to the action of the automorphism
group of  gamma,  then you must first make sure that gamma.group  is that
(full) automorphism group.  This can be accomplished via:

       gamma := NewGroupGraph( AutomorphismGroup(gamma), gamma ); 

Best wishes,
Leonard

On Fri, Apr 26, 2013 at 08:34:38AM +0200, Frederic Vanhove wrote:
> Dear members of the forum,
> 
> I have a question on cliques in GAP, and on the package GRAPE in particular.
> I would like to obtain all maximal cliques (up to isomorphism) of a 
> given size k in a graph.
> 
> CompleteSubgraphsOfGivenSize(graph,k,true);
> will give me representatives (maybe isomorphic ones) of cliques of size k
> 
> Cliques(graph, -1,2);
> will give me representatives (maybe isomorphic ones) of maximal cliques 
> of any size
> 
> But is there any (efficient) way to obtain the maximal cliques of one 
> fixed size k (I am hoping this would be faster than Cliques(graph,-1,2))
> 
> Thanks,
> Kind regards,
> Fr?d?ric
> 
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From hn10 at uakron.edu  Sat Apr 27 14:52:56 2013
From: hn10 at uakron.edu (Nguyen,Hung Ngoc)
Date: Sat, 27 Apr 2013 09:52:56 -0400
Subject: [GAP Forum] checking subgroups and conjugacy classes
In-Reply-To: <F68D4689-0419-417E-ACA5-CAF5C9419747@mcs.st-andrews.ac.uk>
References: <5178690A.7050601@auckland.ac.nz>,
	<F68D4689-0419-417E-ACA5-CAF5C9419747@mcs.st-andrews.ac.uk>
Message-ID: <E223173E24F6974099E50D0C638EF44D8FC9465CE3@MAILBOX.uanet.edu>

Dear all,

The following is beyond my GAP expertise. I appreciate very much if you can help me.

Let g:=M_{10}=A_6 . 2_3 - this is the stabilizer of a point in M_{11}. First I want to check whether g is isomorphic to a subgroup of GL(2,19). If the answer is yes, then list the structures of all groups G such that G/(C_{19} * C_{19}) = g where g acts naturally on C_{19} * C_{19}. Here C_{19} is the cyclic group of order 19.

For such a group G and a prime p dividing |G|, list the number of p-regular conjugacy classes of G (a class is p-regular if its element order is not divisible by p). 

Thank you very much,
Hung.   




From hulpke at me.com  Sat Apr 27 16:12:55 2013
From: hulpke at me.com (Alexander Hulpke)
Date: Sat, 27 Apr 2013 09:12:55 -0600
Subject: [GAP Forum] checking subgroups and conjugacy classes
In-Reply-To: <E223173E24F6974099E50D0C638EF44D8FC9465CE3@MAILBOX.uanet.edu>
References: <5178690A.7050601@auckland.ac.nz>
	<F68D4689-0419-417E-ACA5-CAF5C9419747@mcs.st-andrews.ac.uk>
	<E223173E24F6974099E50D0C638EF44D8FC9465CE3@MAILBOX.uanet.edu>
Message-ID: <EE97F828-0635-44D1-9995-C4433E4E156D@me.com>

Dear Forum, Dear Hung Nguyen,

> \Let g:=M_{10}=A_6 . 2_3 - this is the stabilizer of a point in M_{11}. First I want to check whether g is isomorphic to a subgroup of GL(2,19). If the answer is yes, then list the structures of all groups G such that G/(C_{19} * C_{19}) = g where g acts naturally on C_{19} * C_{19}. Here C_{19} is the cyclic group of order 19.
> 
> For such a group G and a prime p dividing |G|, list the number of p-regular conjugacy classes of G (a class is p-regular if its element order is not divisible by p). 

There is an old theorem (by Dickson, I believe) that classifies the subgroups of PSL_2(q). The theorem is for example in Huppert's first volume but the book is in my office, so I can't find the exact page.
The only simple nonabelian subgroups are the obvious PSL's and A_5. Thus M10 cannot be a subgroup of GL2(19).

Ignoring this, in GAP you probably would use
h:=GL(2,19);
u:=List(ConjugacyClassesSubgroups(h),Representative);
to get a list of representatives of all subgroups up to conjugacy,
u:=Filtered(u,x->IsomorphismGroups(x,g)<>fail);
to find those which are isomorphic to your group g.

To classify the extensions abstractly (assuming that by `*' you mean direct product) you would need cohomology for nonsolvable factor groups, which the `cohomolo' package provides. However, given the small size, you also would find such a group (apart from a few obvioud degenerate cases) in the libary of perfect groups.

Regards,

   Alexander Hulpke



From harshaarora.2008 at gmail.com  Mon Apr 29 12:01:27 2013
From: harshaarora.2008 at gmail.com (Harsha Arora)
Date: Mon, 29 Apr 2013 16:31:27 +0530
Subject: [GAP Forum] TO FIND THE CENTER OFUTOMORPHISM OF A GROUP
Message-ID: <CAMABT+pisC52gtbCwi_OPJJiZg-4vMao0NnSJVsEJr4tFEh8LQ@mail.gmail.com>

HELLO SIR
IWANT HOW CAN I FIND THE AUTOMORPHISM GROUP OF A GROUP AND CENTRAL
AUTOMORPHISM GROUP AND THE CENTER F AUTOMORPHISM GROUP.

From sandeepr.murthy at gmail.com  Mon Apr 29 12:04:58 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Mon, 29 Apr 2013 12:04:58 +0100
Subject: [GAP Forum] TO FIND THE CENTER OFUTOMORPHISM OF A GROUP
In-Reply-To: <CAMABT+pisC52gtbCwi_OPJJiZg-4vMao0NnSJVsEJr4tFEh8LQ@mail.gmail.com>
References: <CAMABT+pisC52gtbCwi_OPJJiZg-4vMao0NnSJVsEJr4tFEh8LQ@mail.gmail.com>
Message-ID: <517E53DA.1090706@gmail.com>

AutomorphismGroup( G ) will give you the automorphism
group of group G.

Sandeep.

Harsha Arora wrote:
> HELLO SIR
> IWANT HOW CAN I FIND THE AUTOMORPHISM GROUP OF A GROUP AND CENTRAL
> AUTOMORPHISM GROUP AND THE CENTER F AUTOMORPHISM GROUP.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From yashakon at mail.ru  Thu Apr 18 19:52:30 2013
From: yashakon at mail.ru (=?UTF-8?B?0K/QutC+0LIg0JrQvtC90L7QvdC+0LI=?=)
Date: Thu, 18 Apr 2013 22:52:30 +0400
Subject: [GAP Forum] =?utf-8?q?Problem_with_computing?=
Message-ID: <1366311150.54706949@f387.i.mail.ru>

 Hello!

I want to compute the abelianization
of the kernel of the map F->G,
where F is finitely presented group
with generators  a_1, ..., a_10 and relations
a_1^2=...=a_10^2=e, a_1*a_2*a_3*a_4*a_5=a_6*a_7*a_8*a_9*a_10=e,
G is abelian group (Z/2)^4 with basis e_1,...,e_4.
The map is given by images
a_1->e_1,
a_2->e_2,
a_3->e_3,
a_4->e_4,
a_5->e_1*e_2*e*3*e_4,
a_6->e_2*e_3*e_4,
a_7->e_1*e_3*e_4,
a_8->e_1*e_3,
a_9->e_2*e_4,
a_10->e_3*e_4.

?I realize it by the following code:

f:=FreeGroup(10);
F:=f/[f.1^2,f.2^2,f.3^2,f.4^2,f.5^2,f.6^2,f.7^2,f.8^2,f.9^f,f.10^2,f.1*f.2*f.3*f.4*f.5,f.6*f.8*f.8*f.9*f.10];
G:=Group((1,2),(3,4),(5,6),(7,8));
hom:=GroupHomomorphismByImages(F,G,[F.1,F.2,F.3,F.4,F.5,F.6,F.7,F.8,F.9,F.10],[(1,2),(3,4),(5,6),(7,8),(1,2)(3,4)(5,6)(7,8),(3,4)(5,6)(7,8),(1,2)(5,6)(7,8),(1,2)(5,6),(3,4)(7,8),(5,6)(7,8)]);
iso:=IsomorphismFpGroup(Kernel(hom));
h:=Range(iso);
comm:=CommutatorFactorGroup(h);
Order(comm);
?

But it says, that the order is infinity, but it is
obviously impossible, because it is finitely
generated subgroup by elements of order
2.

Thank you,
Yakov Kononov.?

From zeinab_foruzanfar at iust.ac.ir  Mon Apr 29 15:27:23 2013
From: zeinab_foruzanfar at iust.ac.ir (zeinab foruzanfar)
Date: Mon, 29 Apr 2013 17:57:23 +0330
Subject: [GAP Forum] (no subject)
Message-ID: <WC20130429142723.9037B7@iust.ac.ir>

Hi. I Want some GAP
program to count the number of Sylow $p$-subgroups which pairwise
intersect trivially. Also I want to show that if $P$ and $Q$ are two
Sylow $p$-subgroups, then the intersection of $P^x$ and $P^y$ is trivial
for $x,y \in Q$. Is it possible to send me a program to count these.
Thank you
Best Regards




From marek at mitros.org  Fri May  3 17:48:46 2013
From: marek at mitros.org (Marek Mitros)
Date: Fri, 3 May 2013 18:48:46 +0200
Subject: [GAP Forum] Sqrt(1+2i)
In-Reply-To: <CAOng4Kgm3_0rVFECOAh=3mbCbyPqazne4o8kS6=KLK_Ufx5wLg@mail.gmail.com>
References: <CAOng4Kgm3_0rVFECOAh=3mbCbyPqazne4o8kS6=KLK_Ufx5wLg@mail.gmail.com>
Message-ID: <CAOng4KjWcTVgiYXGuSQgxOZYnUDhdjafr0d1SdzNA7uU6Rh0ng@mail.gmail.com>

Dear Forum,Consider following GAP code - see below. It means that square
root of unit complex number (1+2i)/Sqrt(5) belongs to cyclotomics CF(40)
field. In the code below I use (2+i)/Sqrt(5) but the same is valid for
(1+2i)/Sqrt(5).Somobody has answered that Sqrt(1+2i) is not cyclotomics.
Maybe it is true, I don't know. For my purpose it is enough to work with
unit complex.Regards,Marekx:=Indeterminate(CF(40),"x"); gap>
a:=(2+i)/Sqrt(5);
1/5*E(20)+2/5*E(20)^4-2/5*E(20)^8
+1/5*E(20)^9-2/5*E(20)^12-1/5*E(20)^13
+2/5*E(20)^16-1/5*E(20)^17
gap> f:=x*x-a;
x^2+(-1/5*E(20)-2/5*E(20)^4+2/5*E(20)^8-1/5*\
E(20)^9+2/5*E(20)^12+1/5*E(20)^13-2/5*E(20)^\
16+1/5*E(20)^17)
gap> sol:=RootsOfPolynomial(CF(40),f);
[ 1/5*E(40)^7-2/5*E(40)^13+1/5*E(40)^21
     -1/5*E(40)^23-1/5*E(40)^29-2/5*E(40)^31
     +2/5*E(40)^37+2/5*E(40)^39,
  -1/5*E(40)^7+2/5*E(40)^13-1/5*E(40)^21
     +1/5*E(40)^23+1/5*E(40)^29+2/5*E(40)^31
     -2/5*E(40)^37-2/5*E(40)^39 ]
03-10-2012 14:13, "Marek Mitros" <marek at mitros.org> napisa?(a):

> Dear Forum Users,
>
> I need to calculate Sqrt(1+2i) i.e. find the complex number z=a+bi
> such that z^2=(1+2i). Using traditional pen and paper I calculated
> that a=Sqrt((1+Sqrt(5))/2) and b=Sqrt((Sqrt(5)-1)/2). But how to
> express these numbers in GAP ? Is this number cyclotomic or not ?
> Using formula for tangent (x/2) = (1-cos(x))/sin(x) I obtain number
> c=1+ ((Sqrt(5)-1)/2)*i which is collinear with needed number i.e. have
> the same angle. So we have ImaginaryPart(c*(1-2*i))=0.
>
> Another question I have is how to normalize complex number in GAP.
> E.g. I have number c=1+ ((Sqrt(5)-1)/2)*i and I would like to find
> number c/|c| i.e. lying on unit circle on complex plane. If the |c|^2
> is rational then I can apply Sqrt. But this does not work for real
> cyclotomics.
>
> Any advice ?
>
> Regards,
> Marek
>

From alexk at mcs.st-andrews.ac.uk  Mon May  6 18:30:57 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 6 May 2013 18:30:57 +0100
Subject: [GAP Forum] GAP 4.6.4 release announcement
Message-ID: <DD36CF7C-EF48-4A6E-B944-5765EA385A6D@mcs.st-andrews.ac.uk>

Dear GAP Forum,

This is to announce the release of GAP 4.6.4.

You can download GAP 4.6.4 from 

	http://www.gap-system.org/Releases/

The alternative GAP distributions listed at 

	http://www.gap-system.org/Download/#alternatives

will be updated in due course.

The overview of changes in GAP 4.6.4 is given below.

New functionality:

 * New command line option -O was introduced to disable loading obsolete
 variables. This option may be used, for example, to check that they are
 not used in a GAP package or one's own GAP code.

Fixed bugs which could lead to incorrect results:

 * Fixed the bug in NewmanInfinityCriterion which may cause returning
 true instead of false. [Reported by Lev Glebsky]

Fixed bugs which could lead to crashes:

 * Fixed the kernel method for Remove which did not raise an error in case
 of empty lists, but corrupted the object. The error message in a library
 method is also improved. [Reported by Roberto R?dina]

Fixed bugs that could lead to break loops:

 * Fixed requirements in a method to multiply a list and an algebraic
 element. [Reported by Sebastian Gutsche]

 * Fixed a bug in NaturalCharacter entering a break loop when being called
 on a homomorphism whose image is not a permutation group. [Reported by
 Sebastian Gutsche]

 * Fixed a bug in ExponentsConjugateLayer which occured, for example, in
 some calls of SubgroupsSolvableGroup [Reported by Ramon Esteban-Romero]

 * Fixed a problem with displaying function fields, e.g.
 Field(Indeterminate(Rationals,"x")). [Reported by Jan Willem Knopper]

 * Fixed two bugs in the code for NaturalHomomorphismByIdeal for
 polynomial rings. [Reported by Martin Leuner]

 * Added  missing method for String for -infinity.

 * Fixed the bug with ONanScottType not recognising product action
 properly in some cases.

 * The method for SlotUsagePattern for straight line programs had a bug
 which triggered an error, if the straight line program contained
 unnecessary steps.

You may also access this overview by scrolling till the end of the
chapter after entering  '?Changes between GAP 4.5 and GAP 4.6' in 
GAP 4.6.4, or view it online at

http://www.gap-system.org/Manuals//doc/changes/chap2.html#X82859C4083F0D7B9

In addition to the improved functionality and fixed bugs in the core 
GAP system listed above, several packages have been updated since the 
previous GAP 4.6.3 release:

================================================
Package name          | Version     | Date      
------------------------------------------------ 
AutoDoc               | 2013.01.16  | 16/01/2013
Example               | 3.4.3       | 27/03/2013
GradedRingForHomalg   | 2013.02.07  | 07/02/2013
MatricesForHomalg     | 2013.04.16  | 16/04/2013
Modules               | 2013.04.19  | 19/04/2013
OpenMath              | 11.1.4      | 27/03/2013
orb                   | 4.6         | 02/05/2013
RingsForHomalg        | 2013.04.19  | 19/04/2013
Smallsemi             | 0.6.6       | 24/04/2013
ToolsForHomalg        | 2013.04.16  | 16/04/2013
Wedderga              | 4.5.4       | 28/03/2013
================================================

We encourage all users to upgrade to GAP 4.6.4. If you need any help 
or would like to report any problems, please do not hesitate to contact 
us at support at gap-system.org.

Please note that we are regularly updating the GAP distribution to 
include new versions of GAP packages, but we may not announce each 
of them to the Forum. We intend to use the Forum to announce updates 
of the core GAP system and only of some packages which may fix serious 
issues or have major influence on GAP. 

Wishing you fun and success using GAP,

The GAP Group



From alexander.konovalov at gmail.com  Mon May  6 18:32:27 2013
From: alexander.konovalov at gmail.com (Alexander Konovalov)
Date: Mon, 6 May 2013 18:32:27 +0100
Subject: [GAP Forum] GAP 4.6.4 release announcement
Message-ID: <16CE73EC-6C50-444C-9DD6-748F2C4A2993@gmail.com>

Dear GAP Forum,

This is to announce the release of GAP 4.6.4.

You can download GAP 4.6.4 from 

	http://www.gap-system.org/Releases/

The alternative GAP distributions listed at 

	http://www.gap-system.org/Download/#alternatives

will be updated in due course.

The overview of changes in GAP 4.6.4 is given below.

New functionality:

* New command line option -O was introduced to disable loading obsolete
variables. This option may be used, for example, to check that they are
not used in a GAP package or one's own GAP code.

Fixed bugs which could lead to incorrect results:

* Fixed the bug in NewmanInfinityCriterion which may cause returning
true instead of false. [Reported by Lev Glebsky]

Fixed bugs which could lead to crashes:

* Fixed the kernel method for Remove which did not raise an error in case
of empty lists, but corrupted the object. The error message in a library
method is also improved. [Reported by Roberto R?dina]

Fixed bugs that could lead to break loops:

* Fixed requirements in a method to multiply a list and an algebraic
element. [Reported by Sebastian Gutsche]

* Fixed a bug in NaturalCharacter entering a break loop when being called
on a homomorphism whose image is not a permutation group. [Reported by
Sebastian Gutsche]

* Fixed a bug in ExponentsConjugateLayer which occured, for example, in
some calls of SubgroupsSolvableGroup [Reported by Ramon Esteban-Romero]

* Fixed a problem with displaying function fields, e.g.
Field(Indeterminate(Rationals,"x")). [Reported by Jan Willem Knopper]

* Fixed two bugs in the code for NaturalHomomorphismByIdeal for
polynomial rings. [Reported by Martin Leuner]

* Added  missing method for String for -infinity.

* Fixed the bug with ONanScottType not recognising product action
properly in some cases.

* The method for SlotUsagePattern for straight line programs had a bug
which triggered an error, if the straight line program contained
unnecessary steps.

You may also access this overview by scrolling till the end of the
chapter after entering  '?Changes between GAP 4.5 and GAP 4.6' in 
GAP 4.6.4, or view it online at

http://www.gap-system.org/Manuals//doc/changes/chap2.html#X82859C4083F0D7B9

In addition to the improved functionality and fixed bugs in the core 
GAP system listed above, several packages have been updated since the 
previous GAP 4.6.3 release:

================================================
Package name          | Version     | Date      
------------------------------------------------ 
AutoDoc               | 2013.01.16  | 16/01/2013
Example               | 3.4.3       | 27/03/2013
GradedRingForHomalg   | 2013.02.07  | 07/02/2013
MatricesForHomalg     | 2013.04.16  | 16/04/2013
Modules               | 2013.04.19  | 19/04/2013
OpenMath              | 11.1.4      | 27/03/2013
orb                   | 4.6         | 02/05/2013
RingsForHomalg        | 2013.04.19  | 19/04/2013
Smallsemi             | 0.6.6       | 24/04/2013
ToolsForHomalg        | 2013.04.16  | 16/04/2013
Wedderga              | 4.5.4       | 28/03/2013
================================================

We encourage all users to upgrade to GAP 4.6.4. If you need any help 
or would like to report any problems, please do not hesitate to contact 
us at support at gap-system.org.

Please note that we are regularly updating the GAP distribution to 
include new versions of GAP packages, but we may not announce each 
of them to the Forum. We intend to use the Forum to announce updates 
of the core GAP system and only of some packages which may fix serious 
issues or have major influence on GAP. 

Wishing you fun and success using GAP,

The GAP Group



From mhxgh at yahoo.com  Tue May  7 06:28:57 2013
From: mhxgh at yahoo.com (M.H.GH)
Date: Mon, 6 May 2013 22:28:57 -0700 (PDT)
Subject: [GAP Forum] Sylow $p$-subgroups which pairwise intersect
	trivially
In-Reply-To: <WC20130429142723.9037B7@iust.ac.ir>
References: <WC20130429142723.9037B7@iust.ac.ir>
Message-ID: <1367904537.87903.YahooMailNeo@web125003.mail.ne1.yahoo.com>

I hope that be useful.

****************

VP := function( G , p )?

local P, N, R, Pi, Pj, i, j, res, szr, SW;?
P := SylowSubgroup( G , p );
N := Normalizer( G , P );
R := AsList( RightTransversal( G , N ) );
res := [];
szr := Size(R);
Print ( "\nUpper Bound = Size( RightCosets( G , Normalizer(G,P) ) ) = " , szr , " ... \n\n" );
for i in [1..szr] do
Pi := P^R[i];
SW := 1;
for j in [1..szr] do
Pj := P^R[j];
if Size( Intersection( Pi , Pj ) ) <> 1 and i<>j then
SW := 0;
continue;
fi;
od;
if SW = 1 then
Add( res , Pi );
#Print( "|res| = " , Size( Set( res ) ) , " ... ?");
fi;
od;
Print ( "\n\nResult = " , Size( Set( res ) ) , " .\n\n");
return Size( Set( res ) );
end;;

**************



________________________________
 From: zeinab foruzanfar <zeinab_foruzanfar at iust.ac.ir>
To: forum at gap-system.org 
Sent: Monday, April 29, 2013 6:57 PM
Subject: [GAP Forum] (no subject)
 

Hi. I Want some GAP
program to count the number of Sylow $p$-subgroups which pairwise
intersect trivially. Also I want to show that if $P$ and $Q$ are two
Sylow $p$-subgroups, then the intersection of $P^x$ and $P^y$ is trivial
for $x,y \in Q$. Is it possible to send me a program to count these.
Thank you
Best Regards



_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum

From A.C.Aitchison at dpmms.cam.ac.uk  Tue May  7 07:12:52 2013
From: A.C.Aitchison at dpmms.cam.ac.uk (Dr Andrew C Aitchison)
Date: Tue, 7 May 2013 07:12:52 +0100 (BST)
Subject: [GAP Forum] cryst2params in varnames.tst
Message-ID: <alpine.LRH.2.02.1305070707250.17782@harrier.dpmms.cam.ac.uk>


Whilst running testall.g with the newly released Gap 4.6.4
I hit a minor? failure in varnames.tst:

  ?????????   GAP, Version 4.6.4 of 04-May-2013 (free sGPL)
  ?  GAP  ?   http://www.gap-system.org
  ?????????   Architecture: x86_64-redhat-linux-gnu-gcc-default64
  Libs used:  gmp, readline
  Loading the library and packages ...
  Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
  Packages:   AClib 1.2, Alnuth 3.0.0, AutPGrp 1.5, CRISP 1.3.6, Cryst 4.1.11,
              CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.3, FGA 1.2.0,
              GAPDoc 1.5.1, IRREDSOL 1.2.1, LAGUNA 3.6.3, Polenta 1.3.1,
              Polycyclic 2.11, RadiRoot 2.6, ResClasses 3.3.0, Sophus 1.23,
              SpinSym 1.5, TomLib 1.2.2
  Try '?help' for help. See also  '?copyright' and  '?authors'

testing: /usr/gap4r6/tst/varnames.tst
########> Diff in /usr/gap4r6/tst/varnames.tst, line 9:
# Input is:
Filtered( NamesSystemGVars(), x -> not x in ALL_KEYWORDS() and
            ( Length(x)=1 or IsLowerAlphaChar(x[1]) ) );
# Expected output:
[ "*", "+", "-", ".", "/", "<", "=", "E", "X", "Z", "^", "fail", 
"infinity",
   "last", "last2", "last3", "time" ]
# But found:
[ "*", "+", "-", ".", "/", "<", "=", "E", "X", "Z", "^", "cryst2params",
   "cryst3params", "cryst4params", "fail", "infinity", "last", "last2",
   "last3", "time" ]
########
varnames.tst               0             22

Looks like either one of the Cryst package is leaking variables,
or the test needs updating ?

-- 
Dr. Andrew C. Aitchison		Computer Officer, DPMMS, Cambridge
A.C.Aitchison at dpmms.cam.ac.uk	http://www.dpmms.cam.ac.uk/~werdna

From colva at mcs.st-and.ac.uk  Tue May  7 14:08:39 2013
From: colva at mcs.st-and.ac.uk (Colva Roney-Dougal)
Date: Tue, 7 May 2013 14:08:39 +0100
Subject: [GAP Forum] Groups St Andrews - Earlybird deadline approaching!
Message-ID: <83A01D06-DC9E-4285-9729-B557BB2FD3FF@mcs.st-and.ac.uk>

Dear Forum,

This is to remind you that Early Bird Discount on registration for Groups St Andrews closes on May 10th. Please see the conference webpages: http://www.groupsstandrews.org/2013/index.shtml

Our Principal Speakers are Emmanuel Breuillard, Martin Liebeck, Alan Reid and Karen Vogtmann. In addition, we have Invited One-Hour Speakers Inna Capdebosq, Radha Kessar, Marcus Lohrey, Derek Robinson and Christopher Voll.

We welcome submission of articles from all participants for the Conference Proceedings, surveying an area of their expertise.  Further information, including the format for submitted papers and the deadline for submission, can be found on the conference webpage.

The facility to submit a title and abstract for a talk is also available.  You can do this and see the talks that are already submitted via the conference webpages.

We hope to see you in August.

Colva Roney-Dougal
(on behalf of the organising committee)

The University of St Andrews is a charity registered in Scotland : No SC013532



From klajok at interia.pl  Tue May  7 20:31:02 2013
From: klajok at interia.pl (Daniel Blazewicz)
Date: Tue, 07 May 2013 21:31:02 +0200
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI stack
	overflows
Message-ID: <qorxgldebujtuqqjwrpa@vsne>


Hi,

I use RootsOfPolynomialAsRadicals from RadiRoot package to compute roots of some simple polynomials of degree 5 and 6. In many cases mentioned method works excellent and produces very nice formulas. However for few specific polynomials it fails with stack overflow error. This is fully deterministic behavior on my environment, e.g. for f(x) = x^6+30*x+93 :


 ?????????   GAP, Version 4.6.2 of 02-Feb-2013 (free software, GPL)
 ?  GAP  ?   http://www.gap-system.org
 ?????????   Architecture: i686-pc-linux-gnu-gcc-default32
 Libs used:  gmp, readline
 Loading the library and packages ...
 Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
 Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, Browse 1.8.2, CRISP 1.3.5, Cryst 4.1.11, CrystCat 1.1.6, CTblLib 1.2.1,
             FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO 4.2, IRREDSOL 1.2.1, LAGUNA 3.6.3, Polenta 1.3.1, Polycyclic 2.10.1, RadiRoot 2.6,
             ResClasses 3.3.0, Sophus 1.23, TomLib 1.2.2
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap> x := Indeterminate( Rationals, "x" );;
gap> f := UnivariatePolynomial( Rationals, [93,30,0,0,0,0,1]);;
gap> RootsOfPolynomialAsRadicals(f, "latex", "x6_30x_93");;
  ***   at top-level: ...n(),[2,4,3])>=0,fac=lift(nffactor(f,pol)),if(
  ***                                             ^--------------------
  *** nffactor: the PARI stack overflows !
  current stack size: 128000000 (122.070 Mbytes)
  [hint] you can increase GP stack with allocatemem()

  ***   at top-level: for(i=1,#fac[,1],for(j=1,fac[i,2
  ***                             ^--------------------
  ***   _[,_]: not a matrix.
Error, List Element: <list>[1] must have an assigned value in
  faktoren[1] := lcoeff * faktoren[1]; called from 
FactorsPolynomialPari( AlgExtEmbeddedPol( H, poly ) ) called from
FactorsPolynomialAlgExt( erw.H, CyclotomicPolynomial( Rationals, i ) ) called from
RR_RootOfUnity( erw, DegreeOverPrimeField( erw.K ) ) called from
CallFuncList( RootsOfPolynomialAsRadicalsNC, arg ) called from
<function "RootsOfPolynomialAsRadicals">( <arguments> )
 called from read-eval loop at line 3 of *stdin*
you can 'return;' after assigning a value
brk> 


Other examples:
f(x) = x^6+105*x+237
f(x) = x^6+243*x+513

I don't know how to work around this problem. Tried to increase workspace size but it did not solve the issue. I will be grateful for your help.

With regards,
Daniel


From andreas at mcs.st-and.ac.uk  Tue May  7 23:46:11 2013
From: andreas at mcs.st-and.ac.uk (Andreas Distler)
Date: Wed, 08 May 2013 00:46:11 +0200
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <qorxgldebujtuqqjwrpa@vsne>
References: <qorxgldebujtuqqjwrpa@vsne>
Message-ID: <51898433.5060902@mcs.st-andrews.ac.uk>

Dear Daniel,

I cannot reproduce your problem. Which version of PARI/GP are you using?

Anyway, you can use the function SetPariStackSize from the Alnuth 
package to increase the amount of memory PARI/GP will use. The function 
takes a positive integer as argument specifying the amount of memory in 
MB. The default value is 128 MB as you may have guessed.

It's an oversight that SetPariStackSize is not documented. I will change 
this in the next version of Alnuth. Thanks for pointing me to this 
shortcoming.

Best wishes,

    Andreas

On 07/05/13 21:31, Daniel Blazewicz wrote:
> Hi,
>
> I use RootsOfPolynomialAsRadicals from RadiRoot package to compute roots of some simple polynomials of degree 5 and 6. In many cases mentioned method works excellent and produces very nice formulas. However for few specific polynomials it fails with stack overflow error. This is fully deterministic behavior on my environment, e.g. for f(x) = x^6+30*x+93 :
>
>
>   ?????????   GAP, Version 4.6.2 of 02-Feb-2013 (free software, GPL)
>   ?  GAP  ?   http://www.gap-system.org
>   ?????????   Architecture: i686-pc-linux-gnu-gcc-default32
>   Libs used:  gmp, readline
>   Loading the library and packages ...
>   Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
>   Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, Browse 1.8.2, CRISP 1.3.5, Cryst 4.1.11, CrystCat 1.1.6, CTblLib 1.2.1,
>               FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO 4.2, IRREDSOL 1.2.1, LAGUNA 3.6.3, Polenta 1.3.1, Polycyclic 2.10.1, RadiRoot 2.6,
>               ResClasses 3.3.0, Sophus 1.23, TomLib 1.2.2
>   Try '?help' for help. See also  '?copyright' and  '?authors'
> gap> x := Indeterminate( Rationals, "x" );;
> gap> f := UnivariatePolynomial( Rationals, [93,30,0,0,0,0,1]);;
> gap> RootsOfPolynomialAsRadicals(f, "latex", "x6_30x_93");;
>    ***   at top-level: ...n(),[2,4,3])>=0,fac=lift(nffactor(f,pol)),if(
>    ***                                             ^--------------------
>    *** nffactor: the PARI stack overflows !
>    current stack size: 128000000 (122.070 Mbytes)
>    [hint] you can increase GP stack with allocatemem()
>
>    ***   at top-level: for(i=1,#fac[,1],for(j=1,fac[i,2
>    ***                             ^--------------------
>    ***   _[,_]: not a matrix.
> Error, List Element: <list>[1] must have an assigned value in
>    faktoren[1] := lcoeff * faktoren[1]; called from
> FactorsPolynomialPari( AlgExtEmbeddedPol( H, poly ) ) called from
> FactorsPolynomialAlgExt( erw.H, CyclotomicPolynomial( Rationals, i ) ) called from
> RR_RootOfUnity( erw, DegreeOverPrimeField( erw.K ) ) called from
> CallFuncList( RootsOfPolynomialAsRadicalsNC, arg ) called from
> <function "RootsOfPolynomialAsRadicals">( <arguments> )
>   called from read-eval loop at line 3 of *stdin*
> you can 'return;' after assigning a value
> brk>
>
>
> Other examples:
> f(x) = x^6+105*x+237
> f(x) = x^6+243*x+513
>
> I don't know how to work around this problem. Tried to increase workspace size but it did not solve the issue. I will be grateful for your help.
>
> With regards,
> Daniel
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From mckay at encs.concordia.ca  Wed May  8 05:08:52 2013
From: mckay at encs.concordia.ca (John McKay)
Date: Wed, 8 May 2013 00:08:52 -0400 (EDT)
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <51898433.5060902@mcs.st-andrews.ac.uk>
References: <qorxgldebujtuqqjwrpa@vsne> <51898433.5060902@mcs.st-andrews.ac.uk>
Message-ID: <Pine.LNX.4.58.1305080001340.5529@focus.encs.concordia.ca>


 I remark on solving for the radical roots of f(x) in Z[x]?

We need all  solution (g,h) to f divides g(h(x)) which I call the
ideal decompositon problem. This - by Casperson, Ford, & McKay -
is in:

Casperson, D., Ford, D., McKay, J., Ideal Decompositions and
Subfields. J. Symbolic Computation, J.Symb.Comp., 21,133-137, (1996).
where we use lattice reduction.

Thanks,

John McKay








On Wed, 8 May 2013, Andreas Distler wrote:

> Dear Daniel,
>
> I cannot reproduce your problem. Which version of PARI/GP are you using?
>
> Anyway, you can use the function SetPariStackSize from the Alnuth
> package to increase the amount of memory PARI/GP will use. The function
> takes a positive integer as argument specifying the amount of memory in
> MB. The default value is 128 MB as you may have guessed.
>
> It's an oversight that SetPariStackSize is not documented. I will change
> this in the next version of Alnuth. Thanks for pointing me to this
> shortcoming.
>
> Best wishes,
>
>     Andreas
>
> On 07/05/13 21:31, Daniel Blazewicz wrote:
> > Hi,
> >
> > I use RootsOfPolynomialAsRadicals from RadiRoot package to compute roots of some simple polynomials of degree 5 and 6. In many cases mentioned method works excellent and produces very nice formulas. However for few specific polynomials it fails with stack overflow error. This is fully deterministic behavior on my environment, e.g. for f(x) = x^6+30*x+93 :
> >
> >
> >   ?????????   GAP, Version 4.6.2 of 02-Feb-2013 (free software, GPL)
> >   ?  GAP  ?   http://www.gap-system.org
> >   ?????????   Architecture: i686-pc-linux-gnu-gcc-default32
> >   Libs used:  gmp, readline
> >   Loading the library and packages ...
> >   Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
> >   Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, Browse 1.8.2, CRISP 1.3.5, Cryst 4.1.11, CrystCat 1.1.6, CTblLib 1.2.1,
> >               FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO 4.2, IRREDSOL 1.2.1, LAGUNA 3.6.3, Polenta 1.3.1, Polycyclic 2.10.1, RadiRoot 2.6,
> >               ResClasses 3.3.0, Sophus 1.23, TomLib 1.2.2
> >   Try '?help' for help. See also  '?copyright' and  '?authors'
> > gap> x := Indeterminate( Rationals, "x" );;
> > gap> f := UnivariatePolynomial( Rationals, [93,30,0,0,0,0,1]);;
> > gap> RootsOfPolynomialAsRadicals(f, "latex", "x6_30x_93");;
> >    ***   at top-level: ...n(),[2,4,3])>=0,fac=lift(nffactor(f,pol)),if(
> >    ***                                             ^--------------------
> >    *** nffactor: the PARI stack overflows !
> >    current stack size: 128000000 (122.070 Mbytes)
> >    [hint] you can increase GP stack with allocatemem()
> >
> >    ***   at top-level: for(i=1,#fac[,1],for(j=1,fac[i,2
> >    ***                             ^--------------------
> >    ***   _[,_]: not a matrix.
> > Error, List Element: <list>[1] must have an assigned value in
> >    faktoren[1] := lcoeff * faktoren[1]; called from
> > FactorsPolynomialPari( AlgExtEmbeddedPol( H, poly ) ) called from
> > FactorsPolynomialAlgExt( erw.H, CyclotomicPolynomial( Rationals, i ) ) called from
> > RR_RootOfUnity( erw, DegreeOverPrimeField( erw.K ) ) called from
> > CallFuncList( RootsOfPolynomialAsRadicalsNC, arg ) called from
> > <function "RootsOfPolynomialAsRadicals">( <arguments> )
> >   called from read-eval loop at line 3 of *stdin*
> > you can 'return;' after assigning a value
> > brk>
> >
> >
> > Other examples:
> > f(x) = x^6+105*x+237
> > f(x) = x^6+243*x+513
> >
> > I don't know how to work around this problem. Tried to increase workspace size but it did not solve the issue. I will be grateful for your help.
> >
> > With regards,
> > Daniel
> >
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>


From mckay at encs.concordia.ca  Wed May  8 06:58:08 2013
From: mckay at encs.concordia.ca (John McKay)
Date: Wed, 8 May 2013 01:58:08 -0400 (EDT)
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <Pine.LNX.4.58.1305080001340.5529@focus.encs.concordia.ca>
References: <qorxgldebujtuqqjwrpa@vsne> <51898433.5060902@mcs.st-andrews.ac.uk>
	<Pine.LNX.4.58.1305080001340.5529@focus.encs.concordia.ca>
Message-ID: <Pine.LNX.4.58.1305080153330.16796@focus.encs.concordia.ca>


Your examples of type f:= x^6+ax+b

have galois group (use maple) S3 wr S3 of order 72.

    Solvable 6-ic polynomials are treated by Tom Hagedorn

 in J.Alg  (2000) 233 pp 704-757.

 Lesser degree polynomials are treated in the book by Dummit & Foote.

 John



From klajok at interia.pl  Wed May  8 20:04:01 2013
From: klajok at interia.pl (Daniel Blazewicz)
Date: Wed, 08 May 2013 21:04:01 +0200
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <Pine.LNX.4.58.1305080153330.16796@focus.encs.concordia.ca>
References: <qorxgldebujtuqqjwrpa@vsne> <51898433.5060902@mcs.st-andrews.ac.uk>
	<Pine.LNX.4.58.1305080001340.5529@focus.encs.concordia.ca>
	<Pine.LNX.4.58.1305080153330.16796@focus.encs.concordia.ca>
Message-ID: <kgxbyerupenyhczyfasn@dhlw>

Dear Andreas and John,

Many thanks for your answers.
I used SetPariStackSize(256) and it helped!

My PARI/GP version:
                  GP/PARI CALCULATOR Version 2.5.0 (released)
             amd64 running linux (x86-64/GMP kernel) 64-bit version
        compiled: Nov 17 2011, gcc-4.6.2 (Ubuntu/Linaro 4.6.2-2ubuntu1) 
                (readline v6.2 disabled, extended help enabled)

Best wishes,
Daniel


Od: "John McKay" <mckay at ...>
Do: "Andreas Distler" <andreas at ...>; 
Wys?ane: 8:05 ?roda 2013-05-08
Temat: Re: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI stack overflows

> 
> Your examples of type f:= x^6+ax+b
> 
> have galois group (use maple) S3 wr S3 of order 72.
> 
>     Solvable 6-ic polynomials are treated by Tom Hagedorn
> 
>  in J.Alg  (2000) 233 pp 704-757.
> 
>  Lesser degree polynomials are treated in the book by Dummit & Foote.
> 
>  John
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
> 





From mckay at encs.concordia.ca  Thu May  9 08:14:13 2013
From: mckay at encs.concordia.ca (John McKay)
Date: Thu, 9 May 2013 03:14:13 -0400 (EDT)
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <51898433.5060902@mcs.st-andrews.ac.uk>
References: <qorxgldebujtuqqjwrpa@vsne> <51898433.5060902@mcs.st-andrews.ac.uk>
Message-ID: <Pine.LNX.4.58.1305072349500.5036@focus.encs.concordia.ca>


Dear all:

A solution to the problem: Given f in Z[x], find all g,h such
that f divides g(h(x)) is relevant to expressing te roots of
f in ems of radicals. This is solved in


From suskudar at gmail.com  Thu May  9 08:59:55 2013
From: suskudar at gmail.com (sumeyra uskudar)
Date: Thu, 9 May 2013 10:59:55 +0300
Subject: [GAP Forum] Thanks!
Message-ID: <CADUzUOhLA-vdd7YMTOJJpsebXPnLK=i8MaDs7dYzDk7bG_F1EQ@mail.gmail.com>

This is a honest appriciation message to all moderators and participants of
this forum. Thank you all,
For answering patiently even the easiest questions,
By simply following this ACTIVE forum, one can easily learn how to use GAP
for basic purposes.
One of the most important archives I have ever had is this forum archive.
Thank you very much!



-- 
*S?meyra Bedir*

From suskudar at gmail.com  Thu May  9 09:02:41 2013
From: suskudar at gmail.com (sumeyra uskudar)
Date: Thu, 9 May 2013 11:02:41 +0300
Subject: [GAP Forum] Thanks!
In-Reply-To: <CADUzUOhLA-vdd7YMTOJJpsebXPnLK=i8MaDs7dYzDk7bG_F1EQ@mail.gmail.com>
References: <CADUzUOhLA-vdd7YMTOJJpsebXPnLK=i8MaDs7dYzDk7bG_F1EQ@mail.gmail.com>
Message-ID: <CADUzUOi4krutCYih46CPYPQLL5_0R7gy+o6r=0n04yLpfHaR6A@mail.gmail.com>

This is a honest appriciation message to all moderators and participants of
this forum. Thank you all,
For answering patiently even the easiest questions,
By simply following this ACTIVE forum, one can easily learn how to use GAP
for basic purposes.
One of the most important archives I have ever had is this forum archive.
Thank you very much!



-- 
*S?meyra Bedir*



-- 
*S?meyra Bedir*

From mathieu.dutour at gmail.com  Fri May 10 07:38:36 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Fri, 10 May 2013 08:38:36 +0200
Subject: [GAP Forum] Conjugacy in GLn(Z)
Message-ID: <CADm_teOjn9_94P3YJRMZY542bZOLUsMGGjvK=E-VS5a95aFSHw@mail.gmail.com>

I have a set of matrices in GLn(Z) and I want to reduce them
by conjugacy. The problem is that the existing tools in GAP
seem too slow.

Two matrices (but there are many others) that pose me problem
now are:
g1:=
[ [  -1,   0,   0,   0,   0,   0,   0,   0 ],
  [   0,  -1,   0,   0,   0,   0,   0,   0 ],
  [   0,   0,   0,   0,   0,   0,   1,   0 ],
  [   0,   0,   0,   0,   1,   0,  -1,   0 ],
  [   0,   0,   0,   1,   0,   0,   0,   0 ],
  [   0,   0,   0,   0,   1,   0,   0,   1 ],
  [   0,   0,  -1,   0,   0,   0,   1,   0 ],
  [   0,   0,   0,  -1,   0,   1,  -1,   0 ] ] ;
g2:=
[ [   1,   0,   0,   0,   0,   0,   0,   0 ],
  [   1,  -1,   0,   0,   0,   0,   0,   0 ],
  [   0,   0,   1,   0,   0,   0,   0,   0 ],
  [   0,   0,   1,  -1,   0,   0,   0,   0 ],
  [   0,   0,   0,   0,  -1,   0,   0,   0 ],
  [   0,   0,   0,   0,   0,  -1,   0,   0 ],
  [   0,   0,   0,   0,   1,   1,   1,   1 ],
  [   0,   0,   0,   0,  -1,   0,  -1,   0 ] ];

Two general strategy are available in GAP
1> Use
   RepresentativeAction(GL(8, Integers), g1, g2)
2> Use carat by computing the Bravais groups
   of Gi = BravaisGroup( Group( [gi] ) ), testing
   for conjugacy, computing the normalizer and then
   concluding.

Both approaches fail for g1 and g2, i.e. take too
much time. Of course it is possible to use the
eigenvalue -1 of multiplicity 4 to do a reduction, but
I have been designing a lot of such special cases
algorithm and now I am wondering if there is possibility
of improving the general algorithm.

In Newman, "Integral matrices" it is mentioned for
example that there is a one-to-one correspondence
between the conjugacy classes of matrices A in M_n(Z)
such that f(A)=0 with f irreducible over Q and the ideal
classes of the ring Z[theta] with theta a root of f. Are
such methods used in GAP ?

But this is of course only one aspect of the problem.
For example the matrices [ [0, 1], [1, 0] ] and [ [1, 0], [0,-1]]
are not conjugate because the sum of integral eigenspaces
form a basis of determinant 2 in the first case and 1 in the
second. The enumeration of all sum V1 + V2 of integral
spaces with determinant k is equivalent to the enumeration
of all double cosets H A K with H = GL(n1,Z) x GL(n2,Z),
K = GL(n,Z) and det A = k. Is there a way for achieving this
in GAP ?

Thanks in advance for any help.

  Mathieu

From Bill.Allombert at math.u-bordeaux1.fr  Fri May 10 11:04:18 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Fri, 10 May 2013 12:04:18 +0200
Subject: [GAP Forum] RootsOfPolynomialAsRadicals - nffactor: the PARI
 stack overflows
In-Reply-To: <kgxbyerupenyhczyfasn@dhlw>
References: <qorxgldebujtuqqjwrpa@vsne> <51898433.5060902@mcs.st-andrews.ac.uk>
	<Pine.LNX.4.58.1305080001340.5529@focus.encs.concordia.ca>
	<Pine.LNX.4.58.1305080153330.16796@focus.encs.concordia.ca>
	<kgxbyerupenyhczyfasn@dhlw>
Message-ID: <20130510100418.GA28801@yellowpig>

On Wed, May 08, 2013 at 09:04:01PM +0200, Daniel Blazewicz wrote:
> Dear Andreas and John,
> 
> Many thanks for your answers.
> I used SetPariStackSize(256) and it helped!
> 
> My PARI/GP version:
>                   GP/PARI CALCULATOR Version 2.5.0 (released)
>              amd64 running linux (x86-64/GMP kernel) 64-bit version
>         compiled: Nov 17 2011, gcc-4.6.2 (Ubuntu/Linaro 4.6.2-2ubuntu1) 
>                 (readline v6.2 disabled, extended help enabled)

PARI 2.5.1 and later includes a fix which improve performance and reduce memory
usage for this kind of computation. Probably the reason Andreas could not
reproduce this. (It is available in Ubuntu versions 12.10 and 13.04. I assume
you use 12.04).

Cheers,
Bill.


From waechtjn at studi.informatik.uni-stuttgart.de  Fri May 10 12:11:22 2013
From: waechtjn at studi.informatik.uni-stuttgart.de (=?iso-8859-1?Q?Jan_Philipp_W=E4chter?=)
Date: Fri, 10 May 2013 13:11:22 +0200
Subject: [GAP Forum] Wreath Product for Monoids
Message-ID: <000401ce4d6f$1ac52780$504f7680$@informatik.uni-stuttgart.de>

Hi,

WreathProduct only accepts groups as arguments. Is there a way to calculate
the wreath product of two (finite) monoids?

Regards,
Jan Philipp



From A.Egri-Nagy at herts.ac.uk  Fri May 10 13:00:03 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Fri, 10 May 2013 22:00:03 +1000
Subject: [GAP Forum] Wreath Product for Monoids
In-Reply-To: <000401ce4d6f$1ac52780$504f7680$@informatik.uni-stuttgart.de>
References: <000401ce4d6f$1ac52780$504f7680$@informatik.uni-stuttgart.de>
Message-ID: <CAP=h6j3iCqeppaZfnDcWjyyQOD2MfyLddKJ83DbMHrbM8RhQ8g@mail.gmail.com>

Dear Jan Philip,

With the development version of the SgpDec package,
https://bitbucket.org/dersu/sgpdec, you can simply do

gap> S1 := Semigroup(Transformation([5,4,2,2,2]),
Transformation([2,3,4,4,5]));
<semigroup with 2 generators>
gap> S2 := Semigroup(Transformation([6,5,4,2,2,2]),
Transformation([6,2,3,4,4,5]));
<semigroup with 2 generators>

gap> S1wrS2 := SemigroupWreathProduct(S1,S2);
<wreath product of semigroups>
gap> Size(S1wrS2);
9143008

This gives the wreath product represented as the full cascade product,
definitions here: http://arxiv.org/abs/1303.0091

However, you already heard the bad news: it is in the development
version. Please let me know if you need help to set it up.

best,
attila


On Fri, May 10, 2013 at 9:11 PM, Jan Philipp W?chter
<waechtjn at studi.informatik.uni-stuttgart.de> wrote:
>
> Hi,
>
> WreathProduct only accepts groups as arguments. Is there a way to calculate
> the wreath product of two (finite) monoids?
>
> Regards,
> Jan Philipp
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From e.obrien at auckland.ac.nz  Fri May 10 20:48:27 2013
From: e.obrien at auckland.ac.nz (Eamonn O'Brien)
Date: Sat, 11 May 2013 07:48:27 +1200
Subject: [GAP Forum] Final announcement: Workshop at Braunschweig, May 21-24
In-Reply-To: <512FF243.3050601@auckland.ac.nz>
References: <512FF243.3050601@auckland.ac.nz>
Message-ID: <518D4F0B.4060308@auckland.ac.nz>

Dear Colleagues:

We will run a workshop entitled
"Questions, Algorithms, and Computations in Abstract Group Theory",
at the University of Braunschweig from May 21-24.

Our aim is to combine researchers from the areas of group theory,
computer science and algebraic geometry to obtain new advances
in the algorithmic theory of abstract groups.

The program for the workshop can be found at
http://www.icm.tu-bs.de/ag_algebra/ws-qac

Best wishes.
Eamonn O'Brien

From mhxgh at yahoo.com  Sun May 12 05:45:09 2013
From: mhxgh at yahoo.com (M.H.GH)
Date: Sat, 11 May 2013 21:45:09 -0700 (PDT)
Subject: [GAP Forum] Sylow $p$-subgroups which pairwise intersect
	trivially
In-Reply-To: <1367904537.87903.YahooMailNeo@web125003.mail.ne1.yahoo.com>
References: <WC20130429142723.9037B7@iust.ac.ir>
	<1367904537.87903.YahooMailNeo@web125003.mail.ne1.yahoo.com>
Message-ID: <1368333909.43835.YahooMailNeo@web125004.mail.ne1.yahoo.com>

VP := function( G , p )?
local P, N, R, Pi, Pj, i, ResultsSet, SizeR, SW;?
P := SylowSubgroup( G , p );
N := Normalizer( G , P );
R := AsList( RightTransversal( G , N ) );
ResultsSet := [];
SizeR := Size( R );
Print ( "\nUpper Bound = Size( RightCosets( G , Normalizer(G,P) ) ) = " , SizeR , " ... \n\n" );
for i in [1..Size( R )] do
Pi := P^R[i];
SW := 1;
for Pj in ResultsSet ?do
if Size( Intersection( Pi , Pj ) ) <> 1 then
SW := 0;
continue;
fi;
od;
if SW = 1 then
Add( ResultsSet , Pi );
fi;
od;
Print ( "Result = " , Size( Set( ResultsSet ) ) , " .\n\n");
return Size( Set( ResultsSet ) );
end;;



________________________________
 From: zeinab foruzanfar <zeinab_foruzanfar at iust.ac.ir>
To: forum at gap-system.org 
Sent: Monday, April 29, 2013 6:57 PM
Subject: [GAP Forum] (no subject)
 

Hi. I Want some GAP
program to count the number of Sylow $p$-subgroups which pairwise
intersect trivially. Also I want to show that if $P$ and $Q$ are two
Sylow $p$-subgroups, then the intersection of $P^x$ and $P^y$ is trivial
for $x,y \in Q$. Is it possible to send me a program to count these.
Thank you
Best Regards



_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum

From mhxgh at yahoo.com  Sun May 12 06:22:53 2013
From: mhxgh at yahoo.com (M.H.GH)
Date: Sat, 11 May 2013 22:22:53 -0700 (PDT)
Subject: [GAP Forum] Finding all minimal generators of a group
In-Reply-To: <000401ce4d6f$1ac52780$504f7680$@informatik.uni-stuttgart.de>
References: <000401ce4d6f$1ac52780$504f7680$@informatik.uni-stuttgart.de>
Message-ID: <1368336173.62340.YahooMailNeo@web125004.mail.ne1.yahoo.com>

Hi,


Is there any way to find?all minimal generators of a group?
(Except testing all subset of group elements!)

Regards,
MH Ghaffari

From Jan_Waechter at gmx.de  Fri May 10 12:08:01 2013
From: Jan_Waechter at gmx.de (=?iso-8859-1?Q?Jan_Philipp_W=E4chter?=)
Date: Fri, 10 May 2013 13:08:01 +0200
Subject: [GAP Forum] Wreath Product for Monoids
Message-ID: <000301ce4d6e$a3216860$e9643920$@de>

Hi,

WreathProduct only accepts groups as arguments. Is there a way to calculate
the wreath product of two (finite) monoids?

Regards,
Jan Philipp



From hatlam at gmail.com  Mon May 13 11:39:41 2013
From: hatlam at gmail.com (Ha T. Lam)
Date: Mon, 13 May 2013 06:39:41 -0400
Subject: [GAP Forum] Curious behavior of IsAlgExtRep
Message-ID: <CAFxJ0Mwwqb40xv3DCh_ehY=P1hOZ6G5WhtOf7YoEm188C+XqJQ@mail.gmail.com>

Dear GAP forum,

I encountered a curious behavior when I tried to use IsAlgExtRep:

x:=Indeterminate(GF(2), "x");
f:=x^5+x^3+Z(2)^0;
gf:=GF(2,f);
prim:=PrimitiveElement(gf);
IsAlgExtRep(prim);

In the above code, I expected IsAlgExtRep(prim) to return true, but it
tells me that it's false instead. If I change the polynomial to:
f:=x^17+x^13+x^11+x^10+x^9+x^7+x^6+x^5+x^4+x^2+Z(2)^0, it correctly tells
me that IsAlgExtRep(prim) is true. I've tried a few other irreducible
polynomial of degree smaller than 17 but they all returned false.

Can you explain what's going on for me?

Best regards,

Ha T. Lam

From hulpke at math.colostate.edu  Mon May 13 19:55:15 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Mon, 13 May 2013 12:55:15 -0600
Subject: [GAP Forum] Curious behavior of IsAlgExtRep
In-Reply-To: <CAFxJ0Mwwqb40xv3DCh_ehY=P1hOZ6G5WhtOf7YoEm188C+XqJQ@mail.gmail.com>
References: <CAFxJ0Mwwqb40xv3DCh_ehY=P1hOZ6G5WhtOf7YoEm188C+XqJQ@mail.gmail.com>
Message-ID: <63F09D95-374F-4D04-8131-CEB9161B6949@math.colostate.edu>



Dear Forum,

On May 13, 2013, at 5/13/13 4:39, "Ha T. Lam" <hatlam at gmail.com> wrote:

> I encountered a curious behavior when I tried to use IsAlgExtRep:
> 
> x:=Indeterminate(GF(2), "x");
> f:=x^5+x^3+Z(2)^0;
> gf:=GF(2,f);
> prim:=PrimitiveElement(gf);
> IsAlgExtRep(prim);
> 
> In the above code, I expected IsAlgExtRep(prim) to return true, but it
> tells me that it's false instead. If I change the polynomial to:

IsAlgExtRep indicates whether an element is represented internally as element of a formal (quotient of polynomial ring) algebraic extension. Fields of order <=2^16 are represented using Zech logarithms, thus they are not IsAlgExtRep (their representation is `IsInternalRep').

Regards,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke




From ahulpke at gmail.com  Mon May 13 22:29:05 2013
From: ahulpke at gmail.com (Alexander Hulpke)
Date: Mon, 13 May 2013 15:29:05 -0600
Subject: [GAP Forum] Conjugacy in GLn(Z)
In-Reply-To: <CADm_teOjn9_94P3YJRMZY542bZOLUsMGGjvK=E-VS5a95aFSHw@mail.gmail.com>
References: <CADm_teOjn9_94P3YJRMZY542bZOLUsMGGjvK=E-VS5a95aFSHw@mail.gmail.com>
Message-ID: <E9CCE8DA-06AF-4B8B-8FA3-2DDA04033A9B@gmail.com>



Dear Forum, Dear Mathieu,

> I have a set of matrices in GLn(Z) and I want to reduce them
> by conjugacy. The problem is that the existing tools in GAP
> seem too slow.

[...]
> 
> Two general strategy are available in GAP
> 1> Use
>   RepresentativeAction(GL(8, Integers), g1, g2)

This will start an orbit calculation on g1, trying to find g2. Thus not only will it be slow to succeed, it will not terminate if they are not conjugate.

> 2> Use carat by computing the Bravais groups
>   of Gi = BravaisGroup( Group( [gi] ) ), testing
>   for conjugacy, computing the normalizer and then
>   concluding.

This is probably the best possible with existing code.

GAP doesn't really have much built-in for infinite matrix groups, in particular none of the methods you allude to have been implemented for GL over the integers.

If you wanted to implement it yourself,
http://www.math.uconn.edu/~kconrad/blurbs/gradnumthy/matrixconj.pdf
might be a good starting point, but it in the end becomes a problem in number theory and the lack of ideal class functions would be inconvenient.
Your best bet might be to see what kind of conjugacy (either over larger ring, or not perfect) you could live with.

Sorry!

   Alexander




From hulpke at math.colostate.edu  Mon May 13 22:30:21 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Mon, 13 May 2013 15:30:21 -0600
Subject: [GAP Forum] Wreath Product for Monoids
In-Reply-To: <000301ce4d6e$a3216860$e9643920$@de>
References: <000301ce4d6e$a3216860$e9643920$@de>
Message-ID: <A2154130-DBA3-4182-BB28-70EAB35055D9@math.colostate.edu>



Dear Forum, Dear Jan-Philip W"achter,

> WreathProduct only accepts groups as arguments. Is there a way to calculate
> the wreath product of two (finite) monoids?

The GAP library only provides methods to construct wreath products of (finite) groups. It would be possible to install methods for monoids using InstallOtherMethod, but I am not aware of such code. Your bet bet might be to simply construct the wreath product ``by hand''.

   Best,

      Alexander Hulpke




From A.Egri-Nagy at herts.ac.uk  Mon May 13 22:38:14 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Tue, 14 May 2013 07:38:14 +1000
Subject: [GAP Forum] Wreath Product for Monoids
In-Reply-To: <A2154130-DBA3-4182-BB28-70EAB35055D9@math.colostate.edu>
References: <000301ce4d6e$a3216860$e9643920$@de>
	<A2154130-DBA3-4182-BB28-70EAB35055D9@math.colostate.edu>
Message-ID: <CAP=h6j1WV4w=Pi8=ouSzGEiCdSW9KjFVpDNBZ4FJToWgUirDaw@mail.gmail.com>

Hi,

It seems that my previous answer made it to the Forum archive, but it
was not dispatched to Forum members.
Here it is:

Dear Jan Philip,

With the development version of the SgpDec package,
https://bitbucket.org/dersu/sgpdec, you can simply do

gap> S1 := Semigroup(Transformation([5,4,2,2,2]),
Transformation([2,3,4,4,5]));
<semigroup with 2 generators>
gap> S2 := Semigroup(Transformation([6,5,4,2,2,2]),
Transformation([6,2,3,4,4,5]));
<semigroup with 2 generators>

gap> S1wrS2 := SemigroupWreathProduct(S1,S2);
<wreath product of semigroups>
gap> Size(S1wrS2);
9143008

This gives the wreath product represented as the full cascade product,
definitions here: http://arxiv.org/abs/1303.0091

However, you already heard the bad news: it is in the development
version. Please let me know if you need help to set it up.

best,
attila

On Tue, May 14, 2013 at 7:30 AM, Alexander Hulpke
<hulpke at math.colostate.edu> wrote:
>
>
> Dear Forum, Dear Jan-Philip W"achter,
>
>> WreathProduct only accepts groups as arguments. Is there a way to calculate
>> the wreath product of two (finite) monoids?
>
> The GAP library only provides methods to construct wreath products of (finite) groups. It would be possible to install methods for monoids using InstallOtherMethod, but I am not aware of such code. Your bet bet might be to simply construct the wreath product ``by hand''.
>
>    Best,
>
>       Alexander Hulpke
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From Sven.Reichard at tu-dresden.de  Fri May 17 09:53:55 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Fri, 17 May 2013 10:53:55 +0200
Subject: [GAP Forum] Fast Orbit Computation for Custom Objects?
Message-ID: <5195F023.7090703@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Dear Forum,

I have the following data:
- - A permutation group G;
- - a set of objects obj;
- - an action function.

I would like to get the following:
- - The union D of the orbits of obj under G (not necessarily sorted);
- - the action H of G on D;
- - orbit representatives.

What I do is the following:

orbits := Orbits(G, obj, action);
representatives := List(orbits, Representative);
D := Union(orbits); # sorted to accelerate the next step
H := Action(G, D, action);

This works well when action is a standard action such as OnSetsSets.
However, for custom actions this can be very slow, suggesting that
different algorithms are used. (In some of my examples, D has a
million elements.)

Is there a way in GAP4 to accelerate this process, for example by
providing hash functions? In GAP3 there existed a solution in the
contributed file coco.grp by Thei?en based on work by Faradzev et al.
The question is whether there is a better way than porting that file
to GAP4.

Regards,
Sven Reichard.

- -- 

Institut f?r Algebra
TU Dresden
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From A.Egri-Nagy at herts.ac.uk  Fri May 17 10:07:11 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Fri, 17 May 2013 19:07:11 +1000
Subject: [GAP Forum] Fast Orbit Computation for Custom Objects?
In-Reply-To: <5195F023.7090703@tu-dresden.de>
References: <5195F023.7090703@tu-dresden.de>
Message-ID: <CAP=h6j2WpJoPpJg40Qjro2kY9cVEvOsKRo0GRSKdTfapF8KDAw@mail.gmail.com>

Dear Sven,

Most probably the orb package is what you need:
http://www.gap-system.org/Packages/orb.html

best,
attila

On Fri, May 17, 2013 at 6:53 PM, Sven Reichard
<Sven.Reichard at tu-dresden.de> wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Dear Forum,
>
> I have the following data:
> - - A permutation group G;
> - - a set of objects obj;
> - - an action function.
>
> I would like to get the following:
> - - The union D of the orbits of obj under G (not necessarily sorted);
> - - the action H of G on D;
> - - orbit representatives.
>
> What I do is the following:
>
> orbits := Orbits(G, obj, action);
> representatives := List(orbits, Representative);
> D := Union(orbits); # sorted to accelerate the next step
> H := Action(G, D, action);
>
> This works well when action is a standard action such as OnSetsSets.
> However, for custom actions this can be very slow, suggesting that
> different algorithms are used. (In some of my examples, D has a
> million elements.)
>
> Is there a way in GAP4 to accelerate this process, for example by
> providing hash functions? In GAP3 there existed a solution in the
> contributed file coco.grp by Thei?en based on work by Faradzev et al.
> The question is whether there is a better way than porting that file
> to GAP4.
>
> Regards,
> Sven Reichard.
>
> - --
>
> Institut f?r Algebra
> TU Dresden
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> =JAOJ
> -----END PGP SIGNATURE-----
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From hulpke at math.colostate.edu  Fri May 17 18:25:02 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri, 17 May 2013 11:25:02 -0600
Subject: [GAP Forum] Fast Orbit Computation for Custom Objects?
In-Reply-To: <5195F023.7090703@tu-dresden.de>
References: <5195F023.7090703@tu-dresden.de>
Message-ID: <FC8F3B8F-8FAB-452B-93D0-7546D8E23120@math.colostate.edu>



Dear Forum, Dear Sven,

> I have the following data:
> - - A permutation group G;
> - - a set of objects obj;
> - - an action function.
> 
> I would like to get the following:
> - - The union D of the orbits of obj under G (not necessarily sorted);
> - - the action H of G on D;
> - - orbit representatives.
> 
> What I do is the following:
> 
> orbits := Orbits(G, obj, action);
> representatives := List(orbits, Representative);
> D := Union(orbits); # sorted to accelerate the next step
> H := Action(G, D, action);
> 
> This works well when action is a standard action such as OnSetsSets.
> However, for custom actions this can be very slow, suggesting that
> different algorithms are used. (In some of my examples, D has a
> million elements.)

For `Orbits' and `Action' there aren't really different algorithms used, but performance is crucially impacted by the methods available for recording the orbit elements. This is likely where you are seeing the slowdown.
Also, by first computing orbits, joining and then computing the action, you are doing the same work twice. In certain situations `SparseActionHomomorphism' might help you do this, but frankly I found that if is near impossible to define a universal optimal orbit/action routine and (given the simplicity of the code) you might be better off to code a bespoke version, modeled on the code for `SparseActionHomomorphism'.

The basic operations (and time sinks) for group actions are essentially the book keeping for the orbit elements found so far (and seed elements still to treat). To unify different approaches, GAP uses its dictionary data type. Very roughly the following things happen: (This is in the code for `NewDictionary' in lib/dict.gi.

- If no domain (set containing all orbits) is given GAP calls `DomainForAction' to try to construct one. A typical case would be a matrix group acting on vectors where the generic domain is the row space.

- If a domain exists (was given or determined in the previous step) and this domain is a `IsQuickPositionList' (finding an element is faster than binary search) or a list known to be sorted and elements can be compared cheaply by < (indicated by `CanEasilySortElements'), and the domain has not more than 2^22 elements (avoiding too long bit lists if the domain is too large) the dictionary uses `Position'. Possibly the `Enumerator' of the domain is chosen for `Position'.

- GAP calls `SparseIntKey(domain,seed)'. If this returns a function, it is taken as hash function, and a hash dictionary is used.

- Otherwise if the seed fulfills `CanEasilySortElements', the dictionary uses a sorted list of elements (binary search).

- Otherwise just a list is used with linear search by `=' only.

This means, if you act on your ``own' objects, your preference of interventions to make the code faster is the following (always if possible):

1. If you can enumerate all elements cheaply, create a domain object that provides this enumeration via \[\] and `\Position'

2. Implement a method for `SparseIntKey' that returns a hash key function.

3. If you can implement a \< comparison method for your objects. install a method for `CanEasilySortElements' that returns `true' for these.

I realize that if your objects are complicated (say you are acting on chains of subgroups) all of this is hard, but a cheap test for whether an orbit element was found already is at the heart of any orbits/action computation.

> Is there a way in GAP4 to accelerate this process, for example by
> providing hash functions? In GAP3 there existed a solution in the
> contributed file coco.grp by Thei?en based on work by Faradzev et al.
> The question is whether there is a better way than porting that file
> to GAP4.

Basically all of the functionality in this file is superseded by this dictionary setup.

If you want help, please let me know what kinds of objects you are working with, in particular how they are represented.

   Alexander 

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke




From Sven.Reichard at mailbox.tu-dresden.de  Sat May 18 08:29:51 2013
From: Sven.Reichard at mailbox.tu-dresden.de (Sven Reichard)
Date: Sat, 18 May 2013 07:29:51 +0000
Subject: [GAP Forum] Fast Orbit Computation for Custom Objects?
In-Reply-To: <FC8F3B8F-8FAB-452B-93D0-7546D8E23120@math.colostate.edu>
References: <5195F023.7090703@tu-dresden.de>
	<FC8F3B8F-8FAB-452B-93D0-7546D8E23120@math.colostate.edu>
Message-ID: <20130518072951.Horde.aQHosGaXyz2NtUjHTIyDHA2@mail.zih.tu-dresden.de>

Dear Alexander,

thank you for your thorough answer. My objects aren't terribly  
complicated. They are partitions of [1..n] (for some fixed n) that  
have some classes marked as "special". They are local to a search  
algorithm, so their representation can be easily changed. Currently I  
represent them as records with two components - the partition itself  
as a set of sets, and the subset of special classes. From your remarks  
I gather that I would be better off with an ordered list (of length 2)  
of sets of sets.

For further background: Some partitions are "stable", and I can  
compute - at considerable cost -  the coarsest stable refinement for a  
given partition. The set of stable partitions is invariant under some  
subgroup G of SymmetricGroup(n). Now I would like to enumerate all  
stable partitions up to isomorphism under G. This is related to the  
enumeration of Schur rings. In the search objects the partition is the  
coarsest stable partition containing the given special classes.

Cheers,
Sven.

Zitat von Alexander Hulpke <hulpke at math.colostate.edu>:

> Dear Forum, Dear Sven,
>
>> I have the following data:
>> - - A permutation group G;
>> - - a set of objects obj;
>> - - an action function.
>>
>> I would like to get the following:
>> - - The union D of the orbits of obj under G (not necessarily sorted);
>> - - the action H of G on D;
>> - - orbit representatives.
>>
>> What I do is the following:
>>
>> orbits := Orbits(G, obj, action);
>> representatives := List(orbits, Representative);
>> D := Union(orbits); # sorted to accelerate the next step
>> H := Action(G, D, action);
>>
>> This works well when action is a standard action such as OnSetsSets.
>> However, for custom actions this can be very slow, suggesting that
>> different algorithms are used. (In some of my examples, D has a
>> million elements.)
>
> For `Orbits' and `Action' there aren't really different algorithms  
> used, but performance is crucially impacted by the methods available  
> for recording the orbit elements. This is likely where you are  
> seeing the slowdown.
> Also, by first computing orbits, joining and then computing the  
> action, you are doing the same work twice. In certain situations  
> `SparseActionHomomorphism' might help you do this, but frankly I  
> found that if is near impossible to define a universal optimal  
> orbit/action routine and (given the simplicity of the code) you  
> might be better off to code a bespoke version, modeled on the code  
> for `SparseActionHomomorphism'.
>
> The basic operations (and time sinks) for group actions are  
> essentially the book keeping for the orbit elements found so far  
> (and seed elements still to treat). To unify different approaches,  
> GAP uses its dictionary data type. Very roughly the following things  
> happen: (This is in the code for `NewDictionary' in lib/dict.gi.
>
> - If no domain (set containing all orbits) is given GAP calls  
> `DomainForAction' to try to construct one. A typical case would be a  
> matrix group acting on vectors where the generic domain is the row  
> space.
>
> - If a domain exists (was given or determined in the previous step)  
> and this domain is a `IsQuickPositionList' (finding an element is  
> faster than binary search) or a list known to be sorted and elements  
> can be compared cheaply by < (indicated by `CanEasilySortElements'),  
> and the domain has not more than 2^22 elements (avoiding too long  
> bit lists if the domain is too large) the dictionary uses  
> `Position'. Possibly the `Enumerator' of the domain is chosen for  
> `Position'.
>
> - GAP calls `SparseIntKey(domain,seed)'. If this returns a function,  
> it is taken as hash function, and a hash dictionary is used.
>
> - Otherwise if the seed fulfills `CanEasilySortElements', the  
> dictionary uses a sorted list of elements (binary search).
>
> - Otherwise just a list is used with linear search by `=' only.
>
> This means, if you act on your ``own' objects, your preference of  
> interventions to make the code faster is the following (always if  
> possible):
>
> 1. If you can enumerate all elements cheaply, create a domain object  
> that provides this enumeration via \[\] and `\Position'
>
> 2. Implement a method for `SparseIntKey' that returns a hash key function.
>
> 3. If you can implement a \< comparison method for your objects.  
> install a method for `CanEasilySortElements' that returns `true' for  
> these.
>
> I realize that if your objects are complicated (say you are acting  
> on chains of subgroups) all of this is hard, but a cheap test for  
> whether an orbit element was found already is at the heart of any  
> orbits/action computation.
>
>> Is there a way in GAP4 to accelerate this process, for example by
>> providing hash functions? In GAP3 there existed a solution in the
>> contributed file coco.grp by Thei?en based on work by Faradzev et al.
>> The question is whether there is a better way than porting that file
>> to GAP4.
>
> Basically all of the functionality in this file is superseded by  
> this dictionary setup.
>
> If you want help, please let me know what kinds of objects you are  
> working with, in particular how they are represented.
>
>    Alexander
>
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
> http://www.math.colostate.edu/~hulpke





From jdm3 at st-and.ac.uk  Sat May 18 18:48:04 2013
From: jdm3 at st-and.ac.uk (James Mitchell)
Date: Sat, 18 May 2013 18:48:04 +0100
Subject: [GAP Forum] Fast Orbit Computation for Custom Objects?
In-Reply-To: <4437d77f446143949d7d4a595686cd32@UOS-DUN-CAS2.st-andrews.ac.uk>
References: <5195F023.7090703@tu-dresden.de>
	<FC8F3B8F-8FAB-452B-93D0-7546D8E23120@math.colostate.edu>
	<4437d77f446143949d7d4a595686cd32@UOS-DUN-CAS2.st-andrews.ac.uk>
Message-ID: <CAE7PsybMpkNZ+5L0v9nXZB3D7cmpOuA1hJ5Bit=B78sAkPhnnw@mail.gmail.com>

Dear Sven,

I would second Attila's suggestion to use the Orb package. Orb
contains generic orbit algorithms, and implementations for hash
tables.

If I were try to find an orbit of a partition with special classes
under a group I would probably represent the partition as a flat list
of integers: [[1,2],[3,4,6],[5]] where [1,2] and [5] are special
becomes [1,1,2,2,3,2,1,0,1] (the value in the i-th position, i=1..6,
is class that i belongs to and position j+6 is 1 if the j-th class is
special and 0 if it is not (j=1..3)). Then you can compute the orbit
by doing:

o:=Orb(G, [1,1,2,2,3,2,1,0,1], MyAction, rec(forflatplainlists:=true));
Enumerate(o);

where G is your group,  [1,1,2,2,3,2,1,0,1] is your partition,
MyAction is the action of G on partitions with special classes, and
the final argument is a record which can be used to pass options to
Orb. In this case, forflatplainlists:=true tells Orb that the points
in the orbit you are trying to calculate are flat plain lists (lists
containing no subobjects) and Orb knows how to hash such objects
efficiently. Doing this you can take advantage of all the
functionality of the Orb package, including hash functions and so on,
without having to write your own code beyond the function MyAction. In
particular, you can probably get this to work, with good performance,
in a relatively short amount of time.

I'd be happy to help if you have any further queries, or if something
I've written is unclear.

Regards,

James




On 18 May 2013 08:29, Sven Reichard <Sven.Reichard at mailbox.tu-dresden.de> wrote:
> Dear Alexander,
>
> thank you for your thorough answer. My objects aren't terribly
> complicated. They are partitions of [1..n] (for some fixed n) that
> have some classes marked as "special". They are local to a search
> algorithm, so their representation can be easily changed. Currently I
> represent them as records with two components - the partition itself
> as a set of sets, and the subset of special classes. From your remarks
> I gather that I would be better off with an ordered list (of length 2)
> of sets of sets.
>
> For further background: Some partitions are "stable", and I can
> compute - at considerable cost -  the coarsest stable refinement for a
> given partition. The set of stable partitions is invariant under some
> subgroup G of SymmetricGroup(n). Now I would like to enumerate all
> stable partitions up to isomorphism under G. This is related to the
> enumeration of Schur rings. In the search objects the partition is the
> coarsest stable partition containing the given special classes.
>
> Cheers,
> Sven.
>
> Zitat von Alexander Hulpke <hulpke at math.colostate.edu>:
>
>> Dear Forum, Dear Sven,
>>
>>> I have the following data:
>>> - - A permutation group G;
>>> - - a set of objects obj;
>>> - - an action function.
>>>
>>> I would like to get the following:
>>> - - The union D of the orbits of obj under G (not necessarily sorted);
>>> - - the action H of G on D;
>>> - - orbit representatives.
>>>
>>> What I do is the following:
>>>
>>> orbits := Orbits(G, obj, action);
>>> representatives := List(orbits, Representative);
>>> D := Union(orbits); # sorted to accelerate the next step
>>> H := Action(G, D, action);
>>>
>>> This works well when action is a standard action such as OnSetsSets.
>>> However, for custom actions this can be very slow, suggesting that
>>> different algorithms are used. (In some of my examples, D has a
>>> million elements.)
>>
>> For `Orbits' and `Action' there aren't really different algorithms
>> used, but performance is crucially impacted by the methods available
>> for recording the orbit elements. This is likely where you are
>> seeing the slowdown.
>> Also, by first computing orbits, joining and then computing the
>> action, you are doing the same work twice. In certain situations
>> `SparseActionHomomorphism' might help you do this, but frankly I
>> found that if is near impossible to define a universal optimal
>> orbit/action routine and (given the simplicity of the code) you
>> might be better off to code a bespoke version, modeled on the code
>> for `SparseActionHomomorphism'.
>>
>> The basic operations (and time sinks) for group actions are
>> essentially the book keeping for the orbit elements found so far
>> (and seed elements still to treat). To unify different approaches,
>> GAP uses its dictionary data type. Very roughly the following things
>> happen: (This is in the code for `NewDictionary' in lib/dict.gi.
>>
>> - If no domain (set containing all orbits) is given GAP calls
>> `DomainForAction' to try to construct one. A typical case would be a
>> matrix group acting on vectors where the generic domain is the row
>> space.
>>
>> - If a domain exists (was given or determined in the previous step)
>> and this domain is a `IsQuickPositionList' (finding an element is
>> faster than binary search) or a list known to be sorted and elements
>> can be compared cheaply by < (indicated by `CanEasilySortElements'),
>> and the domain has not more than 2^22 elements (avoiding too long
>> bit lists if the domain is too large) the dictionary uses
>> `Position'. Possibly the `Enumerator' of the domain is chosen for
>> `Position'.
>>
>> - GAP calls `SparseIntKey(domain,seed)'. If this returns a function,
>> it is taken as hash function, and a hash dictionary is used.
>>
>> - Otherwise if the seed fulfills `CanEasilySortElements', the
>> dictionary uses a sorted list of elements (binary search).
>>
>> - Otherwise just a list is used with linear search by `=' only.
>>
>> This means, if you act on your ``own' objects, your preference of
>> interventions to make the code faster is the following (always if
>> possible):
>>
>> 1. If you can enumerate all elements cheaply, create a domain object
>> that provides this enumeration via \[\] and `\Position'
>>
>> 2. Implement a method for `SparseIntKey' that returns a hash key function.
>>
>> 3. If you can implement a \< comparison method for your objects.
>> install a method for `CanEasilySortElements' that returns `true' for
>> these.
>>
>> I realize that if your objects are complicated (say you are acting
>> on chains of subgroups) all of this is hard, but a cheap test for
>> whether an orbit element was found already is at the heart of any
>> orbits/action computation.
>>
>>> Is there a way in GAP4 to accelerate this process, for example by
>>> providing hash functions? In GAP3 there existed a solution in the
>>> contributed file coco.grp by Thei?en based on work by Faradzev et al.
>>> The question is whether there is a better way than porting that file
>>> to GAP4.
>>
>> Basically all of the functionality in this file is superseded by
>> this dictionary setup.
>>
>> If you want help, please let me know what kinds of objects you are
>> working with, in particular how they are represented.
>>
>>    Alexander
>>
>> -- Colorado State University, Department of Mathematics,
>> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
>> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
>> http://www.math.colostate.edu/~hulpke
>
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



-- 
James Mitchell
tinyurl.com/jdmitchell

The University of St Andrews is a charity registered in Scotland : No SC013532


From kozmos1986 at gmail.com  Sun May 26 17:50:50 2013
From: kozmos1986 at gmail.com (kozmos kozmos)
Date: Sun, 26 May 2013 19:50:50 +0300
Subject: [GAP Forum] memory allocation in GAP
Message-ID: <CAHpeWE-+bD4aRYSuhVj9+zbUF+0YWOuzmAQzi7F-FM4uHZSixA@mail.gmail.com>

Hi,
I tried to use the -a memory and -a memory commands but they are not
working please tell me how these commands are exactly used

From alexk at mcs.st-andrews.ac.uk  Mon May 27 10:19:15 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 27 May 2013 10:19:15 +0100
Subject: [GAP Forum] International Workshop "Parallel programming in GAP"
Message-ID: <561D569B-E50D-48FA-B6EF-2CAFB9D6074F@mcs.st-andrews.ac.uk>

This is a reminder that registration deadlines are July 15th 2013
for the full registration, and August 5th 2013 if you don't need 
an accommodation. Apologies if you receive this more than once.

* * *

International Workshop "Parallel programming in GAP"

August 18th-24th, 2013, University of St Andrews, Scotland

http://www.gap-system.org/hpcgap2013/

The workshop is organised by the Centre of Interdisciplinary 
Research in Computational Algebra of the University of St Andrews.
It is supported by the EPSRC project "HPC-GAP: High Performance 
Computational Algebra and Discrete Mathematics":

	http://www-circa.mcs.st-and.ac.uk/hpcgap.php

In this project we are reengineering the GAP system to take 
advantage of computer architectures suitable for parallel
computations. The workshop is organised to present the results 
of the project to the GAP community, and we invite everyone who
is interested in parallel programming in GAP. Developers of GAP 
and authors of GAP packages are particularly welcome, since your
contribution will be important to eventually transform the HPC-GAP 
version of the system into the next mainstream release.

The workshop will comprise of lectures and tutorials given by 
the participants of the HPC-GAP project, and case studies sessions
where we intend to look at some particular GAP packages and 
estimate main tasks needed to adapt them to HPC-GAP. We plan 
to allow enough time to work in small groups and have informal
discussions about HPC-GAP and GAP development in general.

Schedule:

- August 18th (Sunday): Arrival day
- August 19th-23th (Monday-Friday): Workshop
- August 24th (Saturday): Departure day

Registration and accommodation:

The organisers will provide a limited number of B&B places in McIntosh 
Hall <http://www.st-andrews.ac.uk/accommodation/ug/residences/mcintosh/>. 
These will be provided free of charge and will be allocated on a first 
come - first served basis, so early registration is advised. If there 
will be larger demand for accommodation, we will help you to find another 
place to stay and will partially contribute towards the costs of your 
accommodation. We regret that there is no support available for daily 
expenses and travel.

To register, please send your contact details to organisers by email to

	hpcgap2013 at gap-system.org 

Deadlines:

- for the full registration: July 15th 2013
- for the non-residential registration: August 5th 2013

Organisers:
- Steve Linton
- Reimer Behrends
- Vladimir Janjic
- Alexander Konovalov
- John McDermott
- Angela Miguel
- Max Neunh?ffer


From msorouhesh at gmail.com  Thu May 30 14:19:08 2013
From: msorouhesh at gmail.com (Mohammad Reza Sorouhesh)
Date: Thu, 30 May 2013 17:49:08 +0430
Subject: [GAP Forum] (no subject)
Message-ID: <CAJn1Z0MhTxkyGtuudyALPVCfOgzv=7XC2DrK25p0QSrZuqEMSg@mail.gmail.com>

Dear Forum,

Here is my question on MathSE [http://math.stackexchange.com/q/406425/8581].
I think, I should not bring up the question there so please have a look at
it. The main point I am looking for is "Is there any codes in GAP in which
if we are given a finite group inside a semigroup, as Clifford cited, then
we can find the similar finite group to it? "

Thanks for the time you give me and Best

From jjm at mcs.st-and.ac.uk  Fri May 31 14:44:04 2013
From: jjm at mcs.st-and.ac.uk (John McDermott)
Date: Fri, 31 May 2013 14:44:04 +0100
Subject: [GAP Forum] Last chance: LMS/EPSRC Short Course in Computational
	Group Theory
Message-ID: <69911F67-A993-4D2A-9236-03CC74DF5462@mcs.st-andrews.ac.uk>

Dear all,

a reminder about the following:


LMS/EPSRC Short Instructional Course in Computational Group Theory

St Andrews, July 29th to August 2nd 2013

LMS/EPSRC Short Courses aim to provide training for postgraduate students in core areas of mathematics.

There will be four mini-series of lectures as follows

Permutation Groups			Alexander Hulpke (Colorado State University)	
Soluble Groups and p-groups		Bettina Eick (Technische Universit?t Braunschweig)	
Matrix Groups/Constructive Recognition	Derek Holt (University of Warwick)	
Finitely Presented Groups		Max Neunh?ffer (University of St Andrews)

along with two specialist lectures and extensive laboratory time, primarily using GAP (http://www.gap-system.org).

The deadline for applications for places on this course is Monday 17th of June. However we have already had a good many applications and the number of available places (more particularly the amount of available accommodation) is limited.

See the course website - http://www-circa.mcs.st-and.ac.uk/cgt2013/index.shtml - for full details and a link to the LMS pages for applications.


John McDermott, for the organisers.


--
John McDermott
Scientific Officer
Centre for Interdisciplinary Research in Computational Algebra
School of Computer Science
University of St Andrews
North Haugh, St Andrews, Fife
KY16 9SX
SCOTLAND

The University of St Andrews is committed to sustainable practices and the preservation of the environment.
Please do not print this email unless absolutely necessary.

The University of St Andrews is a charity registered in Scotland : No SC013532



From harshaarora.2008 at gmail.com  Mon Jun  3 15:34:02 2013
From: harshaarora.2008 at gmail.com (Harsha Arora)
Date: Mon, 3 Jun 2013 20:04:02 +0530
Subject: [GAP Forum] semi direct product
Message-ID: <CAMABT+o4tNtpBxAv6c4psRzEXNM28DCjSG6xEHtxURvtsPzO2A@mail.gmail.com>

Hello sir

I want to know the syntax of semidirect product. How can i know wih small
group id the group is direct or aemi direct product of ts subgroups

From lonpencs at qq.com  Wed Jun  5 16:08:48 2013
From: lonpencs at qq.com (=?ISO-8859-1?B?Rmxpc3BoeQ==?=)
Date: Wed, 5 Jun 2013 23:08:48 +0800
Subject: [GAP Forum] cyclotomic number
Message-ID: <tencent_389F38B73F7406EB09E4F7B8@qq.com>

Dear gap developers,

  Could I convert cyclotomic number into complex number using gap?

  yours,
  
  Peng Long

From alexk at mcs.st-and.ac.uk  Tue Jun 11 20:31:56 2013
From: alexk at mcs.st-and.ac.uk (Alexander Konovalov)
Date: Tue, 11 Jun 2013 20:31:56 +0100
Subject: [GAP Forum] cyclotomic number
In-Reply-To: <tencent_389F38B73F7406EB09E4F7B8@qq.com>
References: <tencent_389F38B73F7406EB09E4F7B8@qq.com>
Message-ID: <60AFF8D2-39EE-4983-8B22-508E7E3C9CCF@mcs.st-andrews.ac.uk>


On 5 Jun 2013, at 16:08, Flisphy wrote:

> Dear gap developers,
> 
>  Could I convert cyclotomic number into complex number using gap?
> 
>  yours,
> 
>  Peng Long


Dear Peng Long,

cyclotomic numbers *are* complex numbers - I guess what you may have in 
mind is getting a floating-point approximation of the real and imaginary
parts of a cyclotomic number. This can be achieved using the GAP package
Float by Laurent Bartholdi: see 

	http://laurentbartholdi.github.io/float/chap0.html

For example,

gap> LoadPackage("float");
Loading FLOAT 0.5.10 ...
true
gap> SetFloats(MPC);                                                  
gap> Float(E(6));
.5e0+.866025e0?
gap> x:=E(3)+E(5)^2;
-E(15)-E(15)^2-E(15)^8-2*E(15)^11-E(15)^14
gap> y:=Float(x);                                               
-.130902e1+.145381e1?
gap> Norm(y);
.382709e1
gap> RealPart(y);
-.130902e1
gap> ImaginaryPart(y);
.145381e1
gap> ComplexConjugate(y);
-.130902e1-.145381e1?

See the documentation for the Float package for installation requirements
and further details. In particular, I am not aware of Float being usable
under Windows. 

Hope this helps,
Alexander








From colva at mcs.st-and.ac.uk  Fri Jun 14 15:15:20 2013
From: colva at mcs.st-and.ac.uk (Colva Roney-Dougal)
Date: Fri, 14 Jun 2013 15:15:20 +0100
Subject: [GAP Forum] Groups St Andrews 2013: deadlines approaching
Message-ID: <823355B3-4362-4952-9D88-EB2BAFC7D9BC@mcs.st-and.ac.uk>

Dear Colleagues

This is a brief update on preparations for Groups St Andrews 2013.

The website has been substantially updated, and now contains an outline academic programme, as well as much more information about the social programme. There's also travel information, and much else besides. Please see 

http://www.groupsstandrews.org/2013/index.shtml.

Various conference deadlines are approaching!

- 30th June is the deadline for submitting an abstract for a contributed talk.
- 1st July is the deadline for submitting an article to the Proceedings.
- 12th July is the deadline for booking accommodation via the University of St Andrews.

We look forward to seeing you all in St Andrews in August

The Organisers

The University of St Andrews is a charity registered in Scotland : No SC013532



From katie.nil85 at gmail.com  Sat Jun 15 00:43:03 2013
From: katie.nil85 at gmail.com (Katie Nilsson)
Date: Fri, 14 Jun 2013 16:43:03 -0700
Subject: [GAP Forum] A problem to generate output within a loop
Message-ID: <CAL+b2YMx0=xUGkWwMMLuAE1ANwSoi5JmeTm_7_1LcyjHaCkbLg@mail.gmail.com>

Hi,
I want to list the following information for all non-abelian group of order
24. I want their structure, conjugacy classes, orders of the elements of
the conjugacy classes and irreduicble characters.
I wrote this program, but it is not working! the loop create nothing!!!

l := AllSmallGroups(24);;  List(l,StructureDescription);; A:=Filtered(l,
x->IsAbelian(x)=false);

Length(A);

for i in [1..Length(A)]  do

A[i];

Cl:=ConjugacyClasses(A[i]);

RCl:=List(Cl, x->Representative(x));

Ocl:=List(RCl, x->Order(x));

irr:=Irr(A[i]);
od;

Can someone tell me what's wrong? and how can i do it?
to me seems for loop just can run from start to end and at the end can
store the result of the last loop!

thanks
Katie

From nikos.ap at gmail.com  Sat Jun 15 01:44:38 2013
From: nikos.ap at gmail.com (Nikos Apostolakis)
Date: Fri, 14 Jun 2013 20:44:38 -0400
Subject: [GAP Forum] A problem to generate output within a loop
In-Reply-To: <CAL+b2YMx0=xUGkWwMMLuAE1ANwSoi5JmeTm_7_1LcyjHaCkbLg@mail.gmail.com>
References: <CAL+b2YMx0=xUGkWwMMLuAE1ANwSoi5JmeTm_7_1LcyjHaCkbLg@mail.gmail.com>
Message-ID: <CAO2SUm+vdmtXODOgHjXdN2-_xPezJxREpLR2mddoAFv5Z1=FHQ@mail.gmail.com>

If I understand correctly what you're trying to do, you want to do
something like:

l := AllSmallGroups(24);
Ds := List(l,StructureDescription);
A:=Filtered(l, x->IsAbelian(x)=false);

Cl := List( A, ConjugacyClasses);
RCl := List( Cl, Representative);
OCl := List( RCl, Order);
irr := List( A, Irr);

Hope this Helps,
Nikos

On Fri, Jun 14, 2013 at 7:43 PM, Katie Nilsson <katie.nil85 at gmail.com> wrote:
> Hi,
> I want to list the following information for all non-abelian group of order
> 24. I want their structure, conjugacy classes, orders of the elements of
> the conjugacy classes and irreduicble characters.
> I wrote this program, but it is not working! the loop create nothing!!!
>
> l := AllSmallGroups(24);;  List(l,StructureDescription);; A:=Filtered(l,
> x->IsAbelian(x)=false);
>
> Length(A);
>
> for i in [1..Length(A)]  do
>
> A[i];
>
> Cl:=ConjugacyClasses(A[i]);
>
> RCl:=List(Cl, x->Representative(x));
>
> Ocl:=List(RCl, x->Order(x));
>
> irr:=Irr(A[i]);
> od;
>
> Can someone tell me what's wrong? and how can i do it?
> to me seems for loop just can run from start to end and at the end can
> store the result of the last loop!
>
> thanks
> Katie
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From arbautjc at gmail.com  Sun Jun 16 21:48:02 2013
From: arbautjc at gmail.com (Jean-Claude Arbaut)
Date: Sun, 16 Jun 2013 22:48:02 +0200
Subject: [GAP Forum] Idempotents modulo N
Message-ID: <CANufCk4C2OHjX0OYYpws5EN-UeOZRu8Jujv24P98n=CydV4EEg@mail.gmail.com>

Hello GAP users,

GAP can compute idempotents, like this :
a := Idempotents(MatrixAlgebra(Integers mod 3, 2));
List(a, x -> x*x - x);

For Integers mod n, it also works, but it's not very fast. However, it's a
fairly easy task, using chinese remainder theorem, and if n = p1^k1 * ... *
ps^ks, then there are 2^s solutions.
Here is a program to compute them, in case it can be useful.

IdempotentsMod := function(n)
   local a, m, s, r;
   m := List(Collected(FactorsInt(n)), v -> v[1]^v[2]);
   s := Length(m);
   a := [];
   for r in IteratorOfTuples([0, 1], s) do
      Add(a, ChineseRem(m, r));
   od;
   Sort(a);
   return List(a, x -> ZmodnZObj(x, n));
end;

For example :

n := 2000000;
Idempotents(Integers mod n);
IdempotentsMod(n) = last;

Length(IdempotentsMod(Factorial(50)));


Jean-Claude Arbaut

From vale02002 at yahoo.com  Sun Jun 16 21:50:52 2013
From: vale02002 at yahoo.com (hossein akhlaghi)
Date: Sun, 16 Jun 2013 13:50:52 -0700 (PDT)
Subject: [GAP Forum] FW: hossein akhlaghi
Message-ID: <1371415852.61457.YahooMailNeo@web164602.mail.gq1.yahoo.com>


hello! http://www.mebel-cn.com/honqiit/ozbsn/tvajs/ghksf.html   
hossein akhlaghi

From magidin at member.ams.org  Mon Jun 17 17:31:19 2013
From: magidin at member.ams.org (Arturo Magidin)
Date: Mon, 17 Jun 2013 11:31:19 -0500 (CDT)
Subject: [GAP Forum] Computing a nonabelian tensor square
Message-ID: <alpine.DEB.2.02.1306171127160.14948@h140039.louisiana.edu>

Dear GAP Forum,

I'm not very familiar with the sundry methods for computing the 
nonabelian tensor square using GAP, or for testing its structural 
properties. I need a quick computation and I'm hoping someone can 
point me to the right direction for doing so.

Specifically, I'd like to check the following (full disclosure: it has 
to do with a paper I'm refereeing):

Let Z be the infinite cyclic group, and let G be the semidirect 
product of Z with itself, with Z acting nontrivially; that is,

G = < x,y  |   x^y = x^{-1} >

I would like to check whether the nonabelian tensor square of G has 
torsion, and to confirm that the nonabelian tensor square of G/Z(G) 
does in fact have torsion. (G/Z(G) is the infinite dihedral group, as 
Z(G) = <y^2> ).

Thank you,

Arturo


From menger at math.binghamton.edu  Mon Jun 17 21:07:27 2013
From: menger at math.binghamton.edu (Luise Kappe)
Date: Mon, 17 Jun 2013 16:07:27 -0400 (EDT)
Subject: [GAP Forum] Computing a nonabelian tensor square
In-Reply-To: <alpine.DEB.2.02.1306171127160.14948@h140039.louisiana.edu>
References: <alpine.DEB.2.02.1306171127160.14948@h140039.louisiana.edu>
Message-ID: <alpine.LFD.2.03.1306171557380.9223@math.binghamton.edu>

Arturo,
Your question is completely answered by Theorem 4.4 in the paper
  "Infinite metacyclic groups and their non-abelian tensor squares" by 
J.R.Beuerle and L.-C.Kappe, Proceedings Edinburgh Mathematical Society 
(2000) 43, 651-662.
The non-abelian tensor square of G is isomorphic to
      C_4 x C_2 x C_0 x C_0,
and the non-abelian tensor square of G/Z(G) is isomorphic to
      C_2 x C_2 x C_2 x C_0.
                Hope that helps,
                                  LCK

On Mon, 17 Jun 2013, Arturo Magidin wrote:

> Dear GAP Forum,
>
> I'm not very familiar with the sundry methods for computing the nonabelian 
> tensor square using GAP, or for testing its structural properties. I need a 
> quick computation and I'm hoping someone can point me to the right direction 
> for doing so.
>
> Specifically, I'd like to check the following (full disclosure: it has to do 
> with a paper I'm refereeing):
>
> Let Z be the infinite cyclic group, and let G be the semidirect product of Z 
> with itself, with Z acting nontrivially; that is,
>
> G = < x,y  |   x^y = x^{-1} >
>
> I would like to check whether the nonabelian tensor square of G has torsion, 
> and to confirm that the nonabelian tensor square of G/Z(G) does in fact have 
> torsion. (G/Z(G) is the infinite dihedral group, as Z(G) = <y^2> ).
>
> Thank you,
>
> Arturo
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
>


From beick at tu-bs.de  Tue Jun 18 07:19:44 2013
From: beick at tu-bs.de (Bettina Eick)
Date: Tue, 18 Jun 2013 08:19:44 +0200 (CEST)
Subject: [GAP Forum] Computing a nonabelian tensor square
In-Reply-To: <alpine.DEB.2.02.1306171127160.14948@h140039.louisiana.edu>
References: <alpine.DEB.2.02.1306171127160.14948@h140039.louisiana.edu>
Message-ID: <alpine.LRH.2.02.1306180816200.24793@rzlogin01.rz.tu-bs.de>


Dear Arturo,

> Let Z be the infinite cyclic group, and let G be the semidirect product of Z 
> with itself, with Z acting nontrivially; that is,
>
> G = < x,y  |   x^y = x^{-1} >
>
> I would like to check whether the nonabelian tensor square of G has torsion, 
> and to confirm that the nonabelian tensor square of G/Z(G) does in fact have 
> torsion. (G/Z(G) is the infinite dihedral group, as Z(G) = <y^2> ).

This can be done as follows:

# create G as group with power-conjugate presentation
gap> c := FromTheLeftCollector(2);
<<from the left collector with 2 generators>>
gap> SetConjugate(c, 2, 1, [2,-1]);
gap> UpdatePolycyclicCollector(c);
gap> G := PcpGroupByCollector(c);
Pcp-group with orders [ 0, 0 ]

# compute the non-abelian tensor square 
gap> H := NonAbelianTensorSquare(G);
Pcp-group with orders [ 0, 0, 2, 4 ]
gap> TH := TorsionSubgroup(H);
Pcp-group with orders [ 2, 4 ]
gap> Size(TH);
8

# one can also investigate H further
gap> IsAbelian(H);
true
gap> AbelianInvariants(H);
[ 0, 0, 2, 4 ]

# and one can do a similar computation with G/Center(G)
gap> K := G/Center(G);
Pcp-group with orders [ 2, 0 ]
gap> L := NonAbelianTensorSquare(K);
Pcp-group with orders [ 0, 2, 2, 2 ]
gap> IsAbelian(L);
true
gap> AbelianInvariants(L);
[ 0, 2, 2, 2 ]

Best wishes,

Bettina



From arbautjc at gmail.com  Tue Jun 18 11:17:40 2013
From: arbautjc at gmail.com (Jean-Claude Arbaut)
Date: Tue, 18 Jun 2013 12:17:40 +0200
Subject: [GAP Forum] Factoring Mersenne numbers
Message-ID: <CANufCk59UDLQvW-2qABjv6aZRdV7h-30kQB7J4Cks=Y_Ayubgw@mail.gmail.com>

Hello,

While I was playing with FactorsInt and FactInt, I was quite impressed by

FactorsInt(2^467 - 1);

FactorsInt(2^919 - 1);

467 and 919 are prime. The factors found are quite large: 58 decimal digits
for
the first, and 126 for the other. These are not the largest factors, but
the second largest,
and I would have expected the task to be harder.
I'm almost sure they are not "cached", since factorization can take hours
for other
Mersenne numbers, even with much smaller factors (M604 seems to be harder
for GAP, with a second-largest factor of "only" 32 digits).

On the other hand, Yafu takes much more time to factor these two numbers.
Of course, factorization speed depends on the method used, the choice of
parameters... and luck (some numbers will be better broken with the right
combination of parameters I bet).

Now, is this only luck, or is there some good reason for GAP (algorithm
better suited to Mersenne numbers ?) to find these factors so fast ?

Best regards,

Jean-Claude Arbaut

From stefan at mcs.st-and.ac.uk  Tue Jun 18 14:00:45 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Tue, 18 Jun 2013 14:00:45 +0100 (BST)
Subject: [GAP Forum] Factoring Mersenne numbers
In-Reply-To: <CANufCk59UDLQvW-2qABjv6aZRdV7h-30kQB7J4Cks=Y_Ayubgw@mail.gmail.com>
References: <CANufCk59UDLQvW-2qABjv6aZRdV7h-30kQB7J4Cks=Y_Ayubgw@mail.gmail.com>
Message-ID: <submission.1UovWf-00059O-CP@mail-gap.mcs.st-and.ac.uk>

Dear Forum,

Jean-Claude Arbaut wrote:
> While I was playing with FactorsInt and FactInt, I was quite impressed by
>
> FactorsInt(2^467 - 1);
>
> FactorsInt(2^919 - 1);
>
> 467 and 919 are prime. The factors found are quite large: 58 decimal digits
> for
> the first, and 126 for the other. These are not the largest factors, but
> the second largest,
> and I would have expected the task to be harder.
> I'm almost sure they are not "cached", since factorization can take hours
> for other
> Mersenne numbers, even with much smaller factors (M604 seems to be harder
> for GAP, with a second-largest factor of "only" 32 digits).
>
> On the other hand, Yafu takes much more time to factor these two numbers.
> Of course, factorization speed depends on the method used, the choice of
> parameters... and luck (some numbers will be better broken with the right
> combination of parameters I bet).
>
> Now, is this only luck, or is there some good reason for GAP (algorithm
> better suited to Mersenne numbers ?) to find these factors so fast ?

The integer factorization routine implemented in the FactInt package
makes use of a combination of various factoring methods. These include:

  - Trial division,
  - Database lookup,
  - Caches (single factors and complete factorizations),
  - Various tricks for special cases,
  - Pollard Rho,
  - Pollard p-1 / Williams' p+1,
  - ECM (Elliptic Curves Method) and
  - MPQS (Multiple Polynomial Quadratic Sieve)

For Mersenne numbers (or more generally, for numbers of the form a^b +/- 1
for small a and b), it uses Richard P. Brent's Factor Tables
(http://maths-people.anu.edu.au/~brent/factors.html). The copy shipped
together with FactInt has been updated for the last time on June 16, 2011.

The issue with 2^604-1 is simply that the database does not contain
the factor 130530323901899210670077, which therefore needs to be found
by doing 'actual work' (I tried it on my Laptop, and the factor was found
by ECM in about half a minute).

Best regards,

    Stefan Kohl




From arbautjc at gmail.com  Tue Jun 18 16:06:08 2013
From: arbautjc at gmail.com (Jean-Claude Arbaut)
Date: Tue, 18 Jun 2013 17:06:08 +0200
Subject: [GAP Forum] Factoring Mersenne numbers
In-Reply-To: <submission.1UovWf-00059O-CP@mail-gap.mcs.st-and.ac.uk>
References: <CANufCk59UDLQvW-2qABjv6aZRdV7h-30kQB7J4Cks=Y_Ayubgw@mail.gmail.com>
	<submission.1UovWf-00059O-CP@mail-gap.mcs.st-and.ac.uk>
Message-ID: <CANufCk7s4M0oyy6pn3hdw8Hjy1cmcHatFGs+v48o3eC2_7c4OQ@mail.gmail.com>

Thanks !

So there is indeed a table of factors... I know some of the factorization
methods cited, but I wasn't aware of this optimization.

Jean-Claude Arbaut



2013/6/18 Stefan Kohl <stefan at mcs.st-and.ac.uk>

> Dear Forum,
>
> Jean-Claude Arbaut wrote:
> > While I was playing with FactorsInt and FactInt, I was quite impressed by
> >
> > FactorsInt(2^467 - 1);
> >
> > FactorsInt(2^919 - 1);
> >
> > 467 and 919 are prime. The factors found are quite large: 58 decimal
> digits
> > for
> > the first, and 126 for the other. These are not the largest factors, but
> > the second largest,
> > and I would have expected the task to be harder.
> > I'm almost sure they are not "cached", since factorization can take hours
> > for other
> > Mersenne numbers, even with much smaller factors (M604 seems to be harder
> > for GAP, with a second-largest factor of "only" 32 digits).
> >
> > On the other hand, Yafu takes much more time to factor these two numbers.
> > Of course, factorization speed depends on the method used, the choice of
> > parameters... and luck (some numbers will be better broken with the right
> > combination of parameters I bet).
> >
> > Now, is this only luck, or is there some good reason for GAP (algorithm
> > better suited to Mersenne numbers ?) to find these factors so fast ?
>
> The integer factorization routine implemented in the FactInt package
> makes use of a combination of various factoring methods. These include:
>
>   - Trial division,
>   - Database lookup,
>   - Caches (single factors and complete factorizations),
>   - Various tricks for special cases,
>   - Pollard Rho,
>   - Pollard p-1 / Williams' p+1,
>   - ECM (Elliptic Curves Method) and
>   - MPQS (Multiple Polynomial Quadratic Sieve)
>
> For Mersenne numbers (or more generally, for numbers of the form a^b +/- 1
> for small a and b), it uses Richard P. Brent's Factor Tables
> (http://maths-people.anu.edu.au/~brent/factors.html). The copy shipped
> together with FactInt has been updated for the last time on June 16, 2011.
>
> The issue with 2^604-1 is simply that the database does not contain
> the factor 130530323901899210670077, which therefore needs to be found
> by doing 'actual work' (I tried it on my Laptop, and the factor was found
> by ECM in about half a minute).
>
> Best regards,
>
>     Stefan Kohl
>
>
>

From Nick.Gill at open.ac.uk  Fri Jun 21 16:31:50 2013
From: Nick.Gill at open.ac.uk (Nick.Gill)
Date: Fri, 21 Jun 2013 16:31:50 +0100
Subject: [GAP Forum] Converting lists of groups into direct products
Message-ID: <60667691F130CD418BD0D4FC512EF91217B5B1728F@SALCEYCMS1.open.ac.uk>

Hello GAP-forum,

I'm new to the group, so not familiar with the protocol. Forgive me if I'm asking a stupid question and/or omitting vital information...

I have a list of groups - grouplist - and two lists of elements - elist1, elist2 - such that, for each index i, elist1[i] and elist2[i] are members of grouplist[i].

Now I use the command
D:= DirectProduct(grouplist)
Here's what I want to do next:
(1) I would like to convert elist1, elist2 into a format where GAP recognises them as members of D, i.e. I want to convert them from being lists into tuples.
(2) Find the subgroup of D generated by elist1 and elist2.

It's (1) that I'm having trouble with - how do I do it?!

The groups in grouplist, incidentally, are either permutation groups or quotients of the free group on 2 letters. I don't know if this fact is important...

All replies appreciated. Warning: I'm extremely ignorant at GAP so have limited capacity to understand complicated responses!

Nick

-- 
The Open University is incorporated by Royal Charter (RC 000391), an exempt charity in England & Wales and a charity registered in Scotland (SC 038302).



From max at quendi.de  Sun Jun 23 08:02:30 2013
From: max at quendi.de (Max Horn)
Date: Sun, 23 Jun 2013 09:02:30 +0200
Subject: [GAP Forum] Converting lists of groups into direct products
In-Reply-To: <60667691F130CD418BD0D4FC512EF91217B5B1728F@SALCEYCMS1.open.ac.uk>
References: <60667691F130CD418BD0D4FC512EF91217B5B1728F@SALCEYCMS1.open.ac.uk>
Message-ID: <1CFF91D7-5A29-4EB7-BD19-BC19343FB70E@quendi.de>

Dear Nick,

On 21.06.2013, at 17:31, Nick.Gill wrote:

> Hello GAP-forum,
> 
> I'm new to the group, so not familiar with the protocol. Forgive me if I'm asking a stupid question and/or omitting vital information...
> 
> I have a list of groups - grouplist - and two lists of elements - elist1, elist2 - such that, for each index i, elist1[i] and elist2[i] are members of grouplist[i].
> 
> Now I use the command
> D:= DirectProduct(grouplist)
> Here's what I want to do next:
> (1) I would like to convert elist1, elist2 into a format where GAP recognises them as members of D, i.e. I want to convert them from being lists into tuples.

The official way is to use the embedding homomorphisms. Here is a brief example:

gap> g:=Group((1,2,3),(1,2));;
gap> h:=Group((1,2,3,4,5));;
gap> d:=DirectProduct(g,h);
Group([ (1,2,3), (1,2), (4,5,6,7,8) ])
gap> list := [ (1,2), (1,5,4,3,2) ];
gap> e1:=Embedding(d,1);
1st embedding into Group([ (1,2,3), (1,2), (4,5,6,7,8) ])
gap> e2:=Embedding(d,2);
2nd embedding into Group([ (1,2,3), (1,2), (4,5,6,7,8) ])
gap> x := list[1]^e1 * list[2]^e2;
(1,2)(4,8,7,6,5)

This has the advantage of working regardless of how the direct product of your groups is implemented -- as a set of tuples, as a permutation group, a polycyclic group, a finitely presented group or otherwise.

You talk about "tuples". Well, GAP only uses "tuples" to represent elements of direct products if it doesn't know a "better" way (as is the case in the example above). This usually only is the case when you form the direct product of groups of different types, such as the direct product of a permutation group with a finitely presented  groups; since you mention that below, I assume you are doing that.

In this situation, there is a different, (undocumented!) way to indeed convert a list of group elements into a "tuple" element, which might be more convenient in your situation: using DirectProductElement. This could look as follows:

gap> G:=SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> F:=FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> H:=F/[ F.1^2, F.2^2 ];
<fp group on the generators [ f1, f2 ]>
gap> H:=F/[ F.1^2, F.2^2 ];
<fp group on the generators [ f1, f2 ]>
gap> D:=DirectProduct(G,H);
<group with 4 generators>
gap> elist1:=[G.1, H.1];
[ (1,2,3,4), f1 ]
gap> elist2:=[G.2, H.2];
[ (1,2), f2 ]
gap> g1:=DirectProductElement(elist1);
DirectProductElement( [ (1,2,3,4), f1 ] )
gap> g2:=DirectProductElement(elist2);
DirectProductElement( [ (1,2), f2 ] )

Note that this is undocumented, and thus could change in future versions of GAP (but for a one-time computation, that doesn't matter, of course). Moreover, the code using Embedding also would work in this context, e.g. like this:

gap> g1:=Product(List([1,2], i->elist1[i]^Embedding(D,i)));
DirectProductElement( [ (1,2,3,4), f1 ] )


> (2) Find the subgroup of D generated by elist1 and elist2.
> 
> It's (1) that I'm having trouble with - how do I do it?!
> 
> The groups in grouplist, incidentally, are either permutation groups or quotients of the free group on 2 letters. I don't know if this fact is important...

Out of completeness, and continuing the example from above:

gap> K:=Subgroup(D, [g1, g2]);
<group with 2 generators>

However, if the factors of the direct product are indeed of different type, as  above, then the resulting group object will be of limited use, and computations with it may be much less efficient than theoretically possible, since not that much work went into making computations with such groups efficient.

So depending on what exactly you want to do with that subgroup, it might be more effective to first convert the factors of your direct product into groups of the same type, before computing the direct product and working with it.


> 
> All replies appreciated. Warning: I'm extremely ignorant at GAP so have limited capacity to understand complicated responses!

I hope the above was clear enough, but if not, please do not hesitate to ask for clarifications or further examples.


Cheers,
Max



From msorouhesh at gmail.com  Wed Jun 26 09:20:47 2013
From: msorouhesh at gmail.com (Mohammad Reza Sorouhesh)
Date: Wed, 26 Jun 2013 12:50:47 +0430
Subject: [GAP Forum] Simplifying the resulted elements in a Free group
Message-ID: <CAJn1Z0PvnUppbS5XQsG=_NNYxCc5F7haPS40VZQT=aEiBwW4cw@mail.gmail.com>

Dear Forum,

Consider you define a certain free group with,"g:=FreeGroup (...)" as we
usually do. Sometimes, we call the elements by "Element(g)" as well to
examine the elements for some purposes. GAP gives them all like "a*b^2" or
something like this. GAP neither write them as for example "ab^2" (by
omitting the *) nor simplify the elements which can be simplified regarding
to Free group relations. For example if we have (a*b)^3=1 in the relations
of Free group, we still have "a^3*b*a*b" in output. Sometimes, we consider
GAP to simplify this element regard to that relation by writhing it as
a^ib^j for proper positive integers i and j. Any help will be appreciated.

Thanks for the time you give me,

M.R.Sorouhesh

From rrburns at cox.net  Thu Jun 27 22:52:14 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 27 Jun 2013 21:52:14 +0000 (UTC)
Subject: [GAP Forum] =?utf-8?q?How_do_I_study_fields_like_ZN=5BX=7D/=3Cpol?=
	=?utf-8?q?y=3E_in_GAP?=
Message-ID: <loom.20130627T233055-92@post.gmane.org>

Dear Forum,

I am new to GAP and trying hard to come up to speed with all the GAP
documentation.

In particular I can't figure out which functions are available to set up and
solve the following (rather simple) problem:

Consider the a finite field over n elements over a polynomial, for example,
the field Z_2[X]/<x^2+x+1>. Find the elements and give the addition and
multiplication tables.

(I have no problem solving this "by hand" (or using Mathematica), but I
can't seem  to figure how to get the job done in GAP)

Thank you for any specific solution or even pointers to the GAP functions
that I should be using.
   Sopsku



From rrburns at cox.net  Thu Jun 27 23:51:33 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 27 Jun 2013 22:51:33 +0000 (UTC)
Subject: [GAP Forum] Basic help on output (MultiplicationTable)
References: <CALxKSnwZASZAxD_unvL3yivC7U+-FU1Jk0e22fgyNiPyeEvGCQ@mail.gmail.com>
Message-ID: <loom.20130628T004617-285@post.gmane.org>

Luiz Meier <luizrobertomeier at ...> writes:

> 
> Hello people,
> 
> I'm reading and testing the book:
> 
> Abstract Algebra - An Interactive Approach (Mathematica and GAP) Paulsen
> (CRC) ISBN:
> 
 
> OBS.: The book uses the command MultTable (when it was changed to
> MultiplicationTable command?)

> What am I doing wrong? Where can I found informations about such simple
> things to avoid to bore you all? Thank you all in advance.
> 

I believe your problem may rest with the fact that there is a file of
functions for this book and MultTable is one of Paulsen's fuctions and not a
GAP function. 
  Sopsu





From Sven.Reichard at tu-dresden.de  Fri Jun 28 13:59:41 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Fri, 28 Jun 2013 14:59:41 +0200
Subject: [GAP Forum] How do I study fields like ZN[X}/<poly> in GAP
In-Reply-To: <loom.20130627T233055-92@post.gmane.org>
References: <loom.20130627T233055-92@post.gmane.org>
Message-ID: <51CD88BD.9040009@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 27.06.2013 23:52, schrieb Sopsku:
> Dear Forum,
> 
> I am new to GAP and trying hard to come up to speed with all the
> GAP documentation.
> 
> In particular I can't figure out which functions are available to
> set up and solve the following (rather simple) problem:
> 
> Consider the a finite field over n elements over a polynomial, for
> example, the field Z_2[X]/<x^2+x+1>. Find the elements and give the
> addition and multiplication tables.
> 
> (I have no problem solving this "by hand" (or using Mathematica),
> but I can't seem  to figure how to get the job done in GAP)
> 
> Thank you for any specific solution or even pointers to the GAP
> functions that I should be using. Sopsku
> 


Dear Sopsku,

here's one possibility. Probably there are more elegant ways.

gap> x := Indeterminate(GF(2), "x");
x
gap> r := PolynomialRing(GF(2));
GF(2)[x]
gap> p := x^2+x+1;
x^2+x+Z(2)^0
gap> i := Ideal(r, [p]);
<two-sided ideal in GF(2)[x], (1 generators)>
gap> quotient := r/i;
<ring GF(2),(1),(x)>
gap> Size(last);
4
gap> # addition table
gap> PrintArray(List(quotient, x -> List(quotient, y -> x+y)));
[ [    0*(1),      (x),      (1),  (1)+(x) ],
  [      (x),    0*(1),  (1)+(x),      (1) ],
  [      (1),  (1)+(x),    0*(1),      (x) ],
  [  (1)+(x),      (1),      (x),    0*(1) ] ]
gap> # multiplication table
gap> PrintArray(List(quotient, x -> List(quotient, y -> x*y)));
[ [    0*(1),    0*(1),    0*(1),    0*(1) ],
  [    0*(1),  (1)+(x),      (x),      (1) ],
  [    0*(1),      (x),      (1),  (1)+(x) ],
  [    0*(1),      (1),  (1)+(x),      (x) ] ]

Cheers,

Sven Reichard.
- --
Institut f?r Algebra
TU Dresden

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From rrburns at cox.net  Sun Jun 30 21:28:27 2013
From: rrburns at cox.net (Sopsku)
Date: Sun, 30 Jun 2013 20:28:27 +0000 (UTC)
Subject: [GAP Forum] =?utf-8?b?V2hhdCBkb2VzICA8WyBbIDEsIDEgXSBdfGIqYV4t?=
	=?utf-8?q?1=3E_mean?=
Message-ID: <loom.20130630T221902-674@post.gmane.org>

Dear Forum,

I am continuing my struggle to learn a bit about GAP. I formed the
octahedral group using three elements (altho this is not important to to
questions). I asked GAP for
gap> asg:=AllSubgroups(g);;
## Look at the elements for one of these subgroups
gap> Elements(asg[24]);
[ <identity ...>, a*c^-1, <[ [ 1, 1 ] ]|b*a^-1>, c^-1*b, 
  <[ [ 2, 1 ] ]|c*a^-1>, c*b^-1 ]

I do not understand the notation, such as, <[ [ 1, 1 ] ]|b*a^-1> 

I have tried searching through the GAP manuals and some tutorials with no
luck is seeing anything expect the rather obvious <identity ...> which is
defined in the manuals.

Thank you for any help!
    Sopsku



From ahulpke at gmail.com  Mon Jul  1 15:06:14 2013
From: ahulpke at gmail.com (Alexander Hulpke)
Date: Mon, 1 Jul 2013 08:06:14 -0600
Subject: [GAP Forum] What does  <[ [ 1, 1 ] ]|b*a^-1> mean
In-Reply-To: <loom.20130630T221902-674@post.gmane.org>
References: <loom.20130630T221902-674@post.gmane.org>
Message-ID: <C0DE070F-5BF7-4013-892B-4CFB42CC5C85@gmail.com>

Dear Forum, 

On Jun 30, 2013 <rrburns at cox.net>  asked:

> octahedral group using three elements (altho this is not important to to
> questions). I asked GAP for
> gap> asg:=AllSubgroups(g);;
> ## Look at the elements for one of these subgroups
> gap> Elements(asg[24]);
> [ <identity ...>, a*c^-1, <[ [ 1, 1 ] ]|b*a^-1>, c^-1*b, 
>  <[ [ 2, 1 ] ]|c*a^-1>, c*b^-1 ]
> 
> I do not understand the notation, such as, <[ [ 1, 1 ] ]|b*a^-1> 

This is the element b*a, stored via a straight line program. (This representation happens as the calculation of subgroups uses some nontrivial homomorphisms, for larger groups it saves memory.)
These elements behave fr all practical purposes just like the normal words in finitely presented groups.

Regards,

    Alexander Hulpke




From rrburns at cox.net  Mon Jul  1 16:34:58 2013
From: rrburns at cox.net (Sopsku)
Date: Mon, 1 Jul 2013 15:34:58 +0000 (UTC)
Subject: [GAP Forum] =?utf-8?b?V2hhdCBkb2VzICA8WyBbIDEsIDEgXSBdfGIqYV4t?=
	=?utf-8?q?1=3E_mean?=
References: <loom.20130630T221902-674@post.gmane.org>
	<C0DE070F-5BF7-4013-892B-4CFB42CC5C85@gmail.com>
Message-ID: <loom.20130701T172956-709@post.gmane.org>

Alexander Hulpke <ahulpke at ...> writes:

> > I do not understand the notation, such as, <[ [ 1, 1 ] ]|b*a^-1> 
> 
> This is the element b*a, stored via a straight line program. ...  
>     Alexander Hulpke

I still do not understand how to decode b*a from  <[ [ 1, 1 ] ]|b*a^-1>.
Sorry for my denseness!
     Sopsku






From ghorbani1002 at yahoo.com  Thu Jul 11 08:22:35 2013
From: ghorbani1002 at yahoo.com (Ebrahim Ghorbani)
Date: Thu, 11 Jul 2013 00:22:35 -0700 (PDT)
Subject: [GAP Forum] Partitions and orbits of automorphism groups
Message-ID: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>

Dear Forum, 

I have a partition of the vertex set of a vertex-transitive graph G. 
I guess that this partition are the orbit partition of some subgroup of Aut(G). 
Is there any way to find out this?

Thanks,
Ebrahim


From matan at svgalib.org  Thu Jul 11 08:43:25 2013
From: matan at svgalib.org (Matan Ziv-Av)
Date: Thu, 11 Jul 2013 10:43:25 +0300 (IDT)
Subject: [GAP Forum] Partitions and orbits of automorphism groups
In-Reply-To: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>
References: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>
Message-ID: <alpine.LFD.2.03.1307111041150.4875@svgalib.org>

On Thu, 11 Jul 2013, Ebrahim Ghorbani wrote:

> Dear Forum,
>
> I have a partition of the vertex set of a vertex-transitive graph G.
> I guess that this partition are the orbit partition of some subgroup of Aut(G).
> Is there any way to find out this?

Find the stabilizer (as a tuple of sets) of the partition in Aut(G). If 
the orbits of any subgroup gives this partition, then the stabilizer 
also does.


-- 
Matan Ziv-Av.                         matan at svgalib.org




From Sven.Reichard at tu-dresden.de  Thu Jul 11 08:51:46 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Thu, 11 Jul 2013 09:51:46 +0200
Subject: [GAP Forum] Partitions and orbits of automorphism groups
In-Reply-To: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>
References: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>
Message-ID: <51DE6412.8010406@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 11.07.2013 09:22, schrieb Ebrahim Ghorbani:
> Dear Forum,
> 
> I have a partition of the vertex set of a vertex-transitive graph
> G. I guess that this partition are the orbit partition of some
> subgroup of Aut(G). Is there any way to find out this?
> 
> Thanks, Ebrahim
> 
> _______________________________________________ Forum mailing list 
> Forum at mail.gap-system.org 
> http://mail.gap-system.org/mailman/listinfo/forum
> 

Dear Ebrahim,

say the partition is P. If it is the orbit partition of some group of
automorphisms, then in particular it is the orbit partition of its own
stabilizer in the full group Aut(G). Thus, if P is given as a set of
sets, we can simply test as follows:

gap> stab := Stabilizer(Aut(G), P, OnSetsSets);
gap> Length(P) = Length(Orbits(stab, [1..G.order]));

(We just compare the lengths so we don't have to sort the orbits.)

Hope this helps,
Sven.

- --
Sven Reichard
Institut f?r Algebra
TU Dresden
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From Sven.Reichard at tu-dresden.de  Thu Jul 11 08:54:07 2013
From: Sven.Reichard at tu-dresden.de (Sven Reichard)
Date: Thu, 11 Jul 2013 09:54:07 +0200
Subject: [GAP Forum] Partitions and orbits of automorphism groups
In-Reply-To: <alpine.LFD.2.03.1307111041150.4875@svgalib.org>
References: <1373527355.6993.YahooMailBasic@web162802.mail.bf1.yahoo.com>
	<alpine.LFD.2.03.1307111041150.4875@svgalib.org>
Message-ID: <51DE649F.4070200@tu-dresden.de>

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 11.07.2013 09:43, schrieb Matan Ziv-Av:
> On Thu, 11 Jul 2013, Ebrahim Ghorbani wrote:
> 
>> Dear Forum,
>> 
>> I have a partition of the vertex set of a vertex-transitive graph
>> G. I guess that this partition are the orbit partition of some
>> subgroup of Aut(G). Is there any way to find out this?
> 
> Find the stabilizer (as a tuple of sets) of the partition in
> Aut(G). If the orbits of any subgroup gives this partition, then
> the stabilizer also does.
> 
> 

Of course Matan is right; we need to consider tuples of sets, not sets
of sets as I said earlier.

Sven.

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From L.H.Soicher at qmul.ac.uk  Thu Jul 11 16:47:29 2013
From: L.H.Soicher at qmul.ac.uk (Leonard Soicher)
Date: Thu, 11 Jul 2013 16:47:29 +0100 (BST)
Subject: [GAP Forum] Partitions and orbits of automorphism groups
In-Reply-To: <51DE649F.4070200@tu-dresden.de>
Message-ID: <337661218.719618.1373557649814.JavaMail.root@planck.maths.qmul.ac.uk>


Dear GAP-Forum,

Note that you can use the GRAPE function AutGroupGraph (which calls nauty)
to determine directly the stabiliser of an ordered partition of the vertices 
of a graph in the automorphism group of that graph. See the documentation
for AutGroupGraph. For example:

gap> LoadPackage("grape");
true
gap> J:=JohnsonGraph(4,2);
rec( adjacencies := [ [ 2, 3, 4, 5 ] ], group := Group([ (1,4,6,3)(2,5), (2,4)(3,5) ]), isGraph := true,
  isSimple := true, names := [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 4 ] ], order := 6,
  representatives := [ 1 ], schreierVector := [ -1, 2, 1, 1, 1, 1 ] )
gap> H:=AutGroupGraph(J,[[1],[6],[2,5],[3,4]]);
Group([ (3,4), (2,5) ])
gap> Size(H);
4
gap> Orbits(H,[1..J.order]);
[ [ 1 ], [ 2, 5 ], [ 3, 4 ], [ 6 ] ]


Regards,
Leonard
 
----- Original Message -----
From: "Sven Reichard" <Sven.Reichard at tu-dresden.de>
To: forum at gap-system.org
Sent: Thursday, 11 July, 2013 8:54:07 AM
Subject: Re: [GAP Forum] Partitions and orbits of automorphism groups

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am 11.07.2013 09:43, schrieb Matan Ziv-Av:
> On Thu, 11 Jul 2013, Ebrahim Ghorbani wrote:
> 
>> Dear Forum,
>> 
>> I have a partition of the vertex set of a vertex-transitive graph
>> G. I guess that this partition are the orbit partition of some
>> subgroup of Aut(G). Is there any way to find out this?
> 
> Find the stabilizer (as a tuple of sets) of the partition in
> Aut(G). If the orbits of any subgroup gives this partition, then
> the stabilizer also does.
> 
> 

Of course Matan is right; we need to consider tuples of sets, not sets
of sets as I said earlier.

Sven.

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_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum


From stefanosaivazidis at gmail.com  Fri Jul 12 22:58:55 2013
From: stefanosaivazidis at gmail.com (Stefanos Aivazidis)
Date: Fri, 12 Jul 2013 22:58:55 +0100
Subject: [GAP Forum] Order of elements in a group and their statistics
Message-ID: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>

Dear forum,

I have the following (rather naive) question to ask: what is the
most efficient way to find the spectrum of a finite group G, and
compute for each integer in the spectrum the number of elements with
given order? An integer d lies in the spectrum of G iff there exists
at least one g in G such that o(g)=d.  The algorithm, I imagine, should
proceed along these lines:

1) define the group G,
2) compute the set of divisors of |G| and store this as a list L,
3) refine L (by excluding those divisors of |G| which do not
     appear as element orders) to obtain the spectrum of G and
     store this in a new list L',
4) compute how many elements of G have order d, for each d in L'

Your thoughts on how to make this precise algorithmically would
be much appreciated. Also, is it possible to produce a graph with
the statistics found by the main programme?

Many thanks in advance.

Best wishes,
Stefanos

From vkicefire at gmail.com  Fri Jul 12 23:14:58 2013
From: vkicefire at gmail.com (Vee Kay)
Date: Fri, 12 Jul 2013 23:14:58 +0100
Subject: [GAP Forum] Order of elements in a group and their statistics
In-Reply-To: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
References: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
Message-ID: <51E07FE2.3080101@gmail.com>

On 12/07/13 22:58, Stefanos Aivazidis wrote:
> Dear forum,
>
> I have the following (rather naive) question to ask: what is the
> most efficient way to find the spectrum of a finite group G, and
> compute for each integer in the spectrum the number of elements with
> given order? An integer d lies in the spectrum of G iff there exists
> at least one g in G such that o(g)=d.  The algorithm, I imagine, should
> proceed along these lines:
>
> 1) define the group G,
> 2) compute the set of divisors of |G| and store this as a list L,
> 3) refine L (by excluding those divisors of |G| which do not
>       appear as element orders) to obtain the spectrum of G and
>       store this in a new list L',
> 4) compute how many elements of G have order d, for each d in L'
>
> Your thoughts on how to make this precise algorithmically would
> be much appreciated. Also, is it possible to produce a graph with
> the statistics found by the main programme?
>
> Many thanks in advance.
>
> Best wishes,
> Stefanos
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


Are steps 2 and 3 necessary then? I would imagine something like,

i) define the group G
ii) for each element in G, compute its order. add it to the spectrum (if 
not already there) and increment by one the number of times it appears 
(in a separate list presumably).

Don't know if there'd be a more efficient way to do this.

VK


From shahmaths_problem at hotmail.com  Sat Jul 13 07:40:07 2013
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Sat, 13 Jul 2013 11:40:07 +0500
Subject: [GAP Forum] Order of elements in a group and their statistics
In-Reply-To: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
References: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
Message-ID: <BLU169-W31D0E0F9FCC76ED1A6A9D38A650@phx.gbl>

Dear Stefanos,
Imitating and modifying a function "orderFrequency" of  Alexander Hulpke,
your function of spectrum should be as follows.
spectrum:= function(g)
local h,w;
w:= [];
w:= h -> Set(Elements(h), Order);
return w(g);
end;
See also the following application of the function
gap> s3:=SymmetricGroup(IsPermGroup,3);
Sym( [ 1 .. 3 ] )
gap> s7:=SymmetricGroup(IsPermGroup,7);
Sym( [ 1 .. 7 ] )
gap> spectrum(s3);
[ 1, 2, 3 ]
gap> spectrum(s7);
[ 1, 2, 3, 4, 5, 6, 7, 10, 12 ]
Hopes this helps,
Muhammad Shah


> Date: Fri, 12 Jul 2013 22:58:55 +0100
> From: stefanosaivazidis at gmail.com
> To: forum at gap-system.org
> Subject: [GAP Forum] Order of elements in a group and their statistics
> 
> Dear forum,
> 
> I have the following (rather naive) question to ask: what is the
> most efficient way to find the spectrum of a finite group G, and
> compute for each integer in the spectrum the number of elements with
> given order? An integer d lies in the spectrum of G iff there exists
> at least one g in G such that o(g)=d.  The algorithm, I imagine, should
> proceed along these lines:
> 
> 1) define the group G,
> 2) compute the set of divisors of |G| and store this as a list L,
> 3) refine L (by excluding those divisors of |G| which do not
>      appear as element orders) to obtain the spectrum of G and
>      store this in a new list L',
> 4) compute how many elements of G have order d, for each d in L'
> 
> Your thoughts on how to make this precise algorithmically would
> be much appreciated. Also, is it possible to produce a graph with
> the statistics found by the main programme?
> 
> Many thanks in advance.
> 
> Best wishes,
> Stefanos
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
 		 	   		  

From stefan at mcs.st-and.ac.uk  Sat Jul 13 11:45:44 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Sat, 13 Jul 2013 11:45:44 +0100 (BST)
Subject: [GAP Forum] Order of elements in a group and their statistics
In-Reply-To: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
References: <CAPCTGEPN53JvfxecSdtG-GHgkBdyqEront_4O5TZdoT0TTXxFg@mail.gmail.com>
Message-ID: <submission.1UxxKi-0001CO-QL@mail-gap.mcs.st-and.ac.uk>


Stefanos Aivazidis wrote:

> I have the following (rather naive) question to ask: what is the
> most efficient way to find the spectrum of a finite group G, and
> compute for each integer in the spectrum the number of elements with
> given order? An integer d lies in the spectrum of G iff there exists
> at least one g in G such that o(g)=d.  The algorithm, I imagine, should
> proceed along these lines:
>
> 1) define the group G,
> 2) compute the set of divisors of |G| and store this as a list L,
> 3) refine L (by excluding those divisors of |G| which do not
>      appear as element orders) to obtain the spectrum of G and
>      store this in a new list L',
> 4) compute how many elements of G have order d, for each d in L'
>
> Your thoughts on how to make this precise algorithmically would
> be much appreciated.

The following function should do what you want:

OrderStatistics := function ( G )

  local  ccl;

  ccl := List(ConjugacyClasses(G),cl->[Order(Representative(cl)),Size(cl)]);
  return List(Set(TransposedMat(ccl)[1]),
              d->[d,Sum(List(Filtered(ccl,cl->cl[1]=d),cl->cl[2]))]);
end;

For example:

gap> OrderStatistics(AlternatingGroup(20));
[ [ 1, 1 ], [ 2, 11798364735 ], [ 3, 3044269834280 ], [ 4, 147223414987200 ],
  [ 5, 189239120970624 ], [ 6, 4300403589581400 ], [ 7, 34479959558400 ],
  [ 8, 6979977625420800 ], [ 9, 8470676211379200 ], [ 10, 16976210865344640 ],
  [ 11, 609493248000 ], [ 12, 65698234614230400 ], [ 13, 37132204032000 ],
  [ 14, 8807580134496000 ], [ 15, 61842055316670720 ],
  [ 16, 76028187755520000 ], [ 17, 23851980472320000 ],
  [ 18, 81549282342528000 ], [ 19, 128047474114560000 ],
  [ 20, 22125275344972800 ], [ 21, 3030432354892800 ],
  [ 22, 806359567104000 ], [ 24, 54379597079808000 ],
  [ 26, 3898881423360000 ], [ 28, 26584005786624000 ],
  [ 30, 64123306600953600 ], [ 33, 3515557054464000 ],
  [ 35, 6125354900121600 ], [ 36, 22808456326656000 ],
  [ 39, 12996271411200000 ], [ 40, 22301601741619200 ],
  [ 42, 69870172724352000 ], [ 44, 11519422387200000 ],
  [ 45, 11488703927500800 ], [ 51, 47703960944640000 ],
  [ 52, 23393288540160000 ], [ 55, 1843107581952000 ],
  [ 56, 14481559572480000 ], [ 60, 40248008530329600 ],
  [ 63, 14481559572480000 ], [ 65, 18714630832128000 ],
  [ 66, 23038844774400000 ], [ 70, 17920929970944000 ],
  [ 72, 16895152834560000 ], [ 77, 15798064988160000 ],
  [ 78, 7797762846720000 ], [ 84, 12671364625920000 ],
  [ 90, 3379030566912000 ], [ 91, 26735186903040000 ],
  [ 99, 24574767759360000 ], [ 105, 4441011602227200 ],
  [ 110, 5529322745856000 ], [ 120, 20274183401472000 ],
  [ 126, 4827186524160000 ], [ 132, 9215537909760000 ],
  [ 140, 6516701807616000 ], [ 165, 14744860655616000 ],
  [ 168, 7240779786240000 ], [ 180, 6758061133824000 ],
  [ 210, 8688935743488000 ] ]

> Also, is it possible to produce a graph with
> the statistics found by the main programme?

What kind of graph do you wish to produce from the data?

Best regards,

    Stefan Kohl





From colva at mcs.st-and.ac.uk  Mon Jul 15 15:38:05 2013
From: colva at mcs.st-and.ac.uk (Colva Roney-Dougal)
Date: Mon, 15 Jul 2013 15:38:05 +0100
Subject: [GAP Forum] Groups St Andrews, Final deadlines
Message-ID: <27672ED2-65E9-4619-8128-F59940EFB715@mcs.st-and.ac.uk>

Dear Colleagues

The final deadline for booking university accommodation at Groups St Andrews has been extended to 5pm (BST) this WEDNESDAY, 17TH JULY. It will still be possible to register after that, but accommodation options in town may be very limited.

We have also extended the deadline for submitting an abstract for a contributed talk to this FRIDAY, 19TH JULY.

The conference website is here: http://www.groupsstandrews.org/2013/index.shtml

Further details about the conference are at the end of this message.

Best wishes

The Organisers
(Colin Campbell, Max Neunhoeffer, Martyn Quick, Edmund Robertson and Colva Roney-Dougal)

*************
Principal Speakers:
Emmanuel Breuillard: Approximate groups
Martin Liebeck: Width questions for simple groups
Alan Reid: Profinite properties of discrete groups
Karen Vogtmann: Out(F_n), GL(n,Z) and everything in between: automorphism groups of right-angled Artin groups

One Hour Speakers:
Radha Kessar: Finiteness conjectures in modular representation theory
Markus Lohrey: Rational subsets in groups
Derek Robinson: Recent Results on Generalized Baumslag-Solitar Groups
Christopher Voll: Zeta functions of groups and rings: recent developments

Over 100 contributed talks so far! 

In addition, there will be an extensive social programme, including an excursion to Falkland Palace, a Musical Evening, and much more. 

The University of St Andrews is a charity registered in Scotland : No SC013532



From L.H.Soicher at qmul.ac.uk  Thu Jul 25 15:52:19 2013
From: L.H.Soicher at qmul.ac.uk (Leonard Soicher)
Date: Thu, 25 Jul 2013 15:52:19 +0100 (BST)
Subject: [GAP Forum] Mathematics PhD studentships at Queen Mary
Message-ID: <1523183474.736648.1374763938990.JavaMail.root@planck.maths.qmul.ac.uk>

The School of Mathematical Sciences at Queen Mary, Univesity
of London has three studentships available (with some restrictions)
for PhD students starting this autumn, 2013. 

Details on these studentships are available at:
http://www.maths.qmul.ac.uk/projects-and-research-themes/projects-and-research-themes

In particular, I would be very happy for an experienced GAP user
to apply to do my suggested project "Graph colouring exploiting symmetry".
 
The deadline for applications is August 12.
All qualified candidates are encouraged to apply!

Leonard Soicher


From alexander.konovalov at gmail.com  Fri Jul 26 12:35:49 2013
From: alexander.konovalov at gmail.com (Alexander Konovalov)
Date: Fri, 26 Jul 2013 12:35:49 +0100
Subject: [GAP Forum] GAP 4.6.5 release announcement
Message-ID: <53AB6019-1073-4B94-8654-707A95E4D826@gmail.com>

Dear GAP Forum,

This is to announce the release of GAP 4.6.5.

You can download GAP 4.6.5 from 

	http://www.gap-system.org/Releases/

The alternative GAP distributions listed at 

	http://www.gap-system.org/Download/#alternatives

will be updated in due course.

The overview of changes in GAP 4.6.5 is given below.

Improved functionality:

* TraceMethods and UntraceMethods now better check their arguments 
 and provide a sensible error message if being called without 
 arguments. Also, both variants of calling them are now documented.

* Library methods for Sortex are now replaced by faster ones using 
 the kernel SortParallel functionality instead of making expensive 
 zipped lists.

Fixed bugs which could lead to incorrect results:

* IntHexString wrongly produced a large integer when there were too 
 many leading zeros. [Reported by Joe Bohanon]

Fixed bugs that could lead to break loops:

* A bug that may occur in some cases while calling 
 TransitiveIdentification. [Reported by Izumi Miyamoto]

* The new code for semidirect products of permutation groups, 
 introduced in GAP 4.6, had a bug which was causing problems for 
 Projection. [Reported by Graham Ellis]

In addition to the improved functionality and fixed bugs in the 
core GAP system, the following packages have been updated since 
the previous GAP 4.6.4 release: AutoDoc, CRISP, EDIM, Float,
HAP, hecke, IRREDSOL, Modules, NumericalSgps and Smallsemi.

We encourage all users to upgrade to GAP 4.6.5. If you need any 
help or would like to report any problems, please do not hesitate 
to contact us at support at gap-system.org.

Please note that we regularly update the GAP distribution to include 
new versions of GAP packages, but we may not announce each of them 
to the Forum. We intend to use the Forum to announce updates of the 
core GAP system and only of some packages which may fix serious 
issues or have major influence on GAP. 


Wishing you fun and success using GAP,
The GAP Group



From sandeepr.murthy at gmail.com  Fri Jul 26 21:14:49 2013
From: sandeepr.murthy at gmail.com (Sandeep Murthy)
Date: Fri, 26 Jul 2013 21:14:49 +0100
Subject: [GAP Forum] GAP 4.6.5 release announcement
In-Reply-To: <53AB6019-1073-4B94-8654-707A95E4D826@gmail.com>
References: <53AB6019-1073-4B94-8654-707A95E4D826@gmail.com>
Message-ID: <51F2D8B9.2090507@gmail.com>

Hi,

I currently have 4.6.4, but want to upgrade to 4.6.5.  Will there be an 
update soon to the BOB tool for 4.6.5?

Sandeep.



Alexander Konovalov wrote:
> Dear GAP Forum,
>
> This is to announce the release of GAP 4.6.5.
>
> You can download GAP 4.6.5 from
>
> 	http://www.gap-system.org/Releases/
>
> The alternative GAP distributions listed at
>
> 	http://www.gap-system.org/Download/#alternatives
>
> will be updated in due course.
>
> The overview of changes in GAP 4.6.5 is given below.
>
> Improved functionality:
>
> * TraceMethods and UntraceMethods now better check their arguments
>   and provide a sensible error message if being called without
>   arguments. Also, both variants of calling them are now documented.
>
> * Library methods for Sortex are now replaced by faster ones using
>   the kernel SortParallel functionality instead of making expensive
>   zipped lists.
>
> Fixed bugs which could lead to incorrect results:
>
> * IntHexString wrongly produced a large integer when there were too
>   many leading zeros. [Reported by Joe Bohanon]
>
> Fixed bugs that could lead to break loops:
>
> * A bug that may occur in some cases while calling
>   TransitiveIdentification. [Reported by Izumi Miyamoto]
>
> * The new code for semidirect products of permutation groups,
>   introduced in GAP 4.6, had a bug which was causing problems for
>   Projection. [Reported by Graham Ellis]
>
> In addition to the improved functionality and fixed bugs in the
> core GAP system, the following packages have been updated since
> the previous GAP 4.6.4 release: AutoDoc, CRISP, EDIM, Float,
> HAP, hecke, IRREDSOL, Modules, NumericalSgps and Smallsemi.
>
> We encourage all users to upgrade to GAP 4.6.5. If you need any
> help or would like to report any problems, please do not hesitate
> to contact us at support at gap-system.org.
>
> Please note that we regularly update the GAP distribution to include
> new versions of GAP packages, but we may not announce each of them
> to the Forum. We intend to use the Forum to announce updates of the
> core GAP system and only of some packages which may fix serious
> issues or have major influence on GAP.
>
>
> Wishing you fun and success using GAP,
> The GAP Group
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From neunhoef at mcs.st-and.ac.uk  Fri Jul 26 21:17:44 2013
From: neunhoef at mcs.st-and.ac.uk (Max Neunhoeffer)
Date: Fri, 26 Jul 2013 21:17:44 +0100
Subject: [GAP Forum] GAP 4.6.5 release announcement
In-Reply-To: <51F2D8B9.2090507@gmail.com>
References: <53AB6019-1073-4B94-8654-707A95E4D826@gmail.com>
	<51F2D8B9.2090507@gmail.com>
Message-ID: <20130726201744.GA11181@mcs.st-and.ac.uk>

Hi Sandeep,

I will try to provide this as soon as possible but these days are
quite busy for me therefore I cannot promise a time at this stage.

Cheers,
  Max.

On Fri, Jul 26, 2013 at 09:14:49PM +0100, Sandeep Murthy wrote:
> Hi,
> 
> I currently have 4.6.4, but want to upgrade to 4.6.5.  Will there be
> an update soon to the BOB tool for 4.6.5?
> 
> Sandeep.
> 
> 
> 
> Alexander Konovalov wrote:
> >Dear GAP Forum,
> >
> >This is to announce the release of GAP 4.6.5.
> >
> >You can download GAP 4.6.5 from
> >
> >	http://www.gap-system.org/Releases/
> >
> >The alternative GAP distributions listed at
> >
> >	http://www.gap-system.org/Download/#alternatives
> >
> >will be updated in due course.
> >
> >The overview of changes in GAP 4.6.5 is given below.
> >
> >Improved functionality:
> >
> >* TraceMethods and UntraceMethods now better check their arguments
> >  and provide a sensible error message if being called without
> >  arguments. Also, both variants of calling them are now documented.
> >
> >* Library methods for Sortex are now replaced by faster ones using
> >  the kernel SortParallel functionality instead of making expensive
> >  zipped lists.
> >
> >Fixed bugs which could lead to incorrect results:
> >
> >* IntHexString wrongly produced a large integer when there were too
> >  many leading zeros. [Reported by Joe Bohanon]
> >
> >Fixed bugs that could lead to break loops:
> >
> >* A bug that may occur in some cases while calling
> >  TransitiveIdentification. [Reported by Izumi Miyamoto]
> >
> >* The new code for semidirect products of permutation groups,
> >  introduced in GAP 4.6, had a bug which was causing problems for
> >  Projection. [Reported by Graham Ellis]
> >
> >In addition to the improved functionality and fixed bugs in the
> >core GAP system, the following packages have been updated since
> >the previous GAP 4.6.4 release: AutoDoc, CRISP, EDIM, Float,
> >HAP, hecke, IRREDSOL, Modules, NumericalSgps and Smallsemi.
> >
> >We encourage all users to upgrade to GAP 4.6.5. If you need any
> >help or would like to report any problems, please do not hesitate
> >to contact us at support at gap-system.org.
> >
> >Please note that we regularly update the GAP distribution to include
> >new versions of GAP packages, but we may not announce each of them
> >to the Forum. We intend to use the Forum to announce updates of the
> >core GAP system and only of some packages which may fix serious
> >issues or have major influence on GAP.
> >
> >
> >Wishing you fun and success using GAP,
> >The GAP Group
> >
> >
> >_______________________________________________
> >Forum mailing list
> >Forum at mail.gap-system.org
> >http://mail.gap-system.org/mailman/listinfo/forum

-- 
Max Neunhoeffer              http://www-groups.mcs.st-and.ac.uk/~neunhoef/
> > > > > > > > > > >  May the Source be with you! < < < < < < < < < < < < 
The University of St Andrews is a registered Scottish charity: No SC013532



From jnsebastian at hotmail.com  Mon Jul 29 16:34:31 2013
From: jnsebastian at hotmail.com (cbazz ..U8)
Date: Mon, 29 Jul 2013 10:34:31 -0500
Subject: [GAP Forum]
 =?utf-8?q?ayuda_y_soporte_t=C3=A9cnico_-_Help_and_Sup?=
 =?utf-8?q?port?=
In-Reply-To: <BLU163-W53B32B8D65FED9ABC3223ABF550@phx.gbl>
References: <BLU163-W53B32B8D65FED9ABC3223ABF550@phx.gbl>
Message-ID: <BLU163-W2677CC9F02DAE27EB96BE2BF550@phx.gbl>





Primero quiero reconocer la importancia de GAP en la matem?tica su ayuda y su gran beneficio para estudiantes y docentes. Soy un estudiante de Licenciatura en Matem?ticas de la Universidad de Nari?o en Colombia. Mi intencion es mejorar mi proyecto de grado acerca de las bases de Gr?bner presentando algunos algoritmos con ayuda de este importante programa. Solicito ayuda acerca de la siguiente inquietud.   ?Es posible llamar a una funci?n hecha por mi en GAP desde otro ordenador? es decir ?Se puede registrar funciones y utilizarlas en la realizaci?n de otros algoritmos?Para un mejor interpretacion presento el siguiente ejemplo.En GAP existen muchas funciones de algoritmos algebraicos para utilizarlos por ejemplo calculo del cociente y residuo de dos polonomios por medio de la funci?n QuotientRemainder, de la misma manera yo necesito utilizar una funcion que yo realize para utilizarlo en la realizaci?n de otros algoritmos como la anterior funcion anterior. Espero su ayuda y por su colaboraci?n anticipo sinceros agradecimientos.
Muchas Gracias
Sebastian OviedoLicenciatura en Matem?ticasUniversidad de Nari?o - Colombia

First I want to acknowledge the importance of GAP in mathematics your help and your great benefit to students and teachers. I am a student of Bachelor of Mathematics from the University of Nari?o in Colombia. My intention is to improve my graduation project about Gr?bner bases presenting some algorithms using this important program. Request help on the following concern.Is it possible to call a function in GAP made ??by me from another computer? ie Is it possible to register functions and use them in the performance of other algorithms?For better interpretation present the following example.In GAP there are many functions of algebraic algorithms to use for example calculating the quotient and remainder of two polonomios through QuotientRemainder function, in the same way I need to use a function that I Realize for use in the performance of other algorithms as above previous function.I hope your help and advance collaboration sincere thanks.
many Thanks
Sebastian OviedoBachelor of MathematicsUniversity of Nari?o - Colombia 		 	   		   		 	   		  

From hebert.perez at gmail.com  Tue Jul 30 08:50:21 2013
From: hebert.perez at gmail.com (=?ISO-8859-1?B?SGViZXJ0IFDpcmV6LVJvc+lz?=)
Date: Tue, 30 Jul 2013 09:50:21 +0200
Subject: [GAP Forum]
	=?iso-8859-1?q?ayuda_y_soporte_t=E9cnico_-_Help_and_S?=
	=?iso-8859-1?q?upport?=
In-Reply-To: <BLU163-W2677CC9F02DAE27EB96BE2BF550@phx.gbl>
References: <BLU163-W53B32B8D65FED9ABC3223ABF550@phx.gbl>
	<BLU163-W2677CC9F02DAE27EB96BE2BF550@phx.gbl>
Message-ID: <CAOjorGMw51Tbbjnwc2HYWm2JYcnUj_mFOqt_-E8fkhRm6MxiOg@mail.gmail.com>

As far as I know, you cannot use a GAP function outside GAP, but let the
experts say the last word :-)


El 29 de julio de 2013 17:34, cbazz ..U8 <jnsebastian at hotmail.com> escribi?:

>
>
>
>
> Primero quiero reconocer la importancia de GAP en la matem?tica su ayuda y
> su gran beneficio para estudiantes y docentes. Soy un estudiante de
> Licenciatura en Matem?ticas de la Universidad de Nari?o en Colombia. Mi
> intencion es mejorar mi proyecto de grado acerca de las bases de Gr?bner
> presentando algunos algoritmos con ayuda de este importante programa.
> Solicito ayuda acerca de la siguiente inquietud.   ?Es posible llamar a una
> funci?n hecha por mi en GAP desde otro ordenador? es decir ?Se puede
> registrar funciones y utilizarlas en la realizaci?n de otros
> algoritmos?Para un mejor interpretacion presento el siguiente ejemplo.En
> GAP existen muchas funciones de algoritmos algebraicos para utilizarlos por
> ejemplo calculo del cociente y residuo de dos polonomios por medio de la
> funci?n QuotientRemainder, de la misma manera yo necesito utilizar una
> funcion que yo realize para utilizarlo en la realizaci?n de otros
> algoritmos como la anterior funcion anterior. Espero su ayuda y por su
> colaboraci?n anticipo sinceros agradecimientos.
> Muchas Gracias
> Sebastian OviedoLicenciatura en Matem?ticasUniversidad de Nari?o - Colombia
>
> First I want to acknowledge the importance of GAP in mathematics your help
> and your great benefit to students and teachers. I am a student of Bachelor
> of Mathematics from the University of Nari?o in Colombia. My intention is
> to improve my graduation project about Gr?bner bases presenting some
> algorithms using this important program. Request help on the following
> concern.Is it possible to call a function in GAP made by me from another
> computer? ie Is it possible to register functions and use them in the
> performance of other algorithms?For better interpretation present the
> following example.In GAP there are many functions of algebraic algorithms
> to use for example calculating the quotient and remainder of two polonomios
> through QuotientRemainder function, in the same way I need to use a
> function that I Realize for use in the performance of other algorithms as
> above previous function.I hope your help and advance collaboration sincere
> thanks.
> many Thanks
> Sebastian OviedoBachelor of MathematicsUniversity of Nari?o - Colombia
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From dima at ntu.edu.sg  Tue Jul 30 12:30:28 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Tue, 30 Jul 2013 12:30:28 +0100
Subject: [GAP Forum]
	=?utf-8?q?ayuda_y_soporte_t=C3=A9cnico_-_Help_and_Sup?=
	=?utf-8?q?port?=
In-Reply-To: <CAOjorGMw51Tbbjnwc2HYWm2JYcnUj_mFOqt_-E8fkhRm6MxiOg@mail.gmail.com>
References: <BLU163-W53B32B8D65FED9ABC3223ABF550@phx.gbl>
	<BLU163-W2677CC9F02DAE27EB96BE2BF550@phx.gbl>
	<CAOjorGMw51Tbbjnwc2HYWm2JYcnUj_mFOqt_-E8fkhRm6MxiOg@mail.gmail.com>
Message-ID: <CAAWYfq1ipbQmAyUX=cbDS2zXkguXYS=ACg7X+SDmWj+sDZRZqA@mail.gmail.com>

2013/7/30 Hebert P?rez-Ros?s <hebert.perez at gmail.com>:
> As far as I know, you cannot use a GAP function outside GAP, but let the
> experts say the last word :-)

with Sage's libGAP, you can call GAP functions (well, you might need to write
a bit of code to deal with particular functions).
This works not only within Sage, but also without Sage.

See
https://bitbucket.org/vbraun/libgap/overview
and test subdirectory in
https://bitbucket.org/vbraun/libgap/src
for an example of calling GAP from C.

HTH,
Dmitrii

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Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From alexk at mcs.st-andrews.ac.uk  Tue Jul 30 12:38:21 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Tue, 30 Jul 2013 12:38:21 +0100
Subject: [GAP Forum]
 =?iso-8859-1?q?ayuda_y_soporte_t=E9cnico_-_Help_and_S?=
 =?iso-8859-1?q?upport?=
In-Reply-To: <CAOjorGMw51Tbbjnwc2HYWm2JYcnUj_mFOqt_-E8fkhRm6MxiOg@mail.gmail.com>
References: <BLU163-W53B32B8D65FED9ABC3223ABF550@phx.gbl>
	<BLU163-W2677CC9F02DAE27EB96BE2BF550@phx.gbl>
	<CAOjorGMw51Tbbjnwc2HYWm2JYcnUj_mFOqt_-E8fkhRm6MxiOg@mail.gmail.com>
Message-ID: <84C98BD7-5532-4F09-B002-9B0C54DF1A57@mcs.st-andrews.ac.uk>

With GAP SCSCP package (http://www.cs.st-andrews.ac.uk/~alexk/scscp/)
GAP functions may be exported for remote procedure calls by any
SCSCP-compliant client which may be other computer algebra system
or another software - see http://www.symcomp.org/ for systems that
may connect and for APIs to develop own applications.

I am not sure if the original question was about this, though - could
it be about saving GAP function to a file to read it on another
computer? 

Best wishes,
Alexander



On 30 Jul 2013, at 08:50, Hebert P?rez-Ros?s <hebert.perez at gmail.com> wrote:

> As far as I know, you cannot use a GAP function outside GAP, but let the
> experts say the last word :-)
> 
> 
> El 29 de julio de 2013 17:34, cbazz ..U8 <jnsebastian at hotmail.com> escribi?:
> 
>> 
>> 
>> 
>> 
>> Primero quiero reconocer la importancia de GAP en la matem?tica su ayuda y
>> su gran beneficio para estudiantes y docentes. Soy un estudiante de
>> Licenciatura en Matem?ticas de la Universidad de Nari?o en Colombia. Mi
>> intencion es mejorar mi proyecto de grado acerca de las bases de Gr?bner
>> presentando algunos algoritmos con ayuda de este importante programa.
>> Solicito ayuda acerca de la siguiente inquietud.   ?Es posible llamar a una
>> funci?n hecha por mi en GAP desde otro ordenador? es decir ?Se puede
>> registrar funciones y utilizarlas en la realizaci?n de otros
>> algoritmos?Para un mejor interpretacion presento el siguiente ejemplo.En
>> GAP existen muchas funciones de algoritmos algebraicos para utilizarlos por
>> ejemplo calculo del cociente y residuo de dos polonomios por medio de la
>> funci?n QuotientRemainder, de la misma manera yo necesito utilizar una
>> funcion que yo realize para utilizarlo en la realizaci?n de otros
>> algoritmos como la anterior funcion anterior. Espero su ayuda y por su
>> colaboraci?n anticipo sinceros agradecimientos.
>> Muchas Gracias
>> Sebastian OviedoLicenciatura en Matem?ticasUniversidad de Nari?o - Colombia
>> 
>> First I want to acknowledge the importance of GAP in mathematics your help
>> and your great benefit to students and teachers. I am a student of Bachelor
>> of Mathematics from the University of Nari?o in Colombia. My intention is
>> to improve my graduation project about Gr?bner bases presenting some
>> algorithms using this important program. Request help on the following
>> concern.Is it possible to call a function in GAP made by me from another
>> computer? ie Is it possible to register functions and use them in the
>> performance of other algorithms?For better interpretation present the
>> following example.In GAP there are many functions of algebraic algorithms
>> to use for example calculating the quotient and remainder of two polonomios
>> through QuotientRemainder function, in the same way I need to use a
>> function that I Realize for use in the performance of other algorithms as
>> above previous function.I hope your help and advance collaboration sincere
>> thanks.
>> many Thanks
>> Sebastian OviedoBachelor of MathematicsUniversity of Nari?o - Colombia
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From m288.zarei at gmail.com  Wed Jul 31 15:38:19 2013
From: m288.zarei at gmail.com (Masomeh Zarei)
Date: Wed, 31 Jul 2013 19:08:19 +0430
Subject: [GAP Forum] centralizer of a group
Message-ID: <CAFMmbkJDt-=dnmMki8auqHh-dbHsz0J+FDaGuimpdcwHvihX1A@mail.gmail.com>

Dear All,

I am interested in computing the centralizer of a subgroup H of G=O(n, R)
in O(n, R) (the orthogonal group).  I would be thankful if you let me know
whether  I can do the computation while I have the orthogonal group over an
infinite field.

From mbg.nimda at gmail.com  Wed Jul 31 19:34:04 2013
From: mbg.nimda at gmail.com (Mbg Nimda)
Date: Wed, 31 Jul 2013 20:34:04 +0200
Subject: [GAP Forum] Van Kampen theoriem for the Klein bottle applied to fp
	groups
Message-ID: <CAAP6_ddjXfJ4E4c0hTN8tm-mNh6K2NAYzZ2Zmm-b-bj8dyk6XQ@mail.gmail.com>

Hello forum members,

I hope someone can point me out what is missing in the following:
I divide the Klein bottle into two Moebius strips that intersect on a
tubular
neighbourhood that is homotopically equivalent to S^1. The embedding of
this loop
is a^2 in one Moebius strip and b^2 in the other, where a and b are the
homotopy equivalent
loops of each Moebius strip respectively (the border of a Moebius strip
retracts to twice
the "middle circle" of the strip). So the Van Kampen theorem says that the
fundamental group
is the fp group with generators a and b and relator a^2*b^-2.
Now I looked up the funcamental group of the Klein bottle on Google and
found that the litterature declares the
fundamental group to have the relator a*b *a^-1*b (due to how opposite
sides on a square are identified) .
So initially I thought I was wrong but when frolicking around with these
two relators I found the following:
a*b *a^-1*b = 1 implies a*b*a^-2a*b. So if I put u:=a*b and v :=a then the
last equation becomes
u*v^-2*u = 1 or u^2*v^-2, so the two presentations are equivalent.
I found this relationship totally by good luck, but I wonder if there could
have been a way
using Gap to establish an isomorphism between those two groups?

Regards,

Marc Bogaerts

From hulpke at me.com  Thu Aug  1 09:37:46 2013
From: hulpke at me.com (Alexander Hulpke)
Date: Thu, 01 Aug 2013 09:37:46 +0100
Subject: [GAP Forum] centralizer of a group
In-Reply-To: <CAFMmbkJDt-=dnmMki8auqHh-dbHsz0J+FDaGuimpdcwHvihX1A@mail.gmail.com>
References: <CAFMmbkJDt-=dnmMki8auqHh-dbHsz0J+FDaGuimpdcwHvihX1A@mail.gmail.com>
Message-ID: <E6F4B480-5759-4C81-A8D1-E9B0C27BFAB8@me.com>

Dear Forum,

Masomeh Zarei <m288.zarei at gmail.com> wrote:

> I am interested in computing the centralizer of a subgroup H of G=O(n, R)
> in O(n, R) (the orthogonal group).  I would be thankful if you let me know
> whether  I can do the computation while I have the orthogonal group over an
> infinite field.

The facilities for matrix groups over infinite fields are currently rather limited; in particular there is basically nothing for infinite matrix groups. Thus I'm not aware of any tool that would let you do such a calculation, though with normal form theory you are likely to be able to write down concrete centralizers by hand.

Regards,

    Alexander Hulpke




From magfild at yahoo.com  Thu Aug  1 11:13:54 2013
From: magfild at yahoo.com (Magfild Bunyasi)
Date: Thu, 1 Aug 2013 03:13:54 -0700 (PDT)
Subject: [GAP Forum] Subdegrees
Message-ID: <1375352034.69972.YahooMailNeo@web122303.mail.ne1.yahoo.com>

Hi Forum,
I would like to determine ranks and subdegrees of PSL(2,q) acting on the cosets of its cyclic group of order (q-1)/k where k is gcd(2,q-1).
Somebody to bail me out of this please.
Thanks in advance.
Magero Fidelius

From A.Egri-Nagy at herts.ac.uk  Thu Aug  1 11:38:18 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Thu, 1 Aug 2013 20:38:18 +1000
Subject: [GAP Forum] GAP on ARM
Message-ID: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>

Dear Forum,

Just for fun... ;)

http://compsemi.wordpress.com/2013/08/01/gap-on-the-pi/

best,
@


From Bill.Allombert at math.u-bordeaux.fr  Thu Aug  1 13:15:22 2013
From: Bill.Allombert at math.u-bordeaux.fr (Bill Allombert)
Date: Thu, 1 Aug 2013 14:15:22 +0200
Subject: [GAP Forum] GAP on ARM
In-Reply-To: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
References: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
Message-ID: <20130801121521.GA28640@pari.math.u-bordeaux1.fr>

On Thu, Aug 01, 2013 at 08:38:18PM +1000, Attila Egri-Nagy wrote:
> Dear Forum,
> 
> Just for fun... ;)
> 
> http://compsemi.wordpress.com/2013/08/01/gap-on-the-pi/

Well, Debian provides GAP binaries for a dozen platforms, and I regularly test gap
on a PlayStation 3, a Raspberry Pi, an IBM s390 mainframe, etc.

Cheers,
Bill.


From a.j.t.al-juburie at newcastle.ac.uk  Thu Aug  1 20:10:11 2013
From: a.j.t.al-juburie at newcastle.ac.uk (Abdulsatar Al-Juburie)
Date: Thu, 1 Aug 2013 19:10:11 +0000
Subject: [GAP Forum] Help please
Message-ID: <5CA877F40086AF4BA25CA7791864174404B917@EXMBDB01.campus.ncl.ac.uk>

Dear All, 


I am struggling with the following error:


gap> B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);
Error, Variable: 'starcomp' must have an assigned value in
  R1 := starcomp( V, E ); called from
<function "AutGrpOfPCG">( <arguments> )
 called from read-eval loop at line 17 of *stdin*
you can 'return;' after assigning a value


**********
My script is:
*************

AutGrpOfPCG:=function(V,E)  # the main program

local R1,starcomp,St;  # Declaration list

Read("d:/runprogram/starcomp.txt"); # reading another function  (starcomp) written in a separate text file

R1:=starcomp(V,E);        # calling the starcomp function

St:=R1[1];
return[St];

end;


The input to the function is:

B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);



If I remove the "starcomp" from the local declaration list, the code is working but with the following warning message:
    
Syntax error: warning: unbound global variable
R1:=starcomp(V,E);        

Any idea and/or help are more than appreciated


Regards,


Abdulsatar






From A.Egri-Nagy at herts.ac.uk  Fri Aug  2 01:23:27 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Fri, 2 Aug 2013 10:23:27 +1000
Subject: [GAP Forum] GAP on ARM
In-Reply-To: <20130801121521.GA28640@pari.math.u-bordeaux1.fr>
References: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
	<20130801121521.GA28640@pari.math.u-bordeaux1.fr>
Message-ID: <CAP=h6j0sNV=3nrsm_UsR2bxmoTL9qjz+bJZAnc3ogKzweMfHVA@mail.gmail.com>

Dear Bill,

It is very good news about the testing on different platforms!

I am aware of the Debian packages, but unfortunately I need newer
versions of GAP. What is the reason for packaging the older version
for Debian?

Thanks!
@

On Thu, Aug 1, 2013 at 10:15 PM, Bill Allombert
<Bill.Allombert at math.u-bordeaux.fr> wrote:
> On Thu, Aug 01, 2013 at 08:38:18PM +1000, Attila Egri-Nagy wrote:
>> Dear Forum,
>>
>> Just for fun... ;)
>>
>> http://compsemi.wordpress.com/2013/08/01/gap-on-the-pi/
>
> Well, Debian provides GAP binaries for a dozen platforms, and I regularly test gap
> on a PlayStation 3, a Raspberry Pi, an IBM s390 mainframe, etc.
>
> Cheers,
> Bill.


From shahmaths_problem at hotmail.com  Fri Aug  2 02:48:55 2013
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Fri, 2 Aug 2013 06:48:55 +0500
Subject: [GAP Forum] Help please
In-Reply-To: <5CA877F40086AF4BA25CA7791864174404B917@EXMBDB01.campus.ncl.ac.uk>
References: <5CA877F40086AF4BA25CA7791864174404B917@EXMBDB01.campus.ncl.ac.uk>
Message-ID: <BLU169-W122AD0841F83193EFE7BE8B8A510@phx.gbl>

Dear  Abdulsatar,
Experts will give better answer but I think the problem is with the path of the file you are intended to read.
Keep the file in "bin"(Only for convenience) and then use the path in Read command. It should be something like
Read("/cygdrive/C/gap4r6/bin/starcomp");
Good luck,
Muhammad Shah

> From: a.j.t.al-juburie at newcastle.ac.uk
> To: forum at gap-system.org
> Date: Thu, 1 Aug 2013 19:10:11 +0000
> Subject: [GAP Forum] Help please
> 
> Dear All, 
> 
> 
> I am struggling with the following error:
> 
> 
> gap> B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);
> Error, Variable: 'starcomp' must have an assigned value in
>   R1 := starcomp( V, E ); called from
> <function "AutGrpOfPCG">( <arguments> )
>  called from read-eval loop at line 17 of *stdin*
> you can 'return;' after assigning a value
> 
> 
> **********
> My script is:
> *************
> 
> AutGrpOfPCG:=function(V,E)  # the main program
> 
> local R1,starcomp,St;  # Declaration list
> 
> Read("d:/runprogram/starcomp.txt"); # reading another function  (starcomp) written in a separate text file
> 
> R1:=starcomp(V,E);        # calling the starcomp function
> 
> St:=R1[1];
> return[St];
> 
> end;
> 
> 
> The input to the function is:
> 
> B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);
> 
> 
> 
> If I remove the "starcomp" from the local declaration list, the code is working but with the following warning message:
>     
> Syntax error: warning: unbound global variable
> R1:=starcomp(V,E);        
> 
> Any idea and/or help are more than appreciated
> 
> 
> Regards,
> 
> 
> Abdulsatar
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
 		 	   		  

From alexk at mcs.st-andrews.ac.uk  Fri Aug  2 10:43:19 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 2 Aug 2013 10:43:19 +0100
Subject: [GAP Forum] Help please
In-Reply-To: <5CA877F40086AF4BA25CA7791864174404B917@EXMBDB01.campus.ncl.ac.uk>
References: <5CA877F40086AF4BA25CA7791864174404B917@EXMBDB01.campus.ncl.ac.uk>
Message-ID: <8B8D1154-9947-48B0-B156-2AF91087CED1@mcs.st-andrews.ac.uk>

Dear Abdulsatar,

I suggest to do the following two changes:


1) move the line 

Read("d:/runprogram/starcomp.txt");

above defining the function AutGrpOfPCG in your script


2) remove 'starcomp' from 'local ...' in AutGrpOfPCG since
it is defined elsewhere.


Hope this will help,
Alexander


On 1 Aug 2013, at 20:10, Abdulsatar Al-Juburie <a.j.t.al-juburie at newcastle.ac.uk> wrote:

> Dear All, 
> 
> 
> I am struggling with the following error:
> 
> 
> gap> B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);
> Error, Variable: 'starcomp' must have an assigned value in
>  R1 := starcomp( V, E ); called from
> <function "AutGrpOfPCG">( <arguments> )
> called from read-eval loop at line 17 of *stdin*
> you can 'return;' after assigning a value
> 
> 
> **********
> My script is:
> *************
> 
> AutGrpOfPCG:=function(V,E)  # the main program
> 
> local R1,starcomp,St;  # Declaration list
> 
> Read("d:/runprogram/starcomp.txt"); # reading another function  (starcomp) written in a separate text file
> 
> R1:=starcomp(V,E);        # calling the starcomp function
> 
> St:=R1[1];
> return[St];
> 
> end;
> 
> 
> The input to the function is:
> 
> B:=AutGrpOfPCG([1,2,3,4,5],[[1,2],[1,3],[2,3],[4,5],[3,4]]);
> 
> 
> 
> If I remove the "starcomp" from the local declaration list, the code is working but with the following warning message:
> 
> Syntax error: warning: unbound global variable
> R1:=starcomp(V,E);        
> 
> Any idea and/or help are more than appreciated
> 
> 
> Regards,
> 
> 
> Abdulsatar
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From hulpke at me.com  Fri Aug  2 11:50:10 2013
From: hulpke at me.com (Alexander Hulpke)
Date: Fri, 02 Aug 2013 11:50:10 +0100
Subject: [GAP Forum] Van Kampen theoriem for the Klein bottle applied to
 fp groups
In-Reply-To: <CAAP6_ddjXfJ4E4c0hTN8tm-mNh6K2NAYzZ2Zmm-b-bj8dyk6XQ@mail.gmail.com>
References: <CAAP6_ddjXfJ4E4c0hTN8tm-mNh6K2NAYzZ2Zmm-b-bj8dyk6XQ@mail.gmail.com>
Message-ID: <9EA6FEEF-F294-4E4A-8190-22FB0A723A32@me.com>

Dear Forum,

Marc Bogaerts asked:

> So initially I thought I was wrong but when frolicking around with these
> two relators I found the following:
> a*b *a^-1*b = 1 implies a*b*a^-2a*b. So if I put u:=a*b and v :=a then the
> last equation becomes
> u*v^-2*u = 1 or u^2*v^-2, so the two presentations are equivalent.
> I found this relationship totally by good luck, but I wonder if there could
> have been a way
> using Gap to establish an isomorphism between those two groups?

Beyond the trivial (using guided Tietze transformations where you supply the rewriting) there is no method in GAP that would automatically find such an isomorphism. 

The paper 
Holt, D.F.; Rees, Sarah
Testing for isomorphism between finitely presented groups. (English)
Liebeck, Martin (ed.) et al., Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, held July 5-15, 1990 in Durham, UK. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 165, 459-475 (1992).

describes such an algorithm which has been implemented in a system `QUOTPIC', but it is not available in GAP. I am not sure about current availability of an implementation.

Best,

  Alexander Hulpke



From dima at ntu.edu.sg  Fri Aug  2 12:45:16 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Fri, 2 Aug 2013 12:45:16 +0100
Subject: [GAP Forum] GAP on ARM
In-Reply-To: <CAP=h6j0sNV=3nrsm_UsR2bxmoTL9qjz+bJZAnc3ogKzweMfHVA@mail.gmail.com>
References: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
	<20130801121521.GA28640@pari.math.u-bordeaux1.fr>
	<CAP=h6j0sNV=3nrsm_UsR2bxmoTL9qjz+bJZAnc3ogKzweMfHVA@mail.gmail.com>
Message-ID: <CAAWYfq3PdTmo9NTt4576QH80Ejst-RTf0dSX0oxpk6wbrynTmw@mail.gmail.com>

On 2 August 2013 01:23, Attila Egri-Nagy <A.Egri-Nagy at herts.ac.uk> wrote:
> Dear Bill,
>
> It is very good news about the testing on different platforms!
>
> I am aware of the Debian packages, but unfortunately I need newer
> versions of GAP. What is the reason for packaging the older version
> for Debian?

Debian is known to be slow in updating things. Perhaps Bill can make
an unofficial .deb repo
with up to date GAP packages available.

Just in case,
Dima

>
> Thanks!
> @
>
> On Thu, Aug 1, 2013 at 10:15 PM, Bill Allombert
> <Bill.Allombert at math.u-bordeaux.fr> wrote:
>> On Thu, Aug 01, 2013 at 08:38:18PM +1000, Attila Egri-Nagy wrote:
>>> Dear Forum,
>>>
>>> Just for fun... ;)
>>>
>>> http://compsemi.wordpress.com/2013/08/01/gap-on-the-pi/
>>
>> Well, Debian provides GAP binaries for a dozen platforms, and I regularly test gap
>> on a PlayStation 3, a Raspberry Pi, an IBM s390 mainframe, etc.
>>
>> Cheers,
>> Bill.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From Bill.Allombert at math.u-bordeaux1.fr  Fri Aug  2 13:10:10 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Fri, 2 Aug 2013 14:10:10 +0200
Subject: [GAP Forum] GAP on ARM
In-Reply-To: <CAP=h6j0sNV=3nrsm_UsR2bxmoTL9qjz+bJZAnc3ogKzweMfHVA@mail.gmail.com>
References: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
	<20130801121521.GA28640@pari.math.u-bordeaux1.fr>
	<CAP=h6j0sNV=3nrsm_UsR2bxmoTL9qjz+bJZAnc3ogKzweMfHVA@mail.gmail.com>
Message-ID: <20130802121010.GA9462@yellowpig>

On Fri, Aug 02, 2013 at 10:23:27AM +1000, Attila Egri-Nagy wrote:
> Dear Bill,
> 
> It is very good news about the testing on different platforms!
> 
> I am aware of the Debian packages, but unfortunately I need newer
> versions of GAP. What is the reason for packaging the older version
> for Debian?

Indeed, I am working on upgrading the packages to gap 4r6p5.
Unfortunately GAP 4r5 was released one week after the Debian freeze
for wheezy. 

Cheers,
Bill.


From alexk at mcs.st-andrews.ac.uk  Sun Aug  4 21:54:05 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Sun, 4 Aug 2013 21:54:05 +0100
Subject: [GAP Forum] GAP on ARM
In-Reply-To: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
References: <CAP=h6j0Gp7UYaKWepsC2sgRG38MNpdPQSjZF1SbzKccQg9gDTw@mail.gmail.com>
Message-ID: <49D06878-7F96-464D-ABB6-CCE0B1795BCC@mcs.st-andrews.ac.uk>

Thanks for the link, Attila, - interesting to know that!
Now, if you could compile the IO package, you may use SCSCP
package <http://www.cs.st-andrews.ac.uk/~alexk/scscp/> to 
sent remote procedure calls from Raspberry Pi to GAP SCSCP 
servers, for example, when you want to get the result faster 
than you are able to compute it locally.

Best wishes,
Alexander


On 1 Aug 2013, at 11:38, Attila Egri-Nagy <A.Egri-Nagy at herts.ac.uk> wrote:

> Dear Forum,
> 
> Just for fun... ;)
> 
> http://compsemi.wordpress.com/2013/08/01/gap-on-the-pi/
> 
> best,
> @
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From benjamin.sambale at gmail.com  Wed Aug  7 12:30:26 2013
From: benjamin.sambale at gmail.com (Benjamin)
Date: Wed, 07 Aug 2013 13:30:26 +0200
Subject: [GAP Forum] minimal members with respect to inclusion
Message-ID: <52022FD2.50901@gmail.com>

Dear GAP users,

suppose we have a list M of lists of integers. Is there a command which 
computes the set of minimal members of M with respect to inclusion? Of 
course I could implement such a function, but it would certainly not be 
very fast.

Thanks,
Benjamin


From alexk at mcs.st-andrews.ac.uk  Thu Aug  8 20:44:11 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 8 Aug 2013 20:44:11 +0100
Subject: [GAP Forum] minimal members with respect to inclusion
In-Reply-To: <52022FD2.50901@gmail.com>
References: <52022FD2.50901@gmail.com>
Message-ID: <F5F635AF-9341-47B9-BAAE-7AFC9234DAF4@mcs.st-andrews.ac.uk>

Dear Benjamin,

Could you please tell more details about elements of M? Are they 
lists of integers, or are they actually sets of integers (sorted,
dense, no duplicates)? Are they immutable? What are the sizes of
data sets with which you're operating? 

Thanks,
Alexander


On 7 Aug 2013, at 12:30, Benjamin <benjamin.sambale at gmail.com> wrote:

> Dear GAP users,
> 
> suppose we have a list M of lists of integers. Is there a command which computes the set of minimal members of M with respect to inclusion? Of course I could implement such a function, but it would certainly not be very fast.
> 
> Thanks,
> Benjamin
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From ahulpke at gmail.com  Thu Aug  8 23:18:36 2013
From: ahulpke at gmail.com (Alexander Hulpke)
Date: Thu, 8 Aug 2013 23:18:36 +0100
Subject: [GAP Forum] What does  <[ [ 1, 1 ] ]|b*a^-1> mean
In-Reply-To: <loom.20130701T172956-709@post.gmane.org>
References: <loom.20130630T221902-674@post.gmane.org>
	<C0DE070F-5BF7-4013-892B-4CFB42CC5C85@gmail.com>
	<loom.20130701T172956-709@post.gmane.org>
Message-ID: <B21D7873-9C0E-4DAA-B9E4-763E7A5ABB5C@gmail.com>

Since someone pointed out to me that my initial reply to this only was prvately, while the question was sent to the forum:

b*a was a misprint, I meant of course b*a^-1. Alexander




From benjamin.sambale at gmail.com  Fri Aug  9 09:12:20 2013
From: benjamin.sambale at gmail.com (Benjamin Sambale)
Date: Fri, 09 Aug 2013 10:12:20 +0200
Subject: [GAP Forum] minimal members with respect to inclusion
In-Reply-To: <F5F635AF-9341-47B9-BAAE-7AFC9234DAF4@mcs.st-andrews.ac.uk>
References: <52022FD2.50901@gmail.com>
	<F5F635AF-9341-47B9-BAAE-7AFC9234DAF4@mcs.st-andrews.ac.uk>
Message-ID: <5204A464.7050904@gmail.com>

Dear Alexander,

yes, M is a list of sets. Imagine for example a "large" subset of 
Combinations([1..30]). Moreover, M and its elements are mutable.

Meanwhile, I circumvented the problem. However, I guess it would be nice 
to have such a function nevertheless.

Best wishes,
Benjamin

Am 08.08.2013 21:44, schrieb Alexander Konovalov:
> Dear Benjamin,
>
> Could you please tell more details about elements of M? Are they
> lists of integers, or are they actually sets of integers (sorted,
> dense, no duplicates)? Are they immutable? What are the sizes of
> data sets with which you're operating?
>
> Thanks,
> Alexander
>
>
> On 7 Aug 2013, at 12:30, Benjamin <benjamin.sambale at gmail.com> wrote:
>
>> Dear GAP users,
>>
>> suppose we have a list M of lists of integers. Is there a command which computes the set of minimal members of M with respect to inclusion? Of course I could implement such a function, but it would certainly not be very fast.
>>
>> Thanks,
>> Benjamin
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>



From bernhard.boehmler at googlemail.com  Sat Aug 10 16:18:45 2013
From: bernhard.boehmler at googlemail.com (Bernhard Boehmler)
Date: Sat, 10 Aug 2013 17:18:45 +0200
Subject: [GAP Forum] Computing with projective A-modules of a finite
	dimensional k-algebra A
Message-ID: <CAD1scQZNGJX+tcnVj36TEDEPO2h9o0+=q_jDz44x47yRR88R3A@mail.gmail.com>

Dear GAP Forum,

I have the following problem(s):

I made some computations in GAP and I now have an "algebra-with-one" R as a
subalgebra of a full matrix algebra.

Moreover, I have five orthogonal primitive idempotents e_1,...,e_5, which
sum up to the identity element of R.

Now, I would like to let GAP calculate some things concerning the
projective right R-modules P_1 and P_2,..., where P_1 = e_1 * R (and
P_2=e_2 * R and so on).

I would like to test, whether P_i and P_j are isomorphic as R-modules for i
unequal to j. I also would like to compute the algebras e_i R e_j for all i
and j.

I can access the generators (as matrices) of the algebra R and I know
e_1,...,e_5 =... (as matrices).


Unfortunately, I wasn't able to find out, how to define P_1 in GAP as a row
module (I would like GAP to look at P_1 as an R-module (R as an algebra) -
is trying to insert P_1 as a row module the right way of procedure?).  I
also would like to compute the radical of P_1 and factor it out.

I, therefore, would we very thankful, if anybody could give me a hint,
given only the "algebra with one" R as a GAP object, how to implement P_1,
P_2, P_1/rad(P_1) and P_2/rad(P_2), the regular module R_R, and so on, as
modules and do calculations with them.

Thank you very much.

Yours sincerely,

Bernhard Boehmler

From stefano.simonucci at tin.it  Sat Aug 10 17:05:59 2013
From: stefano.simonucci at tin.it (Stefano Simonucci)
Date: Sat, 10 Aug 2013 18:05:59 +0200
Subject: [GAP Forum] Casimir operator of a Lie algebra
Message-ID: <520664E7.1010105@tin.it>

Dear GAP Forum,
    I have the following problem, i.e. to find the Casimir's operators 
of the Lie ALgebra SO(n) and SU(n).
But I realized that it isn't possible to find the center of an
Universal Enveloping Algebra with GAP.
For example:

gap> L:= SimpleLieAlgebra( "A", 1, Rationals );
<Lie algebra of dimension 3 over Rationals>
gap> UL:= UniversalEnvelopingAlgebra( L );
<algebra-with-one of dimension infinity over Rationals>
gap> Center(UL);
Error, this case will eventually be handled by the Vector Enumerator
which is not available yet called from
OperationAlgebraHomomorphism( A, [ [ Zero( A ) ] ], OnRight ) called from
IsomorphismMatrixFLMLOR( A ) called from
IsFiniteDimensional( A ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

Do you know another method.
Thanks

Stefano


From rrburns at cox.net  Mon Aug 12 23:09:10 2013
From: rrburns at cox.net (Sopsku)
Date: Mon, 12 Aug 2013 22:09:10 +0000 (UTC)
Subject: [GAP Forum] extrat the numical values in a permutation
Message-ID: <loom.20130813T000301-186@post.gmane.org>

Hi,

Given a permutation, say p:=(1,3)(5,8,6) how can I extract the numerical
values to say perhaps a list like [[1,3],[5,8,6]] or otherwise access them?

Thanks for any help,
    Sopsku 



From hatlam at gmail.com  Tue Aug 13 08:59:38 2013
From: hatlam at gmail.com (Ha T. Lam)
Date: Tue, 13 Aug 2013 03:59:38 -0400
Subject: [GAP Forum] Reading group elements from CSV file
Message-ID: <CAFxJ0MzCYeqWCz8q5kwjoyqPLKytMFgeij9r2KrPFkQ7m=UZKw@mail.gmail.com>

Dear GAP forum,

I saved the output of some computation as a csv file consisting of group
elements, like so:

a,b,c
g2,g1^2,g1^-1*g2*g3^-2

Now I want to read these elements back and use them as group elements for
the group g:=DihedralGroup(8). I used ReadCSV(filename). First I realized
that group elements need to be referred to as g.1, g.2, etc. An easy search
and replace with my text editor took care of that, so now my csv file looks
like:

a,b,c
g.2,g.1^2,g.1^-1*g.2*g.3^-2

But what I get back is actually a list of records consisting of strings,
not actually group elements. How do I evaluate these strings so that GAP
knows that I'm referring to the group elements instead?

Thank you for your help.

Ha T. Lam

From dima at ntu.edu.sg  Tue Aug 13 14:10:53 2013
From: dima at ntu.edu.sg (Dmitrii (Dima) Pasechnik)
Date: Tue, 13 Aug 2013 14:10:53 +0100
Subject: [GAP Forum] Reading group elements from CSV file
In-Reply-To: <CAFxJ0MzCYeqWCz8q5kwjoyqPLKytMFgeij9r2KrPFkQ7m=UZKw@mail.gmail.com>
References: <CAFxJ0MzCYeqWCz8q5kwjoyqPLKytMFgeij9r2KrPFkQ7m=UZKw@mail.gmail.com>
Message-ID: <CAAWYfq0FgN9hbKsrusEaT=ZZzuUcimxtixm46t-fR1nkQU=ekw@mail.gmail.com>

On 13 August 2013 08:59, Ha T. Lam <hatlam at gmail.com> wrote:
> Dear GAP forum,
>
> I saved the output of some computation as a csv file consisting of group
> elements, like so:
>
> a,b,c
> g2,g1^2,g1^-1*g2*g3^-2
>
> Now I want to read these elements back and use them as group elements for
> the group g:=DihedralGroup(8). I used ReadCSV(filename). First I realized
> that group elements need to be referred to as g.1, g.2, etc. An easy search
> and replace with my text editor took care of that, so now my csv file looks
> like:
>
> a,b,c
> g.2,g.1^2,g.1^-1*g.2*g.3^-2
>
> But what I get back is actually a list of records consisting of strings,
> not actually group elements. How do I evaluate these strings so that GAP
> knows that I'm referring to the group elements instead?

There is the EvalString function that lets you evaluate GAP expressions which
are built up as strings.

Hope this helps,
Dmitrii

>
> Thank you for your help.
>
> Ha T. Lam
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From a.j.t.al-juburie at newcastle.ac.uk  Mon Aug 12 20:50:12 2013
From: a.j.t.al-juburie at newcastle.ac.uk (Abdulsatar Al-Juburie)
Date: Mon, 12 Aug 2013 19:50:12 +0000
Subject: [GAP Forum] Help please
Message-ID: <5CA877F40086AF4BA25CA7791864174404BA9F@EXMBDB01.campus.ncl.ac.uk>

Dear All,


In the following small code when  I try to print  Y , I found that  Y  is changed , but I did change just on Y1.  Is there any way to print  Y 

Without any change.



f:=function(L)
local i,j,Y,Y1;

Y:=L;
Y1:=L;

Y1[1][1]:=90;
Y1[2][1]:=90;

Print(" ","\n");
Print("\ Y =",Y);
Print(" ","\n");

Print("\ Y1=",Y1);
Print(" ","\n");
end;

The input to the function is:

f([ [ 0, 21, 31, 41 ], [ 1, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 0 ] ]);


Result of print is:

 Y =[ [ 90, 21, 31, 41 ], [ 90, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 0 ] ]

 Y1=[ [ 90, 21, 31, 41 ], [ 90, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 0 ] ]


Any idea and/or help are more than appreciated


Regards,


Abdulsatar



From robert.bailey at ryerson.ca  Wed Aug 14 15:51:42 2013
From: robert.bailey at ryerson.ca (Robert Bailey)
Date: Wed, 14 Aug 2013 10:51:42 -0400
Subject: [GAP Forum] Help please
In-Reply-To: <5CA877F40086AF4BA25CA7791864174404BA9F@EXMBDB01.campus.ncl.ac.uk>
References: <5CA877F40086AF4BA25CA7791864174404BA9F@EXMBDB01.campus.ncl.ac.uk>
Message-ID: <5378C72B5ADC4C48BB6A64216FCDDBB4@RFBCompaq2>

Dear Abdulsatar,

When you assign Y and Y1 to be equal to L, GAP will (internally) treat all 
three as the same object.  Thus when you change Y1, it will also change L 
and Y in the same way.

To create duplicates of L, you need the "StructuralCopy" command:

Y:=StructuralCopy(L);
Y1:=StructuralCopy(L);

which will create Y and Y1 as separate objects identical to L.

Regards,
Robert Bailey.

-----Original Message----- 
From: Abdulsatar Al-Juburie
Sent: Monday, August 12, 2013 3:50 PM
To: 'forum at mail.gap-system.org'
Subject: [GAP Forum] Help please

Dear All,


In the following small code when  I try to print  Y , I found that  Y  is 
changed , but I did change just on Y1.  Is there any way to print  Y

Without any change.



f:=function(L)
local i,j,Y,Y1;

Y:=L;
Y1:=L;

Y1[1][1]:=90;
Y1[2][1]:=90;

Print(" ","\n");
Print("\ Y =",Y);
Print(" ","\n");

Print("\ Y1=",Y1);
Print(" ","\n");
end;

The input to the function is:

f([ [ 0, 21, 31, 41 ], [ 1, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 0 ] ]);


Result of print is:

Y =[ [ 90, 21, 31, 41 ], [ 90, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 
0 ] ]

Y1=[ [ 90, 21, 31, 41 ], [ 90, 0, 21, 31 ], [ 0, 0, 0, 21 ], [ 0, 0, 0, 
0 ] ]


Any idea and/or help are more than appreciated


Regards,


Abdulsatar


_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum 



From shahmaths_problem at hotmail.com  Tue Aug 20 12:24:54 2013
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Tue, 20 Aug 2013 16:24:54 +0500
Subject: [GAP Forum] [group-pub-forum] 3-net
In-Reply-To: <1376983828.95920.YahooMailNeo@web121802.mail.ne1.yahoo.com>
References: <1376983828.95920.YahooMailNeo@web121802.mail.ne1.yahoo.com>
Message-ID: <BLU169-W91C82E6393AA0FB0C0DC228A430@phx.gbl>

Dear Arun,
Excellent GAP codes for 3-web written by Dr. Petr are available at
http://web.cs.du.edu/~petr/gap_routines.html
(3-Webs and basic operations on 3-Webs)
and for a nice visualization of 3-web see the paper of 
H. I. Erdorgan (A QUASI-GROUP ASSOCIATED WITH THE WEB
FORMED BY THREE PENCILS OF CIRCLES WHICH
BELONG TO THE SAME BIJNDLE).
Regards,
Muhammad Shah

Date: Tue, 20 Aug 2013 00:30:28 -0700
From: amukti2000 at yahoo.com
To: group-pub-forum at lists.maths.bath.ac.uk
Subject: [group-pub-forum] 3-net

Dear Pubbers,                       I am not able to visualize a 3-net of order 3. Taking three mutually disjoint sets of non-intersecting  lines , every line should pass through 3 points and every point should lie on exactly one line of each class. Can anybody give an example with a diagram ? Thanking you in advance.ArunIndia Dr. Arun Muktibodh 		 	   		  

From mmarco at unizar.es  Tue Aug 20 12:50:04 2013
From: mmarco at unizar.es (Miguel Angel Marco Buzunariz)
Date: Tue, 20 Aug 2013 13:50:04 +0200
Subject: [GAP Forum] [group-pub-forum] 3-net
In-Reply-To: <BLU169-W91C82E6393AA0FB0C0DC228A430@phx.gbl>
References: <1376983828.95920.YahooMailNeo@web121802.mail.ne1.yahoo.com>
	<BLU169-W91C82E6393AA0FB0C0DC228A430@phx.gbl>
Message-ID: <22953149.XcgpkV5n5j@neumann>

With that definition, a 3-net is the same as a latin square. The rows are the 
lines of one pencil. The columns are the lines of the second pencil. And the 
set of all the entries with the same number are the lines of the thirthd 
pencil.
The points would be the entries of the square.

Also, you can construct them geometrically over an affine plane... but not over 
the reals. It can be done over finite fields.


El Martes, 20 de agosto de 2013 16:24:54 muhammad shah escribi?:
> Dear Arun,
> Excellent GAP codes for 3-web written by Dr. Petr are available at
> http://web.cs.du.edu/~petr/gap_routines.html
> (3-Webs and basic operations on 3-Webs)
> and for a nice visualization of 3-web see the paper of 
> H. I. Erdorgan (A QUASI-GROUP ASSOCIATED WITH THE WEB
> FORMED BY THREE PENCILS OF CIRCLES WHICH
> BELONG TO THE SAME BIJNDLE).
> Regards,
> Muhammad Shah
> 
> Date: Tue, 20 Aug 2013 00:30:28 -0700
> From: amukti2000 at yahoo.com
> To: group-pub-forum at lists.maths.bath.ac.uk
> Subject: [group-pub-forum] 3-net
> 
> Dear Pubbers,                       I am not able to visualize a 3-net of 
order 3. Taking three mutually disjoint sets of non-intersecting  lines , 
every line should pass through 3 points and every point should lie on exactly 
one line of each class. Can anybody give an example with a diagram ? Thanking 
you in advance.ArunIndia Dr. Arun Muktibodh 		 	   		  
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From rrburns at cox.net  Mon Aug 26 03:54:23 2013
From: rrburns at cox.net (Sopsku)
Date: Mon, 26 Aug 2013 02:54:23 +0000 (UTC)
Subject: [GAP Forum] Reduced Multiplication
Message-ID: <loom.20130826T043803-928@post.gmane.org>

Hi all,
I have some small confusion about reduced multiplication that I would like
to clear up. Suppose I have:

gap> d4:=DihedralGroup(IsFpGroup,4);;
gap> r:=d4.1;;s:=d4.2;;
gap> SetReducedMultiplication(d4);

Then 

gap> r^2;
<identity ...>

OK - now suppose I look at 

gap> rel:=RelatorsOfFpGroup(d4);
[ r^2, s^2, s^-1*r*s*r ]

rel does not reduce and I guess that makes sense as I would want to see the
the relations not <identitly ...>. Now if I cut and paste

gap> [ r^2, s^2, s^-1*r*s*r ];
[ <identity ...>, <identity ...>, <identity ...> ]

Is there an function that I can apply to rel to force the reduced
multiplication without the cut and paste? 

I tried copies and tests like

gap> rel[1]=Identity(d4);
false

but even  this does not do the reduction before the test.

Thanks for any comments
     Ron





From sl4 at st-andrews.ac.uk  Mon Aug 26 09:33:03 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Mon, 26 Aug 2013 09:33:03 +0100
Subject: [GAP Forum] Reduced Multiplication
In-Reply-To: <loom.20130826T043803-928@post.gmane.org>
References: <loom.20130826T043803-928@post.gmane.org>
Message-ID: <44E7A18E-E733-4BC6-A20E-63FFB768AE34@st-andrews.ac.uk>

Dear Sopsku,

What you need to be aware of here is that the relators of a finitely-presented group are NOT 
elements of the group. They are elements of the underlying free group. So after your commands below we see

gap> rel[1] in d4;
false
gap> rel[1] in FreeGroupOfFpGroup(d4);
true

One way of connecting them is to make the natural quotient homomorphism:

gap> phi := GroupHomomorphismByImages(f,d4,GeneratorsOfGroup(f),GeneratorsOfGroup(d4));
[ r, s ] -> [ r, s ]
gap> List(rel, x->Image(phi,x));
[ <identity ...>, <identity ...>, <identity ...> ]
gap> 

This is a bit confusing here because the generators of the free group print as "r" and "s" as 
do the generators of the finitely-presented group, but th global variables r and s hold the generators of the fp group.

	Steve

On 26 Aug 2013, at 03:54, Sopsku <rrburns at cox.net> wrote:

> Hi all,
> I have some small confusion about reduced multiplication that I would like
> to clear up. Suppose I have:
> 
> gap> d4:=DihedralGroup(IsFpGroup,4);;
> gap> r:=d4.1;;s:=d4.2;;
> gap> SetReducedMultiplication(d4);
> 
> Then 
> 
> gap> r^2;
> <identity ...>
> 
> OK - now suppose I look at 
> 
> gap> rel:=RelatorsOfFpGroup(d4);
> [ r^2, s^2, s^-1*r*s*r ]
> 
> rel does not reduce and I guess that makes sense as I would want to see the
> the relations not <identitly ...>. Now if I cut and paste
> 
> gap> [ r^2, s^2, s^-1*r*s*r ];
> [ <identity ...>, <identity ...>, <identity ...> ]
> 
> Is there an function that I can apply to rel to force the reduced
> multiplication without the cut and paste? 
> 
> I tried copies and tests like
> 
> gap> rel[1]=Identity(d4);
> false
> 
> but even  this does not do the reduction before the test.
> 
> Thanks for any comments
>     Ron
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From pjc at mcs.st-and.ac.uk  Tue Aug 27 11:06:58 2013
From: pjc at mcs.st-and.ac.uk (pjc at mcs.st-and.ac.uk)
Date: Tue, 27 Aug 2013 11:06:58 +0100 (BST)
Subject: [GAP Forum] Numbering of primitive groups
Message-ID: <submission.1VEGAs-0004qT-NY@mail-gap.mcs.st-and.ac.uk>

Dear Forum,

Akos Seress, in Bull. London Math. Soc. 29 (1997), 697-704, listed all the
(finitely many) primitive groups which have no regular orbit on the power
set of their domain. He listed them by GAP number and ATLAS name.

Sad to say, the GAP numbering seems to have changed since then. For
example, Akos thought PrimitiveGroup(16,19) is 2^4.A_7, whereas GAP now
thinks this group is 2^4.A_5.

I have two questions:
1. Does anyone have a list correlating the old and new numbers? I think
that, from the ATLAS names, I can recover what he meant, but it would be
nice to have a check.

2. Is there any way that we can draw the group-theory community's
attention to this, perhaps with an updated list?

Peter.



From ahulpke at gmail.com  Tue Aug 27 16:12:38 2013
From: ahulpke at gmail.com (Alexander Hulpke)
Date: Tue, 27 Aug 2013 09:12:38 -0600
Subject: [GAP Forum] Numbering of primitive groups
In-Reply-To: <submission.1VEGAs-0004qT-NY@mail-gap.mcs.st-and.ac.uk>
References: <submission.1VEGAs-0004qT-NY@mail-gap.mcs.st-and.ac.uk>
Message-ID: <BF7361BE-0331-4004-B9FC-EE9378024D44@gmail.com>



Dear Peter, Dear Forum,

> Akos Seress, in Bull. London Math. Soc. 29 (1997), 697-704, listed all the
> (finitely many) primitive groups which have no regular orbit on the power
> set of their domain. He listed them by GAP number and ATLAS name.
> 
> Sad to say, the GAP numbering seems to have changed since then. For
> example, Akos thought PrimitiveGroup(16,19) is 2^4.A_7, whereas GAP now
> thinks this group is 2^4.A_5.
> 
> I have two questions:
> 1. Does anyone have a list correlating the old and new numbers? I think
> that, from the ATLAS names, I can recover what he meant, but it would be
> nice to have a check.

From the publication date and the citation in the paper I presume that Akos' list was done using GAP3. I append a renumbering of the groups that gives for degrees up to 50 the *new* number for each group. (I believe the reason for renumbering had to do with storing primitive groups in cohorts according to the ONan-Scott Theorem, but I might be remembering wrongly.)
For example in this list, entry 16,19 is 20, i.e. the group formerly numbered 16,19 is nor 16,20.

The reverse permutation is available in GAP via the function SimsNo, that when applied to a primitive group return the old index. E.g.:

gap> SimsNo(PrimitiveGroup(16,20));
19

as expected.

Best,

  Alexander


>  
> 2. Is there any way that we can draw the group-theory community's
> attention to this, perhaps with an updated list?
> 
> Peter.
> 

[ [  ], [ 1 ], [ 1, 2 ], [ 1, 2 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4 ], 
  [ 1, 2, 3, 4, 5, 6, 7 ], [ 1, 2, 4, 5, 3, 6, 7 ], 
  [ 1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 11 ], [ 1, 2, 3, 5, 4, 6, 7, 8, 9 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8 ], [ 3, 4, 1, 2, 5, 6 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ], [ 1, 2, 3, 4 ], [ 2, 3, 1, 4, 5, 6 ], 
  [ 1, 2, 3, 4, 5, 6, 8, 7, 19, 9, 15, 10, 18, 13, 14, 12, 17, 16, 20, 11, 
      21, 22 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], [ 1, 2, 3, 4 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ], 
  [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5, 6, 7 ], [ 2, 3, 1, 4, 5 ], 
  [ 1, 3, 2, 5, 6, 4, 9, 8, 7, 10, 11, 13, 15, 14, 12, 16, 18, 17, 19, 20, 
      21, 23, 22, 24, 25, 26, 27, 28 ], [ 1, 3, 2, 4, 5, 6, 7 ], 
  [ 1, 2, 3, 5, 4, 6, 7, 8, 9, 12, 13, 10, 11, 14, 15 ], 
  [ 1, 2, 3, 4, 9, 5, 10, 7, 11, 8, 12, 6, 13, 14 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ], [ 1, 2, 4, 5, 3, 6, 7 ], 
  [ 1, 2, 3, 4 ], [ 1, 2 ], [ 3, 4, 1, 2, 5, 6 ], 
  [ 1, 4, 3, 5, 2, 6, 17, 7, 19, 18, 8, 20, 9, 11, 13, 12, 15, 14, 16, 10, 
      21, 22 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ], [ 1, 2, 3, 4 ], 
  [ 1, 2 ], [ 1, 3, 2, 4, 5, 6, 7, 8 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], 
  [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ], [ 1, 2, 3, 4 ], 
  [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ], [ 1, 2 ], [ 1, 2, 3, 4, 5, 6 ], 
  [ 1, 2, 3, 4 ], 
  [ 1, 2, 5, 4, 3, 6, 8, 7, 11, 10, 9, 12, 15, 16, 18, 17, 13, 14, 19, 20, 
      21, 25, 22, 23, 24, 27, 26, 28, 29, 30, 31, 32, 34, 33, 35, 36, 37, 38, 
      39, 40 ], [ 3, 6, 4, 5, 1, 7, 2, 8, 9 ] ]



From fvanhove at cage.UGent.be  Thu Aug 29 12:47:45 2013
From: fvanhove at cage.UGent.be (Frederic Vanhove)
Date: Thu, 29 Aug 2013 13:47:45 +0200
Subject: [GAP Forum] Orbits under conjugation by elements of centralizer
Message-ID: <521F34E1.4020801@cage.UGent.be>

Dear members of the forum,

I am considering a group G and a subset S. If H denotes the centralizer 
of S in G, how can I consider the action on S under conjugation by 
elements of H?

For instance, how could I obtain the corresponding partition of S into 
orbits?

The command ConjugacyClasses considers the action of the full group on 
itself.

Many thanks,
Kind regards,
Fr?d?ric


From fvanhove at cage.UGent.be  Thu Aug 29 12:47:45 2013
From: fvanhove at cage.UGent.be (Frederic Vanhove)
Date: Thu, 29 Aug 2013 13:47:45 +0200
Subject: [GAP Forum] Orbits under conjugation by elements of centralizer
Message-ID: <521F34E1.4020801@cage.UGent.be>

Dear members of the forum,

I am considering a group G and a subset S. If H denotes the centralizer 
of S in G, how can I consider the action on S under conjugation by 
elements of H?

For instance, how could I obtain the corresponding partition of S into 
orbits?

The command ConjugacyClasses considers the action of the full group on 
itself.

Many thanks,
Kind regards,
Fr?d?ric


From shahmaths_problem at hotmail.com  Tue Aug 20 12:12:26 2013
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Tue, 20 Aug 2013 16:12:26 +0500
Subject: [GAP Forum] [group-pub-forum] 3-net
In-Reply-To: <1376983828.95920.YahooMailNeo@web121802.mail.ne1.yahoo.com>
References: <1376983828.95920.YahooMailNeo@web121802.mail.ne1.yahoo.com>
Message-ID: <BLU169-W107666745D0213958B994668A430@phx.gbl>

Dear Arun,
Excellent GAP codes for 3-web written by Dr. Petr are available at
http://web.cs.du.edu/~petr/gap_routines.html
(3-Webs and basic operations on 3-Webs)
and for a beautiful visualization of 3-web see the attached paper of 
H. I. Erdorgan 
Regards,
Muhammad Shah

Date: Tue, 20 Aug 2013 00:30:28 -0700
From: amukti2000 at yahoo.com
To: group-pub-forum at lists.maths.bath.ac.uk
Subject: [group-pub-forum] 3-net

Dear Pubbers,                       I am not able to visualize a 3-net of order 3. Taking three mutually disjoint sets of non-intersecting  lines , every line should pass through 3 points and every point should lie on exactly one line of each class. Can anybody give an example with a diagram ? Thanking you in advance.ArunIndia Dr. Arun Muktibodh 		 	   		  

From john.bamberg at uwa.edu.au  Thu Aug 29 13:47:15 2013
From: john.bamberg at uwa.edu.au (John Bamberg)
Date: Thu, 29 Aug 2013 20:47:15 +0800
Subject: [GAP Forum] Orbits under conjugation by elements of centralizer
In-Reply-To: <521F34E1.4020801@cage.UGent.be>
References: <521F34E1.4020801@cage.UGent.be>
Message-ID: <1F172630-FA78-42D9-98B8-D35AE94457B7@uwa.edu.au>

Hi Fr?d?ric,

Could you clarify your question? Wouldn't H fix every element of S by conjugation? (Do you mean "normaliser"?)

Cheers,

John.


On 29/08/2013, at 7:47 PM, Frederic Vanhove <fvanhove at cage.UGent.be> wrote:

> Dear members of the forum,
> 
> I am considering a group G and a subset S. If H denotes the centralizer 
> of S in G, how can I consider the action on S under conjugation by 
> elements of H?
> 
> For instance, how could I obtain the corresponding partition of S into 
> orbits?
> 
> The command ConjugacyClasses considers the action of the full group on 
> itself.
> 
> Many thanks,
> Kind regards,
> Fr?d?ric
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From jaredwarner4 at gmail.com  Fri Sep  6 01:32:24 2013
From: jaredwarner4 at gmail.com (Jared Warner)
Date: Thu, 5 Sep 2013 17:32:24 -0700
Subject: [GAP Forum] Elementary abelian p-subgroups
Message-ID: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>

Dear GAP forum,

I'm interested in studying the Quillen Complex of a finite group G, which
is the lattice of elementary abelian p-subgroups of G.  Magma has a command
ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
do this with GAP (to avoid paying for Magma).

Specifically, given a finite group G I'd like to know:

1. The number of conjugacy classes of elementary abelian p-subgroups of a
certain rank

2. The number of subgroups in each such conjugacy class

3. A set of generators of a representative from each such conjugacy class

I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
list of representatives of elementary abelian p-subgroups, not all
subgroups.

Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
because it seems like a lot of wasted time and memory to compute the whole
subgroup lattice when I'm only interested in a small portion of it.

Thanks for any help!

Jared

From graham.ellis at nuigalway.ie  Fri Sep  6 10:24:08 2013
From: graham.ellis at nuigalway.ie (Ellis, Grahamj)
Date: Fri, 6 Sep 2013 09:24:08 +0000
Subject: [GAP Forum] Elementary abelian p-subgroups
In-Reply-To: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
References: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
Message-ID: <AAAC480E1E08BE469300074BB59C638CAA9D62AA@UDSMBX02.uds.nuigalway.ie>

Dear GAP forum,

I too would like to know how best to access the elementary abelian p-subgroups of a finite group G. Attached is an implementation of the Quillen Complex which uses ConjugacyClassesSubgroups. As Jared mentions, this is a very inefficient approach.

------------------------------------------------------------------------
gap> G:=SmallGroup(64,134);;
gap> Q:=QuillenComplex(G,2);
Simplicial complex of dimension 2.

gap> Homology(Q,0);
[ 0 ]
gap> Homology(Q,1);
[  ]
gap> Homology(Q,2);
[  ]
gap> Q!.nrSimplices(2); #The number of 2-simplices
168
gap> Q!.simplices(2,168); #The last 2-simplex
[ Group([ f6, f2, f3*f4*f5 ]), Group([ f2, f3*f4*f5*f6 ]), 
  Group([ f2*f3*f4*f5*f6 ]) ]
------------------------------------------------------------------------


Graham

School of Mathematics, Statistics & Applied Mathematics
National University of Ireland, Galway
University Road,
Galway
Ireland

http://hamilton.nuigalway.ie
tel: 091 493011
________________________________________
From: forum-bounces at gap-system.org [forum-bounces at gap-system.org] on behalf of Jared Warner [jaredwarner4 at gmail.com]
Sent: Friday, September 06, 2013 1:32 AM
To: forum at gap-system.org
Subject: [GAP Forum] Elementary abelian p-subgroups

Dear GAP forum,

I'm interested in studying the Quillen Complex of a finite group G, which
is the lattice of elementary abelian p-subgroups of G.  Magma has a command
ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
do this with GAP (to avoid paying for Magma).

Specifically, given a finite group G I'd like to know:

1. The number of conjugacy classes of elementary abelian p-subgroups of a
certain rank

2. The number of subgroups in each such conjugacy class

3. A set of generators of a representative from each such conjugacy class

I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
list of representatives of elementary abelian p-subgroups, not all
subgroups.

Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
because it seems like a lot of wasted time and memory to compute the whole
subgroup lattice when I'm only interested in a small portion of it.

Thanks for any help!

Jared
_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum

From mathieu.dutour at gmail.com  Fri Sep  6 13:04:45 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Fri, 6 Sep 2013 14:04:45 +0200
Subject: [GAP Forum] Elementary abelian p-subgroups
In-Reply-To: <AAAC480E1E08BE469300074BB59C638CAA9D62AA@UDSMBX02.uds.nuigalway.ie>
References: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
	<AAAC480E1E08BE469300074BB59C638CAA9D62AA@UDSMBX02.uds.nuigalway.ie>
Message-ID: <CADm_teNyXLYwVwPPXb5kCsXZJtANPhfE_qSEkt+F7Z04edS+Og@mail.gmail.com>

Well, I think that this can be programmed easily:
1> we simply need to consider one Sylow p-group.

2> the ConjugacyClassesSubgroups is an iterative algorithm
starting from a small group and expanding it. Maybe we can
adapt by starting with conjugacy classes in G of order p
and adding commuting elements.

The real challenge, I would say is whether or not the full
list of elementary p-subgroup is stored in memory. If yes,
then memory will be limiting. If not, then the difficulty will be
in programming with only the knowledge of the conjugacy
classes.

  Mathieu


On Fri, Sep 6, 2013 at 11:24 AM, Ellis, Grahamj
<graham.ellis at nuigalway.ie>wrote:

> Dear GAP forum,
>
> I too would like to know how best to access the elementary abelian
> p-subgroups of a finite group G. Attached is an implementation of the
> Quillen Complex which uses ConjugacyClassesSubgroups. As Jared mentions,
> this is a very inefficient approach.
>
> ------------------------------------------------------------------------
> gap> G:=SmallGroup(64,134);;
> gap> Q:=QuillenComplex(G,2);
> Simplicial complex of dimension 2.
>
> gap> Homology(Q,0);
> [ 0 ]
> gap> Homology(Q,1);
> [  ]
> gap> Homology(Q,2);
> [  ]
> gap> Q!.nrSimplices(2); #The number of 2-simplices
> 168
> gap> Q!.simplices(2,168); #The last 2-simplex
> [ Group([ f6, f2, f3*f4*f5 ]), Group([ f2, f3*f4*f5*f6 ]),
>   Group([ f2*f3*f4*f5*f6 ]) ]
> ------------------------------------------------------------------------
>
>
> Graham
>
> School of Mathematics, Statistics & Applied Mathematics
> National University of Ireland, Galway
> University Road,
> Galway
> Ireland
>
> http://hamilton.nuigalway.ie
> tel: 091 493011
> ________________________________________
> From: forum-bounces at gap-system.org [forum-bounces at gap-system.org] on
> behalf of Jared Warner [jaredwarner4 at gmail.com]
> Sent: Friday, September 06, 2013 1:32 AM
> To: forum at gap-system.org
> Subject: [GAP Forum] Elementary abelian p-subgroups
>
> Dear GAP forum,
>
> I'm interested in studying the Quillen Complex of a finite group G, which
> is the lattice of elementary abelian p-subgroups of G.  Magma has a command
> ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
> do this with GAP (to avoid paying for Magma).
>
> Specifically, given a finite group G I'd like to know:
>
> 1. The number of conjugacy classes of elementary abelian p-subgroups of a
> certain rank
>
> 2. The number of subgroups in each such conjugacy class
>
> 3. A set of generators of a representative from each such conjugacy class
>
> I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
> list of representatives of elementary abelian p-subgroups, not all
> subgroups.
>
> Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
> because it seems like a lot of wasted time and memory to compute the whole
> subgroup lattice when I'm only interested in a small portion of it.
>
> Thanks for any help!
>
> Jared
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
>

From sl4 at st-andrews.ac.uk  Fri Sep  6 13:07:50 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Fri, 6 Sep 2013 13:07:50 +0100
Subject: [GAP Forum] Elementary abelian p-subgroups
In-Reply-To: <AAAC480E1E08BE469300074BB59C638CAA9D62AA@UDSMBX02.uds.nuigalway.ie>
References: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
	<AAAC480E1E08BE469300074BB59C638CAA9D62AA@UDSMBX02.uds.nuigalway.ie>
Message-ID: <D58B9BDC-7767-48BE-B5DE-1625650E42CE@st-andrews.ac.uk>

I believe that

ConjugacyClassesSubgroups(LatticeByCyclicExtension(g, IsElementaryAbelian, true));

Does what you want.

	Steve

On 6 Sep 2013, at 10:24, "Ellis, Grahamj" <graham.ellis at nuigalway.ie> wrote:

> Dear GAP forum,
> 
> I too would like to know how best to access the elementary abelian p-subgroups of a finite group G. Attached is an implementation of the Quillen Complex which uses ConjugacyClassesSubgroups. As Jared mentions, this is a very inefficient approach.
> 
> ------------------------------------------------------------------------
> gap> G:=SmallGroup(64,134);;
> gap> Q:=QuillenComplex(G,2);
> Simplicial complex of dimension 2.
> 
> gap> Homology(Q,0);
> [ 0 ]
> gap> Homology(Q,1);
> [  ]
> gap> Homology(Q,2);
> [  ]
> gap> Q!.nrSimplices(2); #The number of 2-simplices
> 168
> gap> Q!.simplices(2,168); #The last 2-simplex
> [ Group([ f6, f2, f3*f4*f5 ]), Group([ f2, f3*f4*f5*f6 ]), 
>  Group([ f2*f3*f4*f5*f6 ]) ]
> ------------------------------------------------------------------------
> 
> 
> Graham
> 
> School of Mathematics, Statistics & Applied Mathematics
> National University of Ireland, Galway
> University Road,
> Galway
> Ireland
> 
> http://hamilton.nuigalway.ie
> tel: 091 493011
> ________________________________________
> From: forum-bounces at gap-system.org [forum-bounces at gap-system.org] on behalf of Jared Warner [jaredwarner4 at gmail.com]
> Sent: Friday, September 06, 2013 1:32 AM
> To: forum at gap-system.org
> Subject: [GAP Forum] Elementary abelian p-subgroups
> 
> Dear GAP forum,
> 
> I'm interested in studying the Quillen Complex of a finite group G, which
> is the lattice of elementary abelian p-subgroups of G.  Magma has a command
> ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
> do this with GAP (to avoid paying for Magma).
> 
> Specifically, given a finite group G I'd like to know:
> 
> 1. The number of conjugacy classes of elementary abelian p-subgroups of a
> certain rank
> 
> 2. The number of subgroups in each such conjugacy class
> 
> 3. A set of generators of a representative from each such conjugacy class
> 
> I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
> list of representatives of elementary abelian p-subgroups, not all
> subgroups.
> 
> Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
> because it seems like a lot of wasted time and memory to compute the whole
> subgroup lattice when I'm only interested in a small portion of it.
> 
> Thanks for any help!
> 
> Jared
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From hulpke at math.colostate.edu  Fri Sep  6 20:08:49 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri, 6 Sep 2013 13:08:49 -0600
Subject: [GAP Forum] Elementary abelian p-subgroups
In-Reply-To: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
References: <CAMRhBQ7CherKkz1M3Vs_8CjyGa1s5WtDtkWzs0QB0pn0Ym6bPQ@mail.gmail.com>
Message-ID: <166CCC5F-9889-448A-B99E-3F1036412D0A@math.colostate.edu>



Dear Forum, Dear Jared Warner,

[From a private email I happen to know that the groups are typically certain classical groups].

> I'm interested in studying the Quillen Complex of a finite group G, which
> is the lattice of elementary abelian p-subgroups of G.  Magma has a command
> ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
> do this with GAP (to avoid paying for Magma).

There are a couple of remarks here. Yes, GAP does not have this specific function, but [I have no access to the Magma Source code to check] I suspect that the magma code simply does the same calculation as a full lattice, just discarding subgroups in the process if they can never lead to elementary abelian subgroups.

GAP has some hooks for this kind of discarding, however the interface is somewhat awkward, in part since it is difficult to decide which kinds of subgroups would turn out to be the popular ones to be used.
Furthermore (as we do provide the full source code) it would be possible to simply copy the appropriate function and to insert test that will do the same kind of discarding. However doing so likely will require at least some basic knowledge of the algorithms involved.

To get some further reduction it seems to be worth to me (assuming there are comparatively few such subgroups -- I'm sure anyone sufficiently malicious could construct examples in which this strategy turns out bad) to work [As Mathieu suggested] in Sylow subgroups first and fuse the found elementary abelian subgroups first under the normalizer (as this is cheaper) and then under conjugation by the whole group. Then the groups in question are solvable and the underlying algorithm for subgroups of a solvable group allows for a hook for discarding.
(This algorithm is different than the cyclic extension which Steve mentioned explicitly, and Mathieu mentioned implicitly, in that it descends, not ascends. My reason for doing so is that I fear that an ascending building process will get choked in subgroup conjugacy tests in the case of larger elementary abelian normal subgroups.)

Also at the moment it is beneficial in GAP to work in an isomorphic permutation group instead of a matrix group.

I have coded this strategy rather naively in GAP in the following function (taking the group and a prime, and returning a list of conjugacy classes of elementary abelian subgroups). Clearly there are many places for optimization, but maybe it is of help. (Also you are likely to run this only finitely many times, depending on how finite this might be good enough for the job at hand.) I also would be curious to hear of examples you wanted to run this on in which it still performs substandard.

Best,

  Alexander Hulpke

#filter function
NonelabUnconsider:=function(c,a,n,b,m)
  return HasElementaryAbelianFactorGroup(a,n) and
    # a may not act on b (as n does not act, otherwise the group obtained
    # will not be abelian)
    (ForAll(GeneratorsOfGroup(a),x->ForAll(GeneratorsOfGroup(b),y->IsOne(Comm(x,y))))
    or IsAbelian(n));
end;

Elabsub:=function(G,p)
local n,s,u,c,i,hom,pc;
  if IsMatrixGroup(G) then
    hom:=IsomorphismPermGroup(G);
    G:=Image(hom,G);
  else
    hom:=fail;
  fi;
  s:=SylowSubgroup(G,p);
  s:=Omega(s,p,1); # elements of order p
  n:=Normalizer(G,s);
  if not IsSolvableGroup(n) then
    # TODO: Better larger solvable subgroup
    pc:=NaturalHomomorphismByNormalSubgroupNC(n,s);
    n:=PreImage(pc,RadicalGroup(Image(pc)));
  fi;
  pc:=IsomorphismSpecialPcGroup(n);
  s:=Image(pc,s);
  u:=SubgroupsSolvableGroup(Image(pc),rec(groups:=[s],
                                          consider:=NonelabUnconsider));
  u:=Filtered(u,x->IsElementaryAbelian(x) and IsSubset(s,x));
  u:=List(u,x->PreImage(pc,x));
  Info(InfoLattice,1,Length(u)," subgroup classes in normalizer, fuse!");
  u:=SubgroupsOrbitsAndNormalizers(G,u,false);
  c:=[];
  for i in u do
    s:=ConjugacyClassSubgroups(G,i.representative);
    SetStabilizerOfExternalSet(s,i.normalizer);
    Add(c,s);
  od;
  if hom<>fail then
    u:=[];
    for i in c do
      s:=ConjugacyClassSubgroups(Source(hom),PreImage(hom,Representative(i)));
      # transfer normalizer data
      SetStabilizerOfExternalSet(s,PreImage(hom,StabilizerOfExternalSet(i)));
      SetSize(s,Size(i));
      Add(u,s);
    od;
    c:=u;
  fi;
  return c;
end;








From neginyavari67 at yahoo.com  Sun Sep  8 13:23:42 2013
From: neginyavari67 at yahoo.com (Negin Yavari)
Date: Sun, 8 Sep 2013 13:23:42 +0100 (BST)
Subject: [GAP Forum] How to load Cohomolo package
Message-ID: <1378643022.26708.YahooMailNeo@web171902.mail.ir2.yahoo.com>

Dear? GAP Forum,


I would like to work with package Cohomolo. But when I type 


LoadPackage("Cohomolo");

the answer in GAP is "fail".

I would appreciate if you help me to load this package.


Bests,
Tina


PS. I am elementary in Linux and actually I do not know how I can load packages in this system.

From D.F.Holt at warwick.ac.uk  Mon Sep  9 09:07:13 2013
From: D.F.Holt at warwick.ac.uk (Holt, Derek)
Date: Mon, 9 Sep 2013 08:07:13 +0000
Subject: [GAP Forum] How to load Cohomolo package
In-Reply-To: <1378643022.26708.YahooMailNeo@web171902.mail.ir2.yahoo.com>
References: <1378643022.26708.YahooMailNeo@web171902.mail.ir2.yahoo.com>
Message-ID: <f861e6ced33248eaa7fa6105650f219d@AMSPR01MB036.eurprd01.prod.exchangelabs.com>

Dear Tina, GAP Forum,

As explained in the README file, before you can load the Cohomolo package from within GAP, (assuming you are using linux or cygwin), you have to open a terminal and go into the pkg/cohomolo GAP directory, and then type first

/bin/sh  ./configure path

and then

make

If that all works OK, then you can start GAP, and

LoadPackage("Cohomolo");

should return true.

Good luck!
Derek Holt.

_______________________________________
From: forum-bounces at gap-system.org <forum-bounces at gap-system.org> on behalf of Negin Yavari <neginyavari67 at yahoo.com>
Sent: 08 September 2013 13:23
To: forum at gap-system.org
Subject: [GAP Forum] How to load Cohomolo package

Dear  GAP Forum,


I would like to work with package Cohomolo. But when I type


LoadPackage("Cohomolo");

the answer in GAP is "fail".

I would appreciate if you help me to load this package.


Bests,
Tina


PS. I am elementary in Linux and actually I do not know how I can load packages in this system.
_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum




From lvluyen at gmail.com  Wed Sep 11 16:21:45 2013
From: lvluyen at gmail.com (Le Van Luyen)
Date: Wed, 11 Sep 2013 16:21:45 +0100
Subject: [GAP Forum] Create a list of functions in GAP
Message-ID: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>

Dear all,

I want to create a list of functions in GAP and I have used the following
code lines:

gap> F:=[];
gap> for i in [1..5] do
>       F[i]:=function( n)
>               return n+i;
>       end;
>       od;

I expect the result will be: F[1](1)=2; F[2](1)=3; F[3](1)=4

But, In GAP

gap>F[1](1);
6
gap>F[2](1);
6
gap>F[3](1);
6

 It looks like all functions of list A are the same.

Could you give me a way to create a list of functions like that?

Thank you very much.

Bests,

Luyen

From rm43 at evansville.edu  Wed Sep 11 17:34:58 2013
From: rm43 at evansville.edu (Robert Morse)
Date: Wed, 11 Sep 2013 11:34:58 -0500
Subject: [GAP Forum] Create a list of functions in GAP
In-Reply-To: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
References: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
Message-ID: <CAMeXfYzZ=U6OwxxnJhZD3yLeptc9ZdGvuyTUWgo=EZ7UZZ+7DQ@mail.gmail.com>

The value of the variable i is not bound at function definition.
Rather, whatever i 's value at function execution is what is used.

After the loop the variable i has the value 5.  Hence calling each
instance F[i] returns the same value.

You can accomplish what you want by writing a function that creates
the function (binding the value i):

factory := function(i) return function(n) return n+i; end; end;

gap> F:=[];
gap> for i in [1..5] do
>       F[i]:=factory(i);
>       od;

Then

gap>F[1](1);
2
gap>F[2](1);
3
gap>F[3](1);
4

Gives what you want.

Robert F. Morse

On Wed, Sep 11, 2013 at 10:21 AM, Le Van Luyen <lvluyen at gmail.com> wrote:
> Dear all,
>
> I want to create a list of functions in GAP and I have used the following
> code lines:
>
> gap> F:=[];
> gap> for i in [1..5] do
>>       F[i]:=function( n)
>>               return n+i;
>>       end;
>>       od;
>
> I expect the result will be: F[1](1)=2; F[2](1)=3; F[3](1)=4
>
> But, In GAP
>
> gap>F[1](1);
> 6
> gap>F[2](1);
> 6
> gap>F[3](1);
> 6
>
>  It looks like all functions of list A are the same.
>
> Could you give me a way to create a list of functions like that?
>
> Thank you very much.
>
> Bests,
>
> Luyen
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From bensums at gmail.com  Wed Sep 11 20:51:15 2013
From: bensums at gmail.com (Ben Summers)
Date: Wed, 11 Sep 2013 20:51:15 +0100
Subject: [GAP Forum] Create a list of functions in GAP
In-Reply-To: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
References: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
Message-ID: <CAAUhpDHJCKMu8BP7XU2MVk2==yDKTU03zis0H6FZA0GZ=2FJig@mail.gmail.com>

F := List([1..5], i -> (n -> n + i));


On 11 September 2013 16:21, Le Van Luyen <lvluyen at gmail.com> wrote:

> Dear all,
>
> I want to create a list of functions in GAP and I have used the following
> code lines:
>
> gap> F:=[];
> gap> for i in [1..5] do
> >       F[i]:=function( n)
> >               return n+i;
> >       end;
> >       od;
>
> I expect the result will be: F[1](1)=2; F[2](1)=3; F[3](1)=4
>
> But, In GAP
>
> gap>F[1](1);
> 6
> gap>F[2](1);
> 6
> gap>F[3](1);
> 6
>
>  It looks like all functions of list A are the same.
>
> Could you give me a way to create a list of functions like that?
>
> Thank you very much.
>
> Bests,
>
> Luyen
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From Bill.Allombert at math.u-bordeaux1.fr  Wed Sep 11 21:10:56 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Wed, 11 Sep 2013 22:10:56 +0200
Subject: [GAP Forum] Create a list of functions in GAP
In-Reply-To: <CAMeXfYzZ=U6OwxxnJhZD3yLeptc9ZdGvuyTUWgo=EZ7UZZ+7DQ@mail.gmail.com>
References: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
	<CAMeXfYzZ=U6OwxxnJhZD3yLeptc9ZdGvuyTUWgo=EZ7UZZ+7DQ@mail.gmail.com>
Message-ID: <20130911201056.GE11112@yellowpig>

On Wed, Sep 11, 2013 at 11:34:58AM -0500, Robert Morse wrote:
> The value of the variable i is not bound at function definition.
> Rather, whatever i 's value at function execution is what is used.

Please excuse my curiosity as someone who wrote some computer algebra system
interpretor.
Are you saying that i is a global variable which is dynamicaly scoped ?

> After the loop the variable i has the value 5.  Hence calling each
> instance F[i] returns the same value.
> 
> You can accomplish what you want by writing a function that creates
> the function (binding the value i):
> 
> factory := function(i) return function(n) return n+i; end; end;

and there i is function parameter which is lexicaly scoped,
and functions are closed over lexicaly scoped variable ?

Cheers,
Bill.


From rm43 at evansville.edu  Wed Sep 11 22:35:51 2013
From: rm43 at evansville.edu (Robert Morse)
Date: Wed, 11 Sep 2013 16:35:51 -0500
Subject: [GAP Forum] Create a list of functions in GAP
In-Reply-To: <20130911201056.GE11112@yellowpig>
References: <CAMMpxrSXNReoVVD3cH9f5VaOe2OJazSRgcZ0OWT5y60wZEBuxw@mail.gmail.com>
	<CAMeXfYzZ=U6OwxxnJhZD3yLeptc9ZdGvuyTUWgo=EZ7UZZ+7DQ@mail.gmail.com>
	<20130911201056.GE11112@yellowpig>
Message-ID: <CAMeXfYyv5UdT7WeA4oWmBNMayg1kUq1K37DmENbd=o0t5M6yGg@mail.gmail.com>

All free variables in a GAP function have a static binding within its
lexicographical closure.  In the original program the same i is a free
variable in each function and the lexicographical closure is global
name space. Hence any modification of i changes all the function
definitions.

factory := function(i) local f; f := function(n) return n+i; end;
i:=5; return f; end;

The lexicographical closure of the variable i is the factory function
definition.  Since i is free in f and the last assignment is within
the lexicographical closure of i we have changed the function
definition.

f1 := factory(1);  f2:=factory(2);

f1(1)  ---> returns 6
f2(1)  ---> returns 6

In the example I gave before and

F := List([1..5], i -> (n -> n + i));

we lose access to the lexicographic scope of i and the values are
fixed as desired.


Robert F. Morse



On Wed, Sep 11, 2013 at 3:10 PM, Bill Allombert
<Bill.Allombert at math.u-bordeaux1.fr> wrote:
> On Wed, Sep 11, 2013 at 11:34:58AM -0500, Robert Morse wrote:
>> The value of the variable i is not bound at function definition.
>> Rather, whatever i 's value at function execution is what is used.
>
> Please excuse my curiosity as someone who wrote some computer algebra system
> interpretor.
> Are you saying that i is a global variable which is dynamicaly scoped ?
>
>> After the loop the variable i has the value 5.  Hence calling each
>> instance F[i] returns the same value.
>>
>> You can accomplish what you want by writing a function that creates
>> the function (binding the value i):
>>
>> factory := function(i) return function(n) return n+i; end; end;
>
> and there i is function parameter which is lexicaly scoped,
> and functions are closed over lexicaly scoped variable ?
>
> Cheers,
> Bill.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From Gallagher.Fergal at itsligo.ie  Thu Sep 12 11:58:16 2013
From: Gallagher.Fergal at itsligo.ie (Fergal Gallagher)
Date: Thu, 12 Sep 2013 11:58:16 +0100
Subject: [GAP Forum] units of group algebras
Message-ID: <283998A06653F84BA510A6DBD1E4B2E5576481565C@coolboy.campus.itsligo.ie>

Hi guys,

I want to check the structure of the unit groups of certain finite group algebras.

I am new to GAP and have tried the manual but it is very complicated even for the most basic task. ie. find the unit group of F2^2C2xC4 for example.

Any help?

Fergal Gallagher


From alexk at mcs.st-andrews.ac.uk  Thu Sep 12 12:07:38 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 12 Sep 2013 12:07:38 +0100
Subject: [GAP Forum] units of group algebras
In-Reply-To: <283998A06653F84BA510A6DBD1E4B2E5576481565C@coolboy.campus.itsligo.ie>
References: <283998A06653F84BA510A6DBD1E4B2E5576481565C@coolboy.campus.itsligo.ie>
Message-ID: <FA6FEF19-12ED-4165-9A54-3AF76625FDBB@mcs.st-andrews.ac.uk>

Dear Fergal,

if you have a p-group and a field of p elements, then
NormalizedUnitGroup and PcNormalizedUnitGroup from the 
LAGUNA package will help:

gap> KG := GroupRing( GF( 2 ), DihedralGroup( 16 ) );
<algebra-with-one over GF(2), with 4 generators>
gap> V := NormalizedUnitGroup( KG );
<group of size 32768 with 15 generators>
gap> u := GeneratorsOfGroup( V )[4];
(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2  
gap> W := PcNormalizedUnitGroup( KG );
<pc group of size 32768 with 15 generators>
gap> w := GeneratorsOfGroup( W )[4];
f4

For other cases I'm afraid that straightforward calculations
will allow to deal only with small examples.

Best wishes,
Alexander
  

On 12 Sep 2013, at 11:58, Fergal Gallagher <Gallagher.Fergal at itsligo.ie> wrote:

> Hi guys,
> 
> I want to check the structure of the unit groups of certain finite group algebras.
> 
> I am new to GAP and have tried the manual but it is very complicated even for the most basic task. ie. find the unit group of F2^2C2xC4 for example.
> 
> Any help?
> 
> Fergal Gallagher
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From saqaas12 at gmail.com  Mon Sep 16 11:06:36 2013
From: saqaas12 at gmail.com (Aasma Shaheen)
Date: Mon, 16 Sep 2013 10:06:36 -0000
Subject: [GAP Forum] Fwd:
Message-ID: <5236d826.e969b40a.0d1c.ffffcbe5@mx.google.com>

http://www.uasgadvisors.com/u1zw9c.php



From yassine_guer at hotmail.fr  Thu Sep 19 20:05:27 2013
From: yassine_guer at hotmail.fr (yassine Guerboussa)
Date: Thu, 19 Sep 2013 20:05:27 +0100
Subject: [GAP Forum] Non-left n-Engel elements in a group
Message-ID: <DUB113-W101BD4E4F10090FC771F6699A210@phx.gbl>

Dear GAP Forum,
I will be pleased if one can help in writing a program such that,
For a group $G$ (usually, a small group in GAP library), it computes the subgroup generatedby the elements that are not left n-Engel, for some fixed n.
Recall that an element $a$ in $G$ is left n-Engel if it satisfies the identity$[x,a,...,a]=1$, where $a$ occurs $n$ times (the commutator is left normed).
Thanks in advance.Best,Yassine Guerboussa 		 	   		  

From williamdemeo at gmail.com  Thu Sep 19 20:45:13 2013
From: williamdemeo at gmail.com (William DeMeo)
Date: Thu, 19 Sep 2013 15:45:13 -0400
Subject: [GAP Forum] Workshop on Computational Universal Algebra
Message-ID: <CAHO_k7SsQhUAn4Lsfcr+nyCOgFJc8fyn0EG1d8JsODK3zC7TgQ@mail.gmail.com>

Dear Forum,

I realize it is short notice, but perhaps some people on the GAP forum
might be interested in the workshop described below.

I apologize to anyone who is receiving this notice more than once.

Sincerely,
William



Dear Colleagues,


We are pleased to invite you to a

    Workshop on Computational Universal Algebra.

This one day workshop will be held on Friday, October 4 (the day
before the AMS Southeastern Sectional Meeting), at the University of
Louisville, from 9:30am to 6pm.


Featured Speakers

Ralph Freese (University of Hawaii) -- Using the UACalc.
Alexander Hulpke (Colorado State University) -- Finding Subgroups.
Peter Jipsen (Chapman University) -- Finite ordered algebraic structures.
Matthew Valeriote (McMaster University) -- Testing for certain
idempotent Maltsev conditions.


The aim of the workshop is to give researchers and graduate students
an opportunity to spend some time with and learn from experts in
computing for algebra research.

The schedule of talks and other details can be found at the workshop
website, but here is the essential information for your reference:

Title: Workshop on Computational Universal Algebra
Date: Friday, October 4, 2013 (9:30am--6pm)
Location: Natural Sciences Bldg, Rm 212D, University of Louisville,
Louisville, KY
Website: http://universalalgebra.org


Thank you for your interest.  We hope to see you in October!


Sincerely,

The Organizers


--
  William DeMeo
  Department of Mathematics
  University of South Carolina
  1523 Greene Street
  Columbia, SC 29208
  http://williamdemeo.org
--

--
  Ralph Freese
  Department of Mathematics
  University of Hawaii
  2565 McCarthy Mall
  Honolulu, HI 96822
  http://math.hawaii.edu/~ralph
--


From stefan at mcs.st-and.ac.uk  Thu Sep 19 21:14:45 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Thu, 19 Sep 2013 21:14:45 +0100 (BST)
Subject: [GAP Forum] Non-left n-Engel elements in a group
In-Reply-To: <DUB113-W101BD4E4F10090FC771F6699A210@phx.gbl>
References: <DUB113-W101BD4E4F10090FC771F6699A210@phx.gbl>
Message-ID: <submission.1VMkcf-0002wO-4m@mail-gap.mcs.st-and.ac.uk>

On Thu, September 19, 2013 8:05 pm, yassine Guerboussa wrote:
> I will be pleased if one can help in writing a program such that,
> For a group $G$ (usually, a small group in GAP library), it computes the subgroup
> generatedby the elements that are not left n-Engel, for some fixed n.
> Recall that an element $a$ in $G$ is left n-Engel if it satisfies the
> identity$[x,a,...,a]=1$, where $a$ occurs $n$ times (the commutator is left normed).

I think the following should serve the purpose, as long as your groups are small:

SubgroupGeneratedByElementsWhichAreNotLeftnEngel := function ( G, n )

  local  elms, gens, H;

  elms := AsList(G);
  gens := Filtered(elms,
            a->ForAny(elms,x->not IsOne(LeftNormedComm(
                 Concatenation([x],ListWithIdenticalEntries(n,a))))));
  H := Group(gens,One(G));
  return H;
end;

Hope this helps,

    Stefan Kohl

-----------------------------------------------------------------------------
http://www.gap-system.org/DevelopersPages/StefanKohl/
-----------------------------------------------------------------------------




From fvanhove at cage.UGent.be  Fri Sep 20 09:30:01 2013
From: fvanhove at cage.UGent.be (Frederic Vanhove)
Date: Fri, 20 Sep 2013 17:30:01 +0900
Subject: [GAP Forum] Checking if permutation action has self-paired orbitals
Message-ID: <523C0789.5060208@cage.UGent.be>

Dear forum,

suppose you have a group acting on a set.  The orbitals are the orbits 
on ordered pairs of elements of that set, and their number
can be computed in GAP using
RankAction(groupname,setname);

But I would like to know if these orbitals are self-paired, i.e. that 
(x1,x2) and (x2,x1) are always in the same orbit.
What is the easiest way to check this?

More generally, I would like to check if the permutation character is at 
least multiplicity-free.

Many thanks,
Kind regards,
Fr?d?ric


From sam at Math.RWTH-Aachen.De  Fri Sep 20 11:20:36 2013
From: sam at Math.RWTH-Aachen.De (Thomas Breuer)
Date: Fri, 20 Sep 2013 12:20:36 +0200
Subject: [GAP Forum] Checking if permutation action has self-paired
 orbitals
In-Reply-To: <523C0789.5060208@cage.UGent.be>
References: <523C0789.5060208@cage.UGent.be>
Message-ID: <20130920102036.GB7711@gemma.math.rwth-aachen.de>

Dear Frederic,

you wrote to the GAP Forum

> suppose you have a group acting on a set.  The orbitals are the
> orbits on ordered pairs of elements of that set, and their number
> can be computed in GAP using
> RankAction(groupname,setname);
> 
> But I would like to know if these orbitals are self-paired, i.e.
> that (x1,x2) and (x2,x1) are always in the same orbit.
> What is the easiest way to check this?
> 
> More generally, I would like to check if the permutation character
> is at least multiplicity-free.

In general, the question whether two pairs are in the same orbit
can be checked with 'RepresentativeAction'.
Here is an example:

    gap> g:= SymmetricGroup( 3 );;
    gap> RepresentativeAction( g, [ 1, 2 ], [ 1, 3 ], OnPairs );
    (2,3)
    gap> RepresentativeAction( g, [ 1, 1 ], [ 1, 3 ], OnPairs );
    fail

For that, you need representatives of the orbitals.
If your group acts transitively then you can get them
from orbit representatives of a point stabilizer.
(See the GAP Reference Manual for more details.)


Concerning the question about the permutation character of the action,
one can compute this character explicitly, and if one knows the
irreducible characters of the group then also the decomposition of the
permutation character into irreducibles can be computed.

However, if the groups in question are large then this is perhaps not
the best approach; if the character tables of these groups are available
in GAP's library of character tables then it might be possible to decide
questions about transitive permutation characters with purely character
theoretic methods.
For relevant GAP functions, see section ``Possible Permutation Characters''
in the GAP Reference Manual.
For some examples, see

    http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblpope.htm

All the best,
Thomas


On Fri, Sep 20, 2013 at 05:30:01PM +0900, Frederic Vanhove wrote:
> Dear forum,
> 
> suppose you have a group acting on a set.  The orbitals are the
> orbits on ordered pairs of elements of that set, and their number
> can be computed in GAP using
> RankAction(groupname,setname);
> 
> But I would like to know if these orbitals are self-paired, i.e.
> that (x1,x2) and (x2,x1) are always in the same orbit.
> What is the easiest way to check this?
> 
> More generally, I would like to check if the permutation character
> is at least multiplicity-free.
> 
> Many thanks,
> Kind regards,
> Fr?d?ric



From robert.bailey at ryerson.ca  Fri Sep 20 12:17:09 2013
From: robert.bailey at ryerson.ca (Robert Bailey)
Date: Fri, 20 Sep 2013 09:17:09 -0200
Subject: [GAP Forum] Checking if permutation action has self-paired
	orbitals
In-Reply-To: <523C0789.5060208@cage.UGent.be>
References: <523C0789.5060208@cage.UGent.be>
Message-ID: <fc63b5adbb1a.523c1295@ryerson.ca>

Dear Fr?d?ric,

You may also be able to approach your problem by thinking of it in terms of coherent configurations and/or association schemes (an area which is unfortunately a terminological minefield), for which there are some useful GAP functions available.  The first is the "Elementary functions for association schemes on GAP" of Hanaki: see 
http://math.shinshu-u.ac.jp/~hanaki/as/gap/association_scheme.gap  

Also, Peter Cameron has some relevant GAP functions on his webpage, which work especially well for CCs obtained from permutation groups: see 
http://www.maths.qmul.ac.uk/~pjc/gapprogs.html

For instance, Peter's programs include a function for testing if a group is generously transitive, i.e. every orbital is self-paired.

I hope this is of some use to you!

Regards,
Robert.

----- Original Message -----
From: Frederic Vanhove <fvanhove at cage.UGent.be>
Date: Friday, September 20, 2013 6:02 am
Subject: [GAP Forum] Checking if permutation action has self-paired orbitals
To: "forum at gap-system.org" <forum at gap-system.org>


> Dear forum,
> 
> suppose you have a group acting on a set.  The orbitals are the orbits 
> 
> on ordered pairs of elements of that set, and their number
> can be computed in GAP using
> RankAction(groupname,setname);
> 
> But I would like to know if these orbitals are self-paired, i.e. that 
> 
> (x1,x2) and (x2,x1) are always in the same orbit.
> What is the easiest way to check this?
> 
> More generally, I would like to check if the permutation character is 
> at 
> least multiplicity-free.
> 
> Many thanks,
> Kind regards,
> Fr?d?ric
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From dima at ntu.edu.sg  Fri Sep 20 14:51:32 2013
From: dima at ntu.edu.sg (Dima Pasechnik)
Date: Fri, 20 Sep 2013 21:51:32 +0800
Subject: [GAP Forum] Checking if permutation action has self-paired
 orbitals
In-Reply-To: <fc63b5adbb1a.523c1295@ryerson.ca>
References: <523C0789.5060208@cage.UGent.be> <fc63b5adbb1a.523c1295@ryerson.ca>
Message-ID: <20130920135132.GA40301@nash.ntu.edu.sg>

Dear forum,

On Fri, Sep 20, 2013 at 07:17:09PM +0800, Robert Bailey wrote:
> Dear Fr?d?ric,
>
> You may also be able to approach your problem by thinking of it in terms of coherent configurations and/or association schemes (an area which is unfortunately a terminological minefield), for which there are some useful GAP functions available.  The first is the "Elementary functions for association schemes on GAP" of Hanaki: see
> http://math.shinshu-u.ac.jp/~hanaki/as/gap/association_scheme.gap
>
> Also, Peter Cameron has some relevant GAP functions on his webpage, which work especially well for CCs obtained from permutation groups: see
> http://www.maths.qmul.ac.uk/~pjc/gapprogs.html
>
> For instance, Peter's programs include a function for testing if a group is generously transitive, i.e. every orbital is self-paired.

it is trivial to read the corresponding information off the output of
GRAPE's OrbitalGraphColadjMats (which works for transitive groups only,
but for intransitive groups you always have non-self-paired orbitals and
the representation is not multiplicity-free).

E.g.
gap> LoadPackage("grape");
gap> g:=PrimitiveGroup(7,3);;
gap> m:=OrbitalGraphColadjMats(g);;
gap> Display(m[2]);
[ [  0,  3,  0 ],
  [  0,  1,  2 ],
  [  1,  1,  1 ] ]

shows that the 2nd orbital is not self-paired, as
an orbital with the collapsed adjacency matrix A is self-paired iff there exists
k such that A[1][k]*A[k][1] is non-0, and the 1st of the matrices in the
output of OrbitalGraphColadjMats is always the identity matrix.

Also,
gap> m[2]*m[3]=m[3]*m[2];
true

shows that the representation is multiplicity-free (for this holds iff
the collapsed adjacency matrices commute).

Hope this helps,
Dmitrii

>
> I hope this is of some use to you!
>
> Regards,
> Robert.
>
> ----- Original Message -----
> From: Frederic Vanhove <fvanhove at cage.UGent.be>
> Date: Friday, September 20, 2013 6:02 am
> Subject: [GAP Forum] Checking if permutation action has self-paired orbitals
> To: "forum at gap-system.org" <forum at gap-system.org>
>
>
> > Dear forum,
> >
> > suppose you have a group acting on a set.  The orbitals are the orbits
> >
> > on ordered pairs of elements of that set, and their number
> > can be computed in GAP using
> > RankAction(groupname,setname);
> >
> > But I would like to know if these orbitals are self-paired, i.e. that
> >
> > (x1,x2) and (x2,x1) are always in the same orbit.
> > What is the easiest way to check this?
> >
> > More generally, I would like to check if the permutation character is
> > at
> > least multiplicity-free.
> >
> > Many thanks,
> > Kind regards,
> > Fr?d?ric
> >
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content.

Towards A Sustainable Earth:Print Only When Necessary.Thank you.


From rrburns at cox.net  Sat Sep 21 23:38:47 2013
From: rrburns at cox.net (Sopsku)
Date: Sat, 21 Sep 2013 22:38:47 +0000 (UTC)
Subject: [GAP Forum] S4 isomorphic to semi-direct product of V4 and S3
Message-ID: <loom.20130922T002118-788@post.gmane.org>

Dear Forum,

I am continuing my struggle with trying to learn GAP and group theory at the
same time.

I am looking at a problem set where it asks to show that S4 is isomorphic to
the semi-direct product of V4 (i.e. C2xC2) and S3. I cannot seem to form
this semi-direct product. [i.e. I cannot find elements in the
AutomorphismGroup that match up with the order of the group in order to find
the GroupHomomorphismbyImages as I have done for simpler examples such as A4
isomorphic to semi-direct product of C3 and V4]

How do I use GAP to form the semi-direct product S3 and V4.

Thank you for your help.
    Ron




From benjamin.sambale at gmail.com  Sun Sep 22 08:49:06 2013
From: benjamin.sambale at gmail.com (Benjamin Sambale)
Date: Sun, 22 Sep 2013 09:49:06 +0200
Subject: [GAP Forum] S4 isomorphic to semi-direct product of V4 and S3
In-Reply-To: <loom.20130922T002118-788@post.gmane.org>
References: <loom.20130922T002118-788@post.gmane.org>
Message-ID: <523EA0F2.60306@gmail.com>

Hi Ron,

you need to take the whole automorphism group:

V:=AbelianGroup([2,2]);
A:=AutomorphismGroup(V);
G:=SemidirectProduct(A,V);
StructureDescription(G); #gives S4
StructureDescription(A); #gives S3

Best wishes,
Benjamin

Am 22.09.2013 00:38, schrieb Sopsku:
> Dear Forum,
>
> I am continuing my struggle with trying to learn GAP and group theory at the
> same time.
>
> I am looking at a problem set where it asks to show that S4 is isomorphic to
> the semi-direct product of V4 (i.e. C2xC2) and S3. I cannot seem to form
> this semi-direct product. [i.e. I cannot find elements in the
> AutomorphismGroup that match up with the order of the group in order to find
> the GroupHomomorphismbyImages as I have done for simpler examples such as A4
> isomorphic to semi-direct product of C3 and V4]
>
> How do I use GAP to form the semi-direct product S3 and V4.
>
> Thank you for your help.
>      Ron
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From rostamihojjat at yahoo.com  Sat Sep 28 09:15:05 2013
From: rostamihojjat at yahoo.com (hojjat Rostami)
Date: Sat, 28 Sep 2013 01:15:05 -0700 (PDT)
Subject: [GAP Forum] program for computing noncommuting elements of groups
Message-ID: <1380356105.52890.YahooMailNeo@web126102.mail.ne1.yahoo.com>

Dear GAP Forum
I would like to compute the maximal set of ?pairwise non commuting elements in a finite groups.
Of course i can find the following program which work through ?a grahp but i do not understand how it work.
I will be more grateful for any help or comments.
best regards

LoadPackage("grape");
N:=function(a,b)
return(IsAbelian(Group(a,b)));
end;
NonCommutingGraph:=function(g)
local k, x, y;
k:=Graph(g,Difference(g,Center(g)),OnPoints,function(x,y) return
N(x,y)=false;end);
return k;
end;
clique:=function(x)
local G1,G2;
G1:=NonCommutingGraph(x);
G2:=ComplementGraph(G1);
return Size(IndependentSet(G2));
end;
CliqueNumber:=function(x)
local c, t, M;
c:=clique(x);
while c>0 do
t:=c;
M:=CompleteSubgraphsOfGivenSize(NonCommutingGraph(x),c+1,0);
c:=Size(M);
if c=0 then???? return(t); fi;
od;
end;?

From lkmp02 at gmail.com  Tue Sep 24 11:31:19 2013
From: lkmp02 at gmail.com (Laxmi Kant Mishra)
Date: Tue, 24 Sep 2013 16:01:19 +0530
Subject: [GAP Forum] How to define own group action in GAP?
Message-ID: <CAHmm7fXLqKuUO_A2iYQJopuXy3DYbiZVmGk3q1WmHFMdighOkw@mail.gmail.com>

Dear forum,
I have a group and a set. I wish to define an action the group on the set
in my own way and wish to calculate its orbits and stabilizers. Is it
possible? What is process?


with regards,
-- 
Laxmi Kant Mishra
Department of Mathematics
University of Allahabad
Allahabad

From hulpke at math.colostate.edu  Mon Sep 30 16:36:58 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Mon, 30 Sep 2013 09:36:58 -0600
Subject: [GAP Forum] How to define own group action in GAP?
In-Reply-To: <CAHmm7fXLqKuUO_A2iYQJopuXy3DYbiZVmGk3q1WmHFMdighOkw@mail.gmail.com>
References: <CAHmm7fXLqKuUO_A2iYQJopuXy3DYbiZVmGk3q1WmHFMdighOkw@mail.gmail.com>
Message-ID: <AFC35F14-AAAA-4F48-B7C0-C000AB45523B@math.colostate.edu>



Dear Forum,

On Sep 24, 2013, at 9/24/13 4:31, Laxmi Kant Mishra <lkmp02 at gmail.com> wrote:

> Dear forum,
> I have a group and a set. I wish to define an action the group on the set
> in my own way and wish to calculate its orbits and stabilizers. Is it
> possible? What is process?

Basically you would have to write a function that implements your action.
The manual chapter on group actions
http://www.gap-system.org/Manuals/doc/ref/chap41.html
describes this.

Please note that for any user-defined action the cost (memory and run time) of a stabilizer calculation is roughly proportional to the stabilizer index.

Regards,

    Alexander Hulpke




From markvs at gmail.com  Tue Oct  1 14:08:05 2013
From: markvs at gmail.com (Mark Sapir)
Date: Tue, 1 Oct 2013 08:08:05 -0500
Subject: [GAP Forum] How much memory is needed?
Message-ID: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>

I am going to buy a computer to run GAP. The main thing I am
interested in are group presentations, Groebner bases and other
memory-eating tasks. If anybody on the form has experience of running
GAP on a computer with large RAM, can you answer whether 512 Gb is
much better than 128 Gb. That is have you had problems that are solved
by a computer with bigger RAM and not solved by a computer with
smaller RAM?

Mark Sapir


From tesleft at hotmail.com  Sun Sep 29 03:13:42 2013
From: tesleft at hotmail.com (Lee Martin CCNP)
Date: Sun, 29 Sep 2013 10:13:42 +0800
Subject: [GAP Forum] How to set the ring for szy computation in homalg in
	gap system
Message-ID: <BAY178-W49CB37015126B4BC6A9F53B62B0@phx.gbl>

How to set the ring for szy computation in homalg in gap systemZZ := HomalgRing();
H := HomalgMatrix("[1,x^2+y, x*y-y*z, 0, 0 \
0, x*z-y, z-x, 0, 0 \
0, 0, 0, x^2+y, x*y-y*z \
1, 0, 0, x*z-y, z-x]", 4, 5, ZZ);Regards,Martin 		 	   		  

From Dmitrii.Pasechnik at cs.ox.ac.uk  Tue Oct  1 14:42:54 2013
From: Dmitrii.Pasechnik at cs.ox.ac.uk (Dmitrii Pasechnik)
Date: Tue, 1 Oct 2013 14:42:54 +0100
Subject: [GAP Forum] How much memory is needed?
In-Reply-To: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
References: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
Message-ID: <20131001134254.GB30981@cs.ox.ac.uk>

Dear Mark,
On Tue, Oct 01, 2013 at 08:08:05AM -0500, Mark Sapir wrote:
> I am going to buy a computer to run GAP. The main thing I am
> interested in are group presentations, Groebner bases and other
> memory-eating tasks. If anybody on the form has experience of running
> GAP on a computer with large RAM, can you answer whether 512 Gb is
> much better than 128 Gb. That is have you had problems that are solved
> by a computer with bigger RAM and not solved by a computer with
> smaller RAM?
last century we had to resolve to using a computer with 512Mb (not Gb!)
of RAM to solve some particularly nasty coset enumeration.
(cf. http://zbmath.org/?q=an:0954.51005)

I guess that 512Gb is quite a lot - you'd need a lot of time to fill
that much RAM with cosets.
(Unless of course you are going to run many suchb  computations at the
same time)

For Groebner bases you probably won't be using GAP's own implementation, 
for there are much faster ones available.

Best,
Dima

> 
> Mark Sapir
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From hulpke at math.colostate.edu  Tue Oct  1 17:21:46 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Tue, 1 Oct 2013 10:21:46 -0600
Subject: [GAP Forum] How much memory is needed?
In-Reply-To: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
References: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
Message-ID: <53BCB477-D745-4FFD-9242-D6C1793326F0@math.colostate.edu>



Dear Mark,

I have had problems where a computer with bigger RAM has helped, though frankly if I had not had that larger computer I probably would have been able to do with a somewhat smaller machine and splitting up the job. In the end the benefit of more memory is somewhat logarithmic, if you give 512GB a 10, then 128GB is a 9 or 9.5.

As far as ordering a computer, I think the question is of the tradeoff what you would have to forgo if buying the larger machine (at the funding level I have, 512GB would be too high a tradeoff; you are probably better funded) and whether you already have calculations that you know failed at 128GB.  However, frankly, again my experience with (say) coset enumeration is that if it did not terminate in Memory x the chance to terminate in memory 2x is somewhere 5% or less, so a factor of 4 in memory is really only buying you a better success chance of 20% or less on these kinds of calculations.

Particularly concerning the calculations I expect you will be doing, also be aware that GAPs built-in Coset enumeration, knuth-bendix and groebner bases are far less powerful than the standalone c-programs and that there are packages that provide interfaces to ACE, KBMAG and singular.

Also often calculations tend to run for a long time and our system administrator wanted to reboot machines for safety updates -- I am now using DMTCP (http://dmtcp.sourceforge.net) to be able to save a running jobs to disk and to restart it after the machine reboot.

Best,

    Alexander




From mohamed.barakat at rwth-aachen.de  Tue Oct  1 18:18:35 2013
From: mohamed.barakat at rwth-aachen.de (Mohamed Barakat)
Date: Tue, 01 Oct 2013 19:18:35 +0200
Subject: [GAP Forum] How to set the ring for szy computation in homalg
	in	gap system
In-Reply-To: <BAY178-W49CB37015126B4BC6A9F53B62B0@phx.gbl>
References: <BAY178-W49CB37015126B4BC6A9F53B62B0@phx.gbl>
Message-ID: <9DF13861-E706-4702-9ADB-8B5A41B6FD06@rwth-aachen.de>

Hello Martin,

> How to set the ring for szy computation in homalg in gap systemZZ := HomalgRing();
> H := HomalgMatrix("[1,x^2+y, x*y-y*z, 0, 0 \
> 0, x*z-y, z-x, 0, 0 \
> 0, 0, 0, x^2+y, x*y-y*z \
> 1, 0, 0, x*z-y, z-x]", 4, 5, ZZ);Regards,Martin

There was a line missing in my previous email.

Best regards,

Mohamed

gap> LoadPackage( "GradedRingForHomalg" );
true
gap> ZZ := HomalgRingOfIntegersInSingular( );
Z
gap> R := ZZ * "x,y,z";
Z[x,y,z]
gap> H := HomalgMatrix("[1,x^2+y, x*y-y*z, 0, 0, \
> 0, x*z-y, z-x, 0, 0, \
> 0, 0, 0, x^2+y, x*y-y*z, \
> 1, 0, 0, x*z-y, z-x]", 4, 5, R);
<A 4 x 5 matrix over an external ring>
gap> SyzygiesOfColumns( H );
<A non-zero right regular 5 x 1 matrix over an external ring>
gap> Display( last );
x^2*y*z-x*y*z^2+x^3-x*y^2-x^2*z+y^2*z+x*y-y*z,
-x+z,
-x*z+y,
-x*y+y*z,
x^2+y



From alexk at mcs.st-andrews.ac.uk  Tue Oct  1 20:19:11 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Tue, 1 Oct 2013 20:19:11 +0100
Subject: [GAP Forum] program for computing noncommuting elements of
	groups
In-Reply-To: <1380356105.52890.YahooMailNeo@web126102.mail.ne1.yahoo.com>
References: <1380356105.52890.YahooMailNeo@web126102.mail.ne1.yahoo.com>
Message-ID: <A98964F4-B8EA-4EDC-8C91-E91B7E44EDA2@mcs.st-andrews.ac.uk>

Dear hojjat Rostami,

On 28 Sep 2013, at 09:15, hojjat Rostami <rostamihojjat at yahoo.com> wrote:

> Dear GAP Forum
> I would like to compute the maximal set of  pairwise non commuting elements in a finite groups.
> Of course i can find the following program which work through  a grahp but i do not understand how it work.
> I will be more grateful for any help or comments.

I think this question might be easier answered if you could be more specific.

If you could post better formatted and more readable code (separate functions by blank 
lines, use indentation) and use comments to explain what the code is doing and where 
exactly do you need Forum's help in explaining it, that may be very helpful.

If you have found this program and there are author contact details there, it may be 
also useful to ask the author directly.

One last remark:

> best regards
> 
> LoadPackage("grape");
> N:=function(a,b)
> return(IsAbelian(Group(a,b)));
> end;

In this function, you create a group given by two generators a and b and then 
check if it is abelian - it would be more efficient just to check that a*b = b*a.

Hope this helps,
Alexander




> NonCommutingGraph:=function(g)
> local k, x, y;
> k:=Graph(g,Difference(g,Center(g)),OnPoints,function(x,y) return
> N(x,y)=false;end);
> return k;
> end;
> clique:=function(x)
> local G1,G2;
> G1:=NonCommutingGraph(x);
> G2:=ComplementGraph(G1);
> return Size(IndependentSet(G2));
> end;
> CliqueNumber:=function(x)
> local c, t, M;
> c:=clique(x);
> while c>0 do
> t:=c;
> M:=CompleteSubgraphsOfGivenSize(NonCommutingGraph(x),c+1,0);
> c:=Size(M);
> if c=0 then     return(t); fi;
> od;
> end; 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From anvita21 at gmail.com  Wed Oct  2 10:54:05 2013
From: anvita21 at gmail.com (Anvita)
Date: Wed, 2 Oct 2013 16:54:05 +0700
Subject: [GAP Forum] A possibly wrong output in MeatAxe
Message-ID: <CAAwatYWK3knU_QBtQzCT8aNimLAnjig_EL5C3RehhwZ2SY0jRw@mail.gmail.com>

Dear Forum,

I am suspecting that GAP's function for finding composition factors
of a MeatAxe module could be producing an incorrect answer in the
following example which counts the multiplicities of composition factors
of the regular module for A_5 over its splitting field GF(4). According to
the theory, A_5 has a unique irreducible module of defect 0 which has
dimension 4 and therefore must occur with multiplicity 4, but the function
returns 3.


A:=AlternatingGroup(5);
G:=Action(A,A);
gg:=GeneratorsOfGroup(GG);
reg:=List(gg,g->PermutationMat(g,60,GF(4)));
M:=GModuleByMats(reg,GF(4));
com:=MTX.CollectedFactors(M);;
List(com,t->[MTX.Dimension(t[1]),t[2]]);

# [ [ 1, 16 ], [ 2, 8 ], [ 2, 8 ], [ 4, 3 ] ]



Here is a similar calculation in Magma which is more in line with the
theory.


A:=AlternatingGroup(5);
_,G:=CosetAction(A,sub<A|>);
M:=PermutationModule(G,GF(4));
ConstituentsWithMultiplicities(M);
[
    <GModule of dimension 1 over GF(2^2), 12>,
    <GModule of dimension 2 over GF(2^2), 8>,
    <GModule of dimension 2 over GF(2^2), 8>,
    <GModule of dimension 4 over GF(2^2), 4>
]
[ 4, 1, 2, 3, 1, 2, 1, 3, 4, 1, 3, 2, 1, 2, 1, 3, 1, 2, 3, 1, 4, 1, 2, 2,
1, 3, 3, 4, 1, 2,
1, 3 ]


Anvita

From sl4 at st-andrews.ac.uk  Wed Oct  2 12:40:26 2013
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Wed, 2 Oct 2013 12:40:26 +0100
Subject: [GAP Forum] How much memory is needed?
In-Reply-To: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
References: <CAAo0A8rbBauyF6+OUCNBu+RdkLxTu4eDK_HhkWmasBYEbJMzNg@mail.gmail.com>
Message-ID: <D86C749B-F51A-417A-A058-E063895B7AC3@st-andrews.ac.uk>

Hi Mark,

I can confirm that GAP will run successfully on a computer of that size. 
We have a couple of 512GB RAM machines and I've used all of that in some single GAP computations.
You may need to use some non-standard options at compile time or run time to get this to work though -- we can advise you at the time if necessary.

I have a few caveats though:

1. Not all the algorithms in GAP and the software it uses through packages, like ACE and KBMAG
are really "tuned" for this much data, so you may run into things that slow down more than they need to. Again, we may be able to advise or assist.

2. Most machines with this much memory have what is called a NUMA architecture -- the memory is divided between the processors and  they are not really designed for one processor to access all the memory in a random way. This may mean things suddenly slowing down by a factor of two or three when you use more than about 25% of your memory.

3. In my, entirely unsystematic, experience, there are not THAT many problems that can  be solved in 512GB that cannot be solved in 128. There will be some, but unless you have a predictable need for the memory, to hold matrices or something, there may not be so many.  Of course your mileage may vary.

	Steve

On 1 Oct 2013, at 14:08, Mark Sapir <markvs at gmail.com> wrote:

> I am going to buy a computer to run GAP. The main thing I am
> interested in are group presentations, Groebner bases and other
> memory-eating tasks. If anybody on the form has experience of running
> GAP on a computer with large RAM, can you answer whether 512 Gb is
> much better than 128 Gb. That is have you had problems that are solved
> by a computer with bigger RAM and not solved by a computer with
> smaller RAM?
> 
> Mark Sapir
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From hulpke at math.colostate.edu  Wed Oct  2 15:46:55 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Wed, 2 Oct 2013 08:46:55 -0600
Subject: [GAP Forum] A possibly wrong output in MeatAxe
In-Reply-To: <CAAwatYWK3knU_QBtQzCT8aNimLAnjig_EL5C3RehhwZ2SY0jRw@mail.gmail.com>
References: <CAAwatYWK3knU_QBtQzCT8aNimLAnjig_EL5C3RehhwZ2SY0jRw@mail.gmail.com>
Message-ID: <D6C6882E-9917-43C9-808D-995CCFFB3CC7@math.colostate.edu>



Dear Forum,

``Anvita'' wrote:
> I am suspecting that GAP's function for finding composition factors
> of a MeatAxe module could be producing an incorrect answer in the
> following example which counts the multiplicities of composition factors
> of the regular module for A_5 over its splitting field GF(4).

No, what is happening in the calculation is that you don't construct the regular action, but the conjugation action of A on itself. (The default action is `OnPoints' which corresponds to the ^ operator.)
> 
> A:=AlternatingGroup(5);
> G:=Action(A,A);
If you use
GG:=Action(A,A,OnRight);

> gg:=GeneratorsOfGroup(GG);
> reg:=List(gg,g->PermutationMat(g,60,GF(4)));
> M:=GModuleByMats(reg,GF(4));
> com:=MTX.CollectedFactors(M);;
> List(com,t->[MTX.Dimension(t[1]),t[2]]);

you get dimensions
[ [ 1, 12 ], [ 2, 8 ], [ 2, 8 ], [ 4, 4 ] ]
which I believe agrees with what some other system calculates.

Regards,

   Alexander Hulpke




From mark.evan.flanagan at gmail.com  Tue Oct  8 20:57:00 2013
From: mark.evan.flanagan at gmail.com (Mark Flanagan)
Date: Tue, 8 Oct 2013 15:57:00 -0400
Subject: [GAP Forum] Problem with ParGap and ParList
Message-ID: <CAPLF6fM-Ma9s1Xtv+Rpf_tCX3bo8bG3KnFzgYw0-x2EwQ5BY5g@mail.gmail.com>

Hello everyone,

Hopefully issues with ParGap are on-topic for the GAP forum.

Running ParGap with open mpi. ParList works with a simple function
loaded into ParGap with ParRead, eg ParList([1..10],testfunc) when

testfunc:= function(x) return x+x; end;;

is used, but in more complicated use cases,
ParList(producehoms(3),loopofhom) does not work:

gap> ParList(producehoms(3),loopofhom);
Error, Variable: 'f1' must have a value
Error, List Assignment: <rhss> must be a list with the same length as
<positions> (14\
) in
  result{range} := tmp; called from
<function "ParList">( <arguments> )
 called from read-eval loop at line 3 of *stdin*
you can replace <rhss> via 'return <rhss>;'
brk> Error, Variable: 'f1' must have a value

producehoms(3) makes a list of homomorphisms and loopofhom is a
function, and  f1 is a generator of a group loaded in with ParRead.
List(producehoms(3),loopofhom) works as expected on master, and it
seems like ParRead worked because

SendRecvMsg("List(producehoms(3),loopofhom)",1);

produces the expected output.

Any thoughts on why ParList isn't working right? Would it just be
easier to parallelize my code manually, rather than relying on
ParList? Any advice is appreciated.

Mark


From alexk at mcs.st-andrews.ac.uk  Wed Oct  9 12:54:32 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Wed, 9 Oct 2013 12:54:32 +0100
Subject: [GAP Forum] Problem with ParGap and ParList
In-Reply-To: <CAPLF6fM-Ma9s1Xtv+Rpf_tCX3bo8bG3KnFzgYw0-x2EwQ5BY5g@mail.gmail.com>
References: <CAPLF6fM-Ma9s1Xtv+Rpf_tCX3bo8bG3KnFzgYw0-x2EwQ5BY5g@mail.gmail.com>
Message-ID: <48514B31-FC53-45DF-885F-DC9F22A5D567@mcs.st-andrews.ac.uk>

Dear Mark,

On 8 Oct 2013, at 20:57, Mark Flanagan <mark.evan.flanagan at gmail.com> wrote:

> Hello everyone,
> 
> Hopefully issues with ParGap are on-topic for the GAP forum.
> 
> Running ParGap with open mpi. ParList works with a simple function
> loaded into ParGap with ParRead, eg ParList([1..10],testfunc) when
> 
> testfunc:= function(x) return x+x; end;;
> 
> is used, but in more complicated use cases,
> ParList(producehoms(3),loopofhom) does not work:
> 
> gap> ParList(producehoms(3),loopofhom);
> Error, Variable: 'f1' must have a value
> Error, List Assignment: <rhss> must be a list with the same length as
> <positions> (14\
> ) in
>  result{range} := tmp; called from
> <function "ParList">( <arguments> )
> called from read-eval loop at line 3 of *stdin*
> you can replace <rhss> via 'return <rhss>;'
> brk> Error, Variable: 'f1' must have a value
> 
> producehoms(3) makes a list of homomorphisms and loopofhom is a
> function, and  f1 is a generator of a group loaded in with ParRead.
> List(producehoms(3),loopofhom) works as expected on master, and it
> seems like ParRead worked because
> 
> SendRecvMsg("List(producehoms(3),loopofhom)",1);
> 
> produces the expected output.
> 
> Any thoughts on why ParList isn't working right? Would it just be
> easier to parallelize my code manually, rather than relying on
> ParList? Any advice is appreciated.
> 
> Mark

I think this is not a problem in ParGap: one can easily reproduce 
an instance of the same problem without ParGap:

gap> F:=FreeGroup("f1","f2");
<free group on the generators [ f1, f2 ]>
gap> f1;
Error, Variable: 'f1' must have a value
not in any function at line 2 of *stdin*

This happens because there is no variable in GAP named 'f1'. 
Instead, you can access generators of the group like here:

gap> F.1;
f1

Alternatively, you may call 'AssignGeneratorVariables':

gap> AssignGeneratorVariables(F);
#I  Assigned the global variables [ f1, f2 ]
gap> f1;
f1

but then remember to call it each time you define a new
group with the same letter denoting generators, otherwise
f1 may still point to a generator of the former group.

Hope this helps,
Alexander




From johannes.hahn at uni-jena.de  Wed Oct  9 16:20:28 2013
From: johannes.hahn at uni-jena.de (Johannes Hahn)
Date: Wed, 09 Oct 2013 17:20:28 +0200
Subject: [GAP Forum] Implementing automatic inheritance of features
Message-ID: <5255743C.2030304@uni-jena.de>

Hi everyone.

Is there a mechanism in GAP that allows one to declare that certain new 
features are inherited by associated objects in a certain way? As an 
example: Let's say I want to implement a category for ordered groups. Is 
there a way to tell GAP that subgroups of a ordered group are also 
ordered with the same ordering?

greetings
Johannes Hahn.


From sdliuy001 at 163.com  Thu Oct 10 08:55:28 2013
From: sdliuy001 at 163.com (Yang Liu)
Date: Thu, 10 Oct 2013 15:55:28 +0800 (CST)
Subject: [GAP Forum] some question about compute the order of centralizer
Message-ID: <4e53994.22705.141a15d003d.Coremail.sdliuy001@163.com>

Dear Forum,
  Let F be  a finite field of order p and V be a vector space over F  of dimension n. Choose a,b belong to GL(n,F) and G=<a,b>, the group generated by a and b. Then V may be viewed as an F[G]-module.
  For any element v of  V, how to compute the order of the centralizer of v in G ?
Best wishes,
Yang Liu.

From sam at Math.RWTH-Aachen.De  Thu Oct 10 15:27:42 2013
From: sam at Math.RWTH-Aachen.De (Thomas Breuer)
Date: Thu, 10 Oct 2013 16:27:42 +0200
Subject: [GAP Forum] Implementing automatic inheritance of features
In-Reply-To: <5255743C.2030304@uni-jena.de>
References: <5255743C.2030304@uni-jena.de>
Message-ID: <20131010142742.GA6017@gemma.math.rwth-aachen.de>

Dear Johannes,

GAP provides a standard mechanism for deriving information about
an object from known information about another object,
see Section ``Relations Between Domains'' of the GAP Reference Manual.

For example, if `g' is a group object and a subgroup is created via
`Subgroup( g, ... )' then certain properties and attributes which are
set (or not set) in `g' are used to derive certain properties and
attributes of the subgroup object
--think of `IsFinite' for `g' implying `IsFinite' for the subgroup.

This transfer of information happens only upon creation of the subgroup
(or one has to call the relevant function explicitly), that is,
the subgroup does not automatically benefit from information about `g'
that is obtained later in the GAP session.

If I understand your question right then you are asking for ``static''
information which is already known when the subgroups are created,
so perhaps this mechanism is of interest.

If also ``dynamic inheritance'' of information is needed then more
involved code is necessary.
Mohamed has implemented something like this in his GAP packages.

All the best,
Thomas


On Wed, Oct 09, 2013 at 05:20:28PM +0200, Johannes Hahn wrote:
> Hi everyone.
> 
> Is there a mechanism in GAP that allows one to declare that certain
> new features are inherited by associated objects in a certain way?
> As an example: Let's say I want to implement a category for ordered
> groups. Is there a way to tell GAP that subgroups of a ordered group
> are also ordered with the same ordering?
> 
> greetings
> Johannes Hahn.



From rrburns at cox.net  Thu Oct 10 18:19:55 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 10 Oct 2013 17:19:55 +0000 (UTC)
Subject: [GAP Forum] Projection for Semidirect Product
Message-ID: <loom.20131010T190950-276@post.gmane.org>

Dear forum,

I am having some difficulty understanding projections and semidirect products. 

I think I understand Projection for a Direct Product:

f:= FreeGroup("a");; a:=f.1;;
g := f/[a^4];; a:=g.1;;    ## C4
f:= FreeGroup("b");; b:=f.1;;
h := f/[b^2];; b:=h.1;;    ## C2
## form
d:=DirectProduct(h,g);
## write elements of d terms of [e_h,e_g]
p1:=Projection(d,1);
p2:=Projection(d,2);
List(Elements(d),x->[Image(p1,x),Image(p2,x)]);

Now I would like to do soemthing similar for a semidirect product group, e.g

a:=AutomorphismGroup(g);
s:=SemidirectProduct(a,g);

but now
Projection(s,1); 
fails.

Can I use the GAP Projections to do a decomposition similar to the  direct
product example above?

Thank you for any help.




From hulpke at math.colostate.edu  Thu Oct 10 18:32:06 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu, 10 Oct 2013 11:32:06 -0600
Subject: [GAP Forum] Projection for Semidirect Product
In-Reply-To: <loom.20131010T190950-276@post.gmane.org>
References: <loom.20131010T190950-276@post.gmane.org>
Message-ID: <B9A69CC5-4366-4204-B4E4-EA5EF3E66E67@math.colostate.edu>



Dear Forum,

On Oct 10, 2013, at 10/10/13 11:19, Sopsku <rrburns at cox.net> wrote:

> Dear forum,
> 
> I am having some difficulty understanding projections and semidirect products. 
> Now I would like to do soemthing similar for a semidirect product group, e.g
> 
> a:=AutomorphismGroup(g);
> s:=SemidirectProduct(a,g);
> 
> but now
> Projection(s,1); 
> fails.
> 
> Can I use the GAP Projections to do a decomposition similar to the  direct
> product example above?

According to the manual, for a semidirect product N:S
Projection(s) 
returns the projection onto S, there is no projection onto N which is a group homomorphism (and thus no numeric parameter to Projection).

If you want to get an N-part of a product element g, you could divide off the canonical representative for the projection image, for example:

PreImagesRepresentative(Embedding(s,1), g/Image(Embedding(s,2),Image(Projection(s),g));

Regards,

    Alexander Hulpke




From rrburns at cox.net  Thu Oct 10 20:44:05 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 10 Oct 2013 19:44:05 +0000 (UTC)
Subject: [GAP Forum] Projection for Semidirect Product
References: <loom.20131010T190950-276@post.gmane.org>
	<B9A69CC5-4366-4204-B4E4-EA5EF3E66E67@math.colostate.edu>
Message-ID: <loom.20131010T212923-809@post.gmane.org>

Alexander Hulpke <hulpke at ...> writes:

> 
> 
> Dear Forum,
> 
> On Oct 10, 2013, at 10/10/13 11:19, Sopsku <rrburns at ...> wrote:
> 
> > Dear forum,
> > 
> > I am having some difficulty understanding projections and semidirect
products. 
> > Now I would like to do soemthing similar for a semidirect product group, e.g
> > 
> > a:=AutomorphismGroup(g);
> > s:=SemidirectProduct(a,g);
> > 
> > but now
> > Projection(s,1); 
> > fails.
> > 
> > Can I use the GAP Projections to do a decomposition similar to the  direct
> > product example above?
> 
> According to the manual, for a semidirect product N:S
> Projection(s) 
> returns the projection onto S, there is no projection onto N which is a
group homomorphism (and thus no
> numeric parameter to Projection).
> 
> If you want to get an N-part of a product element g, you could divide off
the canonical representative for the
> projection image, for example:
> 
> PreImagesRepresentative(Embedding(s,1),
g/Image(Embedding(s,2),Image(Projection(s),g));
> 
> Regards,
> 
>     Alexander Hulpke
> 

Sorry for being so dense, but I do not fully understand the command and it
fails so I am not quite sure what Prof. Hulple intended. I did try the
following:

npart1:=function(elm)
   return Image(e1,Image(p,elm))^p;
end;

npart2:=function(elm)
   return PreImagesRepresentative(e2,elm/Image(e1,Image(p,elm)));
end;

PrintArray(List(Elements(S),e->[npart1(e),npart2(e)]));

Which is more or less what I think I am looking for. Is this kind of what
Prof. Hulpke intended.

Again thank you for any help or comments.
    Ron







From hulpke at math.colostate.edu  Thu Oct 10 21:05:59 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu, 10 Oct 2013 14:05:59 -0600
Subject: [GAP Forum] Projection for Semidirect Product
In-Reply-To: <loom.20131010T212923-809@post.gmane.org>
References: <loom.20131010T190950-276@post.gmane.org>
	<B9A69CC5-4366-4204-B4E4-EA5EF3E66E67@math.colostate.edu>
	<loom.20131010T212923-809@post.gmane.org>
Message-ID: <C00C9697-E3FA-4BD9-B5C1-B5FE42FEBE2A@math.colostate.edu>



On Oct 10, 2013, at 10/10/13 1:44, Sopsku <rrburns at cox.net> wrote:

> 
> Sorry for being so dense, but I do not fully understand the command and it

Indeed, it should have been (swapped indices 1,2)

PreImagesRepresentative(Embedding(s,2), r/Image(Embedding(s,1),Image(Projection(s),r));

> fails so I am not quite sure what Prof. Hulpke intended. I did try the
> following:

Assuming your setup is:

gap> g:=Group((1,2,3,4,5));
Group([ (1,2,3,4,5) ])
gap> a:=AutomorphismGroup(g);
<group with 1 generators>
gap> s:=SemidirectProduct(a,g);
<pc group with 3 generators>
gap> p:=Projection(s);
[ f1, f2, f3 ] -> [ [ (1,2,3,4,5) ] -> [ (1,3,5,2,4) ], 
  [ (1,2,3,4,5) ] -> [ (1,5,4,3,2) ], IdentityMapping( Group([ (1,2,3,4,
   5) ]) ) ]
gap> e1:=Embedding(s,1);
CompositionMapping( [ f1, f2 ] -> [ f1, f2 ], CompositionMapping( Pcgs(
[ (1,2,4,3), (1,4)(2,3) ]) -> [ f1, f2 ], <action isomorphism> ) )
gap> e2:=Embedding(s,2);
[ (1,2,3,4,5) ] -> [ f3 ]


> npart1:=function(elm)
>   return Image(e1,Image(p,elm))^p;
> end;
> 
> npart2:=function(elm)
>   return PreImagesRepresentative(e2,elm/Image(e1,Image(p,elm)));
> end;

> 
> PrintArray(List(Elements(S),e->[npart1(e),npart2(e)]));
> 
> Which is more or less what I think I am looking for. Is this kind of what
> Prof. Hulpke intended.

Yes, though your function npart1 does nothing else but just computing  Image(p,elm)

Best,

Alexander Hulpke

> 
> Again thank you for any help or comments.
>    Ron
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From szgycs at szemerja-szasz.hu  Fri Oct 11 10:41:33 2013
From: szgycs at szemerja-szasz.hu (szgycs at szemerja-szasz.hu)
Date: Fri, 11 Oct 2013 11:41:33 +0200
Subject: [GAP Forum] GAP and PHP
Message-ID: <cf7b98babb1237f0a3619b6c82e7bb79@szemerja-szasz.hu>

How can I exchange data between GAP and PHP?


From mathieu.dutour at gmail.com  Fri Oct 11 10:55:04 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Fri, 11 Oct 2013 11:55:04 +0200
Subject: [GAP Forum] GAP and PHP
In-Reply-To: <cf7b98babb1237f0a3619b6c82e7bb79@szemerja-szasz.hu>
References: <cf7b98babb1237f0a3619b6c82e7bb79@szemerja-szasz.hu>
Message-ID: <CADm_teN0nyiF-giin+_TpbYJLdeCBjaF40qaRpckfZB=WOQa9g@mail.gmail.com>

There are two conceivable solutions:
1) write a GAP program from the PHP and do the output
in the GAP program. Read the output from the GAP program.
Procedure for run
gap.sh < prog.g
So, one computation corresponds to one GAP session.

2) Again use text files and use a system with have both of them
running continuously on some infinite loop. After one text
file "F" is created, create a second one "F.finish" indicating
that F is finished and can be processed.

Those are elementary ways, you have also the streams as
possibility. But I would advise first for simple strategies before
going for more complex harder to debug ones.

  Mathieu


On Fri, Oct 11, 2013 at 11:41 AM, <szgycs at szemerja-szasz.hu> wrote:

> How can I exchange data between GAP and PHP?
>
> ______________________________**_________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/**mailman/listinfo/forum<http://mail.gap-system.org/mailman/listinfo/forum>
>

From caj21 at st-andrews.ac.uk  Fri Oct 11 13:48:41 2013
From: caj21 at st-andrews.ac.uk (Chris Jefferson)
Date: Fri, 11 Oct 2013 13:48:41 +0100
Subject: [GAP Forum] GAP and PHP
In-Reply-To: <cf7b98babb1237f0a3619b6c82e7bb79@szemerja-szasz.hu>
References: <cf7b98babb1237f0a3619b6c82e7bb79@szemerja-szasz.hu>
Message-ID: <5257F3A9.4010205@st-andrews.ac.uk>

On 11/10/13 10:41, szgycs at szemerja-szasz.hu wrote:
> How can I exchange data between GAP and PHP?

I would look at the SCSCP library. For simple transfers, this is not too 
hard if you can generate and read XML and communicate over a network 
(which I imagine is fairly easy in PHP, although I have never used it).

Chris


From sebastian.gutsche at rwth-aachen.de  Fri Oct 11 14:45:34 2013
From: sebastian.gutsche at rwth-aachen.de (Sebastian Gutsche)
Date: Fri, 11 Oct 2013 15:45:34 +0200
Subject: [GAP Forum] Implementing automatic inheritance of features
Message-ID: <525800FE.4060804@rwth-aachen.de>

Dear Johannes,

a while ago, I implemented so-called todo-lists in the ToolsForHomalg 
package, which can propagate knowledge (in form of attributes and 
properties) between mathematically related objects (being a subobject is 
a special case). The basic idea is to attach certain tasks to an object, 
which are triggered once a property or an attribute get set (and acquire 
certain values). So they behave like immediate methods, but are much 
more flexible (dynamic inheritance). These todo-lists might be a 
solution for you. Please see the attachment for a commented example. 
Just copy both files to a directory and follow the file example.gi line 
by line for a demo.

Also, there is the possibility to follow how a propagated property was 
set, i.e., building a proof. But this is still very beta, since the 
proof-tree usually grows too large.

An example of a package that uses todo-lists outside of the homalg 
project is Martin Leuner's alcove: https://github.com/martin-leuner/alcove

If you need any help please feel free to contact us.

Best wishes,
Sebastian
-------------- next part --------------
## Reads some definitions. Please look at that file first.

Read( "example_definitions.gi" );

## We first create a group and a subgroup.

G := CreateOrderedGroup( );

H := CreateOrderedSubgroup( );

## Now we create a todo-list entry, which looks up
## if G has an ordering, and then sets the ordering
## of H to the same object.

entry := ToDoListEntry( [ [ G, "Ordering" ] ], H, "Ordering", [ Ordering, G ] );

## Please read this as follows:
## First argument is a list of preconditions.
## Here the two element list means that the todo-list
## looks up if the attribute Ordering is set.
## If this is the case, it sets the Ordering ( 3th argument ) of
## H (2nd argument) to the ordering of G. This is provided by the last
## argument, which is a list. The first entry is a function, at this time
## applied to the rest of the list. We then get the ordering, which is already known,
## and set the ordering of H to it.

## The next step "activates" the entry.

AddToToDoList( entry );

## This should be false

HasOrdering( H );

SetOrdering( G, "lex" );

## Now the background magic happens, and the ordering of H is set to the same thing.

Ordering( H );

## The todo-lists are capable of even more things, for example launching a function.

G2 := CreateOrderedGroup( );

entry := ToDoListEntry( [ [ G2, "Ordering" ] ], function( ) Print( "Hello world!\n" ); end );

AddToToDoList( entry );

SetOrdering( G2, "lex" );

## The passed function is now launched once the attribute is set.

## We also provide the functionality to create todo-list entries by so
## called blueprints. These install todo-list entries for every created object
## in a category.

ToDoListEntryBlueprint( IsOrderedGroup, [ [ ToDoList_this_object, "Ordering", "lex" ] ], [ function() Print( "Yay, I have an order!\n" ); end ] );

## Now every new object should have a todo-list entry.

G3 := CreateOrderedGroup( );

SetOrdering( G3, "lex" );
-------------- next part --------------
LoadPackage( "ToolsForHomalg" );


## Define types etc. for ordered groups

DeclareCategory( "IsOrderedGroup",
                 IsObject );

DeclareCategory( "IsOrderedSubgroup",
                 IsOrderedGroup );

DeclareRepresentation( "IsOrderedGroupRep",
                       IsOrderedGroup and IsAttributeStoringRep,
                       [ ] );

DeclareRepresentation( "IsOrderedSubgroupRep",
                       IsOrderedSubgroup and IsAttributeStoringRep,
                       [ ] );

BindGlobal( "TheFamilyOfOrderedGroups",
        NewFamily( "TheFamilyOfOrderedGroups" ) );

BindGlobal( "TheTypeOfOrderedGroups",
        NewType( TheFamilyOfOrderedGroups,
                IsOrderedGroupRep ) );

BindGlobal( "TheTypeOfOrderedSubgroups",
        NewType( TheFamilyOfOrderedGroups,
                IsOrderedSubgroupRep ) );

## Please note that this is not meant to work in any case.
## Its just a demo. We might need constructors for objects.

DeclareOperation( "CreateOrderedGroup",
                  [ ] );

InstallMethod( CreateOrderedGroup,
               [ ],
  function( )
    local group;
    
    group := rec();
    
    Objectify( TheTypeOfOrderedGroups, group );
    
    return group;
    
end );

## Creating a subgroup.
## Please note that there is currently no connection
## to the containing group. We will do this later by using todo-lists.
## One might solve this in a different manner.

DeclareOperation( "CreateOrderedSubgroup",
                  [ ] );

InstallMethod( CreateOrderedSubgroup,
               [ ],
  function( )
    local group;
    
    group := rec();
    
    Objectify( TheTypeOfOrderedSubgroups, group );
    
    return group;
    
end );

## The attribute we want to share between group and subgroup,
## or better propagate from group to subgroup

DeclareAttribute( "Ordering",
                  IsOrderedGroup );



From mark.evan.flanagan at gmail.com  Fri Oct 11 15:43:27 2013
From: mark.evan.flanagan at gmail.com (Mark Flanagan)
Date: Fri, 11 Oct 2013 10:43:27 -0400
Subject: [GAP Forum] Problem with ParGap and ParList
In-Reply-To: <48514B31-FC53-45DF-885F-DC9F22A5D567@mcs.st-andrews.ac.uk>
References: <CAPLF6fM-Ma9s1Xtv+Rpf_tCX3bo8bG3KnFzgYw0-x2EwQ5BY5g@mail.gmail.com>
	<48514B31-FC53-45DF-885F-DC9F22A5D567@mcs.st-andrews.ac.uk>
Message-ID: <CAPLF6fNP55yFeqbqe-6CEC=aAWiVLdg6QZSm2BMfAS3g=TzFdw@mail.gmail.com>

That fixed it! I'm still a bit confused because there was no trouble
running this code using gap (not pargap) and nowhere in my code do I
explicitly reference the variable 'f1'.

Thanks!

Best,
Mark
Dear Mark,

On 8 Oct 2013, at 20:57, Mark Flanagan <mark.evan.flanagan at gmail.com> wrote:

> Hello everyone,
>
> Hopefully issues with ParGap are on-topic for the GAP forum.
>
> Running ParGap with open mpi. ParList works with a simple function
> loaded into ParGap with ParRead, eg ParList([1..10],testfunc) when
>
> testfunc:= function(x) return x+x; end;;
>
> is used, but in more complicated use cases,
> ParList(producehoms(3),loopofhom) does not work:
>
> gap> ParList(producehoms(3),loopofhom);
> Error, Variable: 'f1' must have a value
> Error, List Assignment: <rhss> must be a list with the same length as
> <positions> (14\
> ) in
>  result{range} := tmp; called from
> <function "ParList">( <arguments> )
> called from read-eval loop at line 3 of *stdin*
> you can replace <rhss> via 'return <rhss>;'
> brk> Error, Variable: 'f1' must have a value
>
> producehoms(3) makes a list of homomorphisms and loopofhom is a
> function, and  f1 is a generator of a group loaded in with ParRead.
> List(producehoms(3),loopofhom) works as expected on master, and it
> seems like ParRead worked because
>
> SendRecvMsg("List(producehoms(3),loopofhom)",1);
>
> produces the expected output.
>
> Any thoughts on why ParList isn't working right? Would it just be
> easier to parallelize my code manually, rather than relying on
> ParList? Any advice is appreciated.
>
> Mark

I think this is not a problem in ParGap: one can easily reproduce
an instance of the same problem without ParGap:

gap> F:=FreeGroup("f1","f2");
<free group on the generators [ f1, f2 ]>
gap> f1;
Error, Variable: 'f1' must have a value
not in any function at line 2 of *stdin*

This happens because there is no variable in GAP named 'f1'.
Instead, you can access generators of the group like here:

gap> F.1;
f1

Alternatively, you may call 'AssignGeneratorVariables':

gap> AssignGeneratorVariables(F);
#I  Assigned the global variables [ f1, f2 ]
gap> f1;
f1

but then remember to call it each time you define a new
group with the same letter denoting generators, otherwise
f1 may still point to a generator of the former group.

Hope this helps,
Alexander

From hulpke at math.colostate.edu  Fri Oct 11 19:06:11 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri, 11 Oct 2013 12:06:11 -0600
Subject: [GAP Forum] Problem with ParGap and ParList
In-Reply-To: <CAPLF6fNP55yFeqbqe-6CEC=aAWiVLdg6QZSm2BMfAS3g=TzFdw@mail.gmail.com>
References: <CAPLF6fM-Ma9s1Xtv+Rpf_tCX3bo8bG3KnFzgYw0-x2EwQ5BY5g@mail.gmail.com>
	<48514B31-FC53-45DF-885F-DC9F22A5D567@mcs.st-andrews.ac.uk>
	<CAPLF6fNP55yFeqbqe-6CEC=aAWiVLdg6QZSm2BMfAS3g=TzFdw@mail.gmail.com>
Message-ID: <A9A6429A-E46F-4975-9796-793742299B0B@math.colostate.edu>




On Oct 11, 2013, at 10/11/13 8:43, Mark Flanagan <mark.evan.flanagan at gmail.com> wrote:

> That fixed it! I'm still a bit confused because there was no trouble
> running this code using gap (not pargap) and nowhere in my code do I
> explicitly reference the variable 'f1'.

The problem comes up in the communication between processes: ParGAP sends objects to a slave process by printing it into a string and sending this string for evaluation to the other machine. At this point the evaluation of `f1' happens, even if your code does not do so (but sends group elements to the other machine).

Regards,

    Alexander Hulpke


> 
> Thanks!
> 
> Best,
> Mark
> Dear Mark,
> 
> On 8 Oct 2013, at 20:57, Mark Flanagan <mark.evan.flanagan at gmail.com> wrote:
> 
>> Hello everyone,
>> 
>> Hopefully issues with ParGap are on-topic for the GAP forum.
>> 
>> Running ParGap with open mpi. ParList works with a simple function
>> loaded into ParGap with ParRead, eg ParList([1..10],testfunc) when
>> 
>> testfunc:= function(x) return x+x; end;;
>> 
>> is used, but in more complicated use cases,
>> ParList(producehoms(3),loopofhom) does not work:
>> 
>> gap> ParList(producehoms(3),loopofhom);
>> Error, Variable: 'f1' must have a value
>> Error, List Assignment: <rhss> must be a list with the same length as
>> <positions> (14\
>> ) in
>> result{range} := tmp; called from
>> <function "ParList">( <arguments> )
>> called from read-eval loop at line 3 of *stdin*
>> you can replace <rhss> via 'return <rhss>;'
>> brk> Error, Variable: 'f1' must have a value
>> 
>> producehoms(3) makes a list of homomorphisms and loopofhom is a
>> function, and  f1 is a generator of a group loaded in with ParRead.
>> List(producehoms(3),loopofhom) works as expected on master, and it
>> seems like ParRead worked because
>> 
>> SendRecvMsg("List(producehoms(3),loopofhom)",1);
>> 
>> produces the expected output.
>> 
>> Any thoughts on why ParList isn't working right? Would it just be
>> easier to parallelize my code manually, rather than relying on
>> ParList? Any advice is appreciated.
>> 
>> Mark
> 
> I think this is not a problem in ParGap: one can easily reproduce
> an instance of the same problem without ParGap:
> 
> gap> F:=FreeGroup("f1","f2");
> <free group on the generators [ f1, f2 ]>
> gap> f1;
> Error, Variable: 'f1' must have a value
> not in any function at line 2 of *stdin*
> 
> This happens because there is no variable in GAP named 'f1'.
> Instead, you can access generators of the group like here:
> 
> gap> F.1;
> f1
> 
> Alternatively, you may call 'AssignGeneratorVariables':
> 
> gap> AssignGeneratorVariables(F);
> #I  Assigned the global variables [ f1, f2 ]
> gap> f1;
> f1
> 
> but then remember to call it each time you define a new
> group with the same letter denoting generators, otherwise
> f1 may still point to a generator of the former group.
> 
> Hope this helps,
> Alexander
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From szgycs at szemerja-szasz.hu  Sat Oct 12 14:51:54 2013
From: szgycs at szemerja-szasz.hu (szgycs at szemerja-szasz.hu)
Date: Sat, 12 Oct 2013 15:51:54 +0200
Subject: [GAP Forum] =?utf-8?q?InputTextFile_string_input_as_Permutation?=
	=?utf-8?q?=3F?=
Message-ID: <c3259cf161b88840ee4145104ea840ad@szemerja-szasz.hu>

Permutation is not a string, but input from InputTextFile is a string. 
How can I transform a string to  a permutation?


From matan at svgalib.org  Sat Oct 12 15:13:08 2013
From: matan at svgalib.org (Matan Ziv-Av)
Date: Sat, 12 Oct 2013 17:13:08 +0300 (IDT)
Subject: [GAP Forum] InputTextFile string input as Permutation?
In-Reply-To: <c3259cf161b88840ee4145104ea840ad@szemerja-szasz.hu>
References: <c3259cf161b88840ee4145104ea840ad@szemerja-szasz.hu>
Message-ID: <alpine.LFD.2.03.1310121711530.3958@svgalib.org>

On Sat, 12 Oct 2013, szgycs at szemerja-szasz.hu wrote:

> Permutation is not a string, but input from InputTextFile is a string. How 
> can I transform a string to  a permutation?

There is the function EvalString().

I have a function for this purpose:

ReadAsExpression:=function(n)
   local f,e;
   f:=InputTextFile(n);
   e:=ReadAll(f);
   CloseStream(f);
   return EvalString(e);
end;



-- 
Matan Ziv-Av.                         matan at svgalib.org




From dmitrii.pasechnik at cs.ox.ac.uk  Sat Oct 12 21:46:48 2013
From: dmitrii.pasechnik at cs.ox.ac.uk (Dmitrii Pasechnik)
Date: Sat, 12 Oct 2013 21:46:48 +0100
Subject: [GAP Forum] InputTextFile string input as Permutation?
In-Reply-To: <c3259cf161b88840ee4145104ea840ad@szemerja-szasz.hu>
References: <c3259cf161b88840ee4145104ea840ad@szemerja-szasz.hu>
Message-ID: <20131012204648.GA7542@cs.ox.ac.uk>

On Sat, Oct 12, 2013 at 03:51:54PM +0200, szgycs at szemerja-szasz.hu wrote:
> Permutation is not a string, but input from InputTextFile is a
> string. How can I transform a string to  a permutation?

Do you really need to use InputTextFile()?
It is often easier to generate proper GAP input and
use Read().

Just in case,
Dmitrii


From mathpn59 at yahoo.com  Sat Oct 12 22:44:50 2013
From: mathpn59 at yahoo.com (Takjk Taj)
Date: Sat, 12 Oct 2013 14:44:50 -0700 (PDT)
Subject: [GAP Forum] Finding free presentation of a group
Message-ID: <1381614290.91336.YahooMailNeo@web163605.mail.gq1.yahoo.com>

Dear Gap?forum,

For a finite group G, let G\cong F/R for a free group F. If N is a normal subgroup of G. How we can find the normal subgroup S of F by GAP such that N\cong S/R?


Any suggestions are welcome.
Yours,
Takjk

From matliumh at gmail.com  Wed Oct 16 07:40:02 2013
From: matliumh at gmail.com (Minghui Liu)
Date: Wed, 16 Oct 2013 14:40:02 +0800
Subject: [GAP Forum] Urgently Seeking for Help in Calculating the Abelian
 Invariants of a Group with GAP
Message-ID: <CAEUmJrTiRd21Ho+9ms8s3A_eY0eJJk2KtMUU9LQs0WPgR_AtdA@mail.gmail.com>

Dear Sir/Madam,

I am a beginner of GAP and would like to use this program to determine the
structure of some groups. Here is the group I am interested in :

Let K_3 be the group generated by three elements a, b, c subject to the
relation that every simple commutator with repeated generators is equal to
1. (For example, [[[a, c], b], c] = 1.) Now let A_3 be the subgroup of K_3
generated by abc, [a, b][b, c][a, c], [[a, b], c] and [[a, c], b] and I
would like to determine the structure of abelianization of A_3. Here is my
code:

F3:=FreeGroup("a","b","c");
B3:=[Comm(Comm(F3.1,F3.2),F3.1),Comm(Comm(F3.1,F3.2),F3.2),Comm(Comm(F3.2,F3.3),F3.2),Comm(Comm(F3.2,F3.3),F3.3),Comm(Comm(F3.1,F3.3),F3.1),Comm(Comm(F3.1,F3.3),F3.3),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.1),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.1),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.1),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.1),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.1),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.1),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.2),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.2),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.2),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.2),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.2),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.2),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.3),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.3),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.3),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.3),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.3),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.3),];
K3:=F3/B3;
a:=K3.1;
b:=K3.2;
c:=K3.3;
A3:=Subgroup(K3,[a*b*c,Comm(a,b)*Comm(a,c)*Comm(b,c),Comm(Comm(a,b),c),
Comm(Comm(a,c),b)]);

But when I run the command AbelianInvariants(A3), the following error
message appeared:

Error, the coset enumeration has defined more than 4096000 cosets
 called from
TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
TryCosetTableInWholeGroup( H ) called from
CosetTableInWholeGroup( H ) called from
RelatorMatrixAbelianizedSubgroupRrs( G, H ) called from
...  at line 66 of *stdin*
type 'return;' if you want to continue with a new limit of 8192000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit

I thought it was because my groups are too complicated for GAP and thus I
tried a much simpler version of groups:

F2:=FreeGroup("a","b");
B2:=[Comm(Comm(F2.1,F2.2),F2.1),Comm(Comm(F2.1,F2.2),F2.2)];
K2:=F2/B2;
A2:=Subgroup(K2,[K2.1*K2.2,Comm(K2.1,K2.2)])
*
*
When I run the command AbelianInvariants(A2), the same error message
appeared.

As I urgently need to do these calculations, any assistance/advice will be
greatly appreciated. By the way, this is the first time that I write to
this forum; please forgive me if there is anything improper in my question.

Many thanks and best regards,

MH

From hulpke at math.colostate.edu  Wed Oct 16 17:23:27 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Wed, 16 Oct 2013 10:23:27 -0600
Subject: [GAP Forum] Urgently Seeking for Help in Calculating the
	Abelian Invariants of a Group with GAP
In-Reply-To: <CAEUmJrTiRd21Ho+9ms8s3A_eY0eJJk2KtMUU9LQs0WPgR_AtdA@mail.gmail.com>
References: <CAEUmJrTiRd21Ho+9ms8s3A_eY0eJJk2KtMUU9LQs0WPgR_AtdA@mail.gmail.com>
Message-ID: <C6334EE9-1646-4173-9138-9FD6F8F6E45E@math.colostate.edu>



Dear Forum, Dear Minghui Liu,

> 
> I thought it was because my groups are too complicated for GAP and thus I
> tried a much simpler version of groups:
> 
> F2:=FreeGroup("a","b");
> B2:=[Comm(Comm(F2.1,F2.2),F2.1),Comm(Comm(F2.1,F2.2),F2.2)];
> K2:=F2/B2;
> A2:=Subgroup(K2,[K2.1*K2.2,Comm(K2.1,K2.2)])
> *
> *
> When I run the command AbelianInvariants(A2), the same error message
> appeared.

The algorithm for abelian invariants of a subgroup constructs a coset table and rewrites relators. In your case A2 has infinite index in K2, so this will not terminate.

I am not aware of any algorithm that would deal with such situations automatically. What might be of help is to look at subgroups of finite index, containing A2. For example:

gap> pq:=EpimorphismPGroup(K2,2,10);Size(Image(pq));
[ a, b ] -> [ a1, a2 ]
536870912
gap> A3:=PreImage(pq,Image(pq,A2));
Group(<fp, no generators known>)
gap> AbelianInvariants(A3);
[ 0, 0, 1024 ]
gap> pq:=EpimorphismPGroup(K2,3,5);Size(Image(pq)); 
[ a, b ] -> [ a1, a2 ]
4782969
gap> A3:=PreImage(pq,Image(pq,A2));
Group(<fp, no generators known>)
gap> AbelianInvariants(A3);        
[ 0, 0, 243 ]
gap> pq:=EpimorphismPGroup(K2,5,3);Size(Image(pq));
[ a, b ] -> [ a1, a2 ]
390625
gap> A3:=PreImage(pq,Image(pq,A2));
Group(<fp, no generators known>)
gap> Index(K2,A3);
125
gap> AbelianInvariants(A3);         
[ 0, 0, 125 ]

from which I would naively guess that the invariants of A2 might be [0,0,0], but this is certainly no proof.

Best,

   Alexander Hulpke



From lvluyen at gmail.com  Thu Oct 17 16:42:52 2013
From: lvluyen at gmail.com (Le Van Luyen)
Date: Thu, 17 Oct 2013 16:42:52 +0100
Subject: [GAP Forum] Does there exist an isomorphism such that...
Message-ID: <CAMMpxrQGW9yJhwSP8Tn-ODZ7T04C+_2x3U+mOCMsAkdvYSXLow@mail.gmail.com>

Let G be a group with the order of Aut(G) very big.

Example:
gap>G:=SmallGroup(256,56092);;
gap> AutomorphismGroup(G);
<group of size 5348063769211699200 with 2 generators>

We suppose that s,t: G->G are group homomorphisms.
In GAP, Could you tell me a way to know whether there exists a group
isomorphism f:G->G such that fs=tf?

Thank you very much,

Bests,

Luyen

From hulpke at math.colostate.edu  Thu Oct 17 17:35:00 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu, 17 Oct 2013 10:35:00 -0600
Subject: [GAP Forum] Does there exist an isomorphism such that...
In-Reply-To: <CAMMpxrQGW9yJhwSP8Tn-ODZ7T04C+_2x3U+mOCMsAkdvYSXLow@mail.gmail.com>
References: <CAMMpxrQGW9yJhwSP8Tn-ODZ7T04C+_2x3U+mOCMsAkdvYSXLow@mail.gmail.com>
Message-ID: <AAE7B448-9164-452A-A3E3-B95C35C2A51A@math.colostate.edu>


Dear Forum,

On Oct 17, 2013, at 10/17/13 9:42, Le Van Luyen <lvluyen at gmail.com> wrote:

> Let G be a group with the order of Aut(G) very big.
> 
> Example:
> gap>G:=SmallGroup(256,56092);;
> gap> AutomorphismGroup(G);
> <group of size 5348063769211699200 with 2 generators>
> 
> We suppose that s,t: G->G are group homomorphisms.
> In GAP, Could you tell me a way to know whether there exists a group
> isomorphism f:G->G such that fs=tf?

I would try to first find, by having the automorphism group act on subgroups, an automorphism e, such that ker(s)=ker(t)^e and that Image(s)=Image(t)^e. After that we can assume WLOG that s and t have same kernel and image, and Aut(G) is reduced to the stabilizer A of these two subgroups.
Now you can look at these maps as isomorphism between G/ker(s) and Image(s). Go into the direct product of G/ker(s) with Image(s). For generators g1,g2,... of G/ker(s) you can represent s by the list of pairs (g1,g1^s),(g2,g2^s),... and t ditto.

Under the induced action of A on this direct product you now want to map the one list of pairs to the other.

How to do this best in practice might depend on the orders of kernel and image, feel free to send me an example for s and t and I'll have a look.

Best,

   Alexander Hulpke




-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke




From mathpn59 at yahoo.com  Thu Oct 17 22:52:04 2013
From: mathpn59 at yahoo.com (Takjk Taj)
Date: Thu, 17 Oct 2013 14:52:04 -0700 (PDT)
Subject: [GAP Forum] help
In-Reply-To: <1382044099.72841.YahooMailNeo@web163605.mail.gq1.yahoo.com>
References: <1381614290.91336.YahooMailNeo@web163605.mail.gq1.yahoo.com>
	<1382044099.72841.YahooMailNeo@web163605.mail.gq1.yahoo.com>
Message-ID: <1382046724.5254.YahooMailNeo@web163601.mail.gq1.yahoo.com>








Dear Gap?forum,



For a finite group G, let G\cong F/R for a free group F. If N is a normal subgroup of G. How we can find the normal subgroup S of F by GAP such that N\cong S/R?


Any suggestions are welcome.
Yours,
Takjk

From hulpke at math.colostate.edu  Thu Oct 17 22:59:22 2013
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Thu, 17 Oct 2013 15:59:22 -0600
Subject: [GAP Forum] Finding free presentation of a group
In-Reply-To: <1381614290.91336.YahooMailNeo@web163605.mail.gq1.yahoo.com>
References: <1381614290.91336.YahooMailNeo@web163605.mail.gq1.yahoo.com>
Message-ID: <302CBC19-1FAC-463C-A9B0-496455A5B1C8@math.colostate.edu>


Dear Forum,

On Oct 12, 2013, at 10/12/13 3:44, Takjk Taj <mathpn59 at yahoo.com> wrote:

> Dear Gap forum,
> 
> For a finite group G, let G\cong F/R for a free group F. If N is a normal subgroup of G. How we can find the normal subgroup S of F by GAP such that N\cong S/R?

If phi is a homomorphism from F to G   (likely constructed as
GroupHomomorphismByImages on the generators), take
PreImage(Phi,N)

Regards,

   Alexander Hulpke




From tendshumba at yahoo.com  Sun Oct 20 13:02:24 2013
From: tendshumba at yahoo.com (Tendshumba)
Date: Sun, 20 Oct 2013 14:02:24 +0200
Subject: [GAP Forum] (no subject)
Message-ID: <r0hvb71gf8nye5bs07ctwjvs.1382269714237@email.android.com>


I would like to have the permutation description of a collection of group elements {g1,g2,...,g_m} acting on the Cosets G/U_i where you have a descending chain G=U_0>U_1>...U_n-1>U_n=H for each i=1,...,n , n the order of G.How can I achieve this?
Tendai?
Sent from Samsung Mobile

From tendshumba at yahoo.com  Sun Oct 20 13:20:51 2013
From: tendshumba at yahoo.com (Tendshumba)
Date: Sun, 20 Oct 2013 14:20:51 +0200
Subject: [GAP Forum] (no subject)
Message-ID: <hu216ma2ak2wd7ebjfnoittd.1382271375816@email.android.com>

I would like get the description of the action of the action of a collection { g_1,..,g_m} of elements of a group G of order n on the Cosets G/U_i for each i=1
,...,n by right multiplication given a descending chain G=U_0>U_1>...>U_n-1>U_n=H of subgroups . How can i achieve this ?
Tendai?
?
Sent from Samsung Mobile

From matliumh at gmail.com  Mon Oct 21 16:33:59 2013
From: matliumh at gmail.com (Minghui Liu)
Date: Mon, 21 Oct 2013 23:33:59 +0800
Subject: [GAP Forum] Responding Time (Group Homomorphisms by Images)
Message-ID: <CAEUmJrRvY+b6zoeJmUo2vPy-R=MiUUoMUDVM+aQF3yfR+V2zkQ@mail.gmail.com>

Dear Sir/Madam,

I am trying to use GAP to construct group homomorphisms. In fact, I have a
list of groups K_n, each K_n is generated by n elements x_1, ... x_n
subject to some relations where n is at least 2. Now I want to construct
group homomorphisms f_{n,k} from K_n to K_{n-1} defined by f_{n,k}(x_1) =
x_1, ..., f_{n,k}(x_{k-1}) = x_{k-1}, f_{n,k}(x_k) = e, f_{n,k}(x_{k+1}) =
x_{k}, ..., f_{n,k}(x_n) = x_{n-1}.

For example,

f_{3,1} from K_3 to K_2 maps x_1 to e, x_2 to x_1 and x_3 to x_2;

f_{3,2} from K_3 to K_2 maps x_1 to x_1, x_2 to e and x_3 to x_2;

f_{3,3} from K_3 to K_2 maps x_1 to x_1, x_2 to x_2 and x_3 to e.

Now I am interested in studying the intersection of ker(f_{n, k}), where n
is some fixed integer and k runs from 1 to n. When I put my question to
GAP, I have used the following commands:

F2:=FreeGroup("a","b");

B2:=[Comm(Comm(F2.1,F2.2),F2.1),Comm(Comm(F2.1,F2.2),F2.2)];

K2:=F2/B2;

F3:=FreeGroup("a","b","c");

B3:=[Comm(Comm(F3.1,F3.2),F3.1),Comm(Comm(F3.1,F3.2),F3.2),
Comm(Comm(F3.1,F3.3),F3.1),Comm(Comm(F3.1,F3.3),F3.3),
Comm(Comm(F3.2,F3.1),F3.2),Comm(Comm(F3.2,F3.1),F3.1),
Comm(Comm(F3.2,F3.3),F3.2),Comm(Comm(F3.2,F3.3),F3.3),
Comm(Comm(F3.3,F3.1),F3.3),Comm(Comm(F3.3,F3.1),F3.1),
Comm(Comm(F3.3,F3.2),F3.3),Comm(Comm(F3.3,F3.2),F3.2),
Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.1),
Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.2),
Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.3),
Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.1),
Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.2),
Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.3),
Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.1),
Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.2),
Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.3),
Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.1),
Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.2),
Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.3),
Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.1),
Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.2),
Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.3),
Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.1),
Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.2),
Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.3)];

K3:=F3/B3;

f321:=GroupHomomorphismByImages(K3,K2,[K3.1,K3.2,K3.3],[One(K2),K2.1,K2.2]);

Then it takes like forever for my GAP to respond. Thus it seems hopeless to
deal with the cases where n is 4 or larger. Just in case that you need this
information, I am running GAP4.6.5 on my six-year-old computer.

Any comments or suggestions? Your assistance will be greatly appreciated.

By the way, after hitting "Enter" how can we roughly know how long it would
take for GAP to respond? From my experience sometimes it could be a few
minutes and sometimes it does not respond after about one hour and I choose
to terminate it. If I know it would respond in say two hours I probably can
wait; but what if it takes dozens or hundreds of hours?

Best regards,

Minghui

From aliasar at gazi.edu.tr  Wed Oct 23 10:00:13 2013
From: aliasar at gazi.edu.tr (Ali Osman ASAR)
Date: Wed, 23 Oct 2013 12:00:13 +0300 (EEST)
Subject: [GAP Forum] (no subject)
Message-ID: <1046585706.633278.1382518813615.JavaMail.root@gazi.edu.tr>



Dear GAP Foum, 
I have a simple problem which I cannot overcome. I do not know how to save , where to save a GAP work. I would be grateful if someone could?explain this by a? short example.?(In GAP there is an example gap>a:=1; gap>Saveworkspace("savefile");true gap>quit. What is the value of "savefile" here? 
Sincerely yours 
A.O.Asar

From zeinab_foruzanfar at iust.ac.ir  Sat Oct 19 10:52:03 2013
From: zeinab_foruzanfar at iust.ac.ir (zeinab foruzanfar)
Date: Sat, 19 Oct 2013 13:22:03 +0330
Subject: [GAP Forum] disjoint cycle decompositions
Message-ID: <WC20131019095203.5802ED@iust.ac.ir>

Hi
I want a command in GAP to show the cycle structure of elements of a Group 
in their disjoint cycle decompositions. For instance the Symmetric group S_3 
has 3 cycles of length 2 and 2 cycles of length 3.Generraly I want to see 
the elements of a group in their disjoint cycle decompositions.
Thanks




From urvashi131 at gmail.com  Tue Oct 22 17:06:18 2013
From: urvashi131 at gmail.com (Urvashi Sharma)
Date: Tue, 22 Oct 2013 21:36:18 +0530
Subject: [GAP Forum] Program to find central automorphisms
Message-ID: <000001cecf40$a76761f0$f63625d0$@com>

Dear Sir/Madam

 

I am Mahak Sharma, a research scholar at Thapar University(Patiala),India
working on automorphisms of finite p-groups. I am using GAP and I want to
know

 

how to find central automorphisms of a finite p-group in GAP.

 

Please send the program for the same in GAP.

 

 

Best Regards

Mahak Sharma

Research Scholar

School of Mathematics and Computer Applications

Thapar University,Patiala(Punjab)

India

 

 


From rrburns at cox.net  Thu Oct 24 02:07:03 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 24 Oct 2013 01:07:03 +0000 (UTC)
Subject: [GAP Forum] D8 as a product of Q=D8/Center and its Center
Message-ID: <loom.20131024T030134-180@post.gmane.org>

Dear Forum

I am tryng to use GAP to "reconstruct" the group D8 as some sort of product
of its quotient group Q=D8/Center(D8) and its Center(D8).

gap> D8:=DihedralGroup(8); # or however best defined for this
<pc group of size 8 with 3 generators>
gap> ZD8:=Center(D8);
Group([ f3 ])
gap> Q:=D8/ZD8;
Group([ f1, f2, <identity> of ... ])
gap> StructureDescription(Q);
"C2 x C2"

I know it can't be direct product. I reorganized the Cayley Graph for D8 by
grouping the cosets as nodes and and looking at the lines connecting the
nodes. They cross and so a direct product will not do it. Verify this:

gap> d:=DirectProduct(Q,ZD8);
<pc group of size 8 with 3 generators>
gap> StructureDescription(d);
"C2 x C2 x C2"

Not a direct product. See if I can make a semidirect product

gap> A:=AutomorphismGroup(ZD8);
<group of size 1 with 2 generators>
gap> List(A,Order);
[ 1 ]

I don't see how to match up any orders and proceed from here.

I would appreciate any help as how to use GAP functionality to construct 
this product Thank you for any help.
      Ron



From A.Egri-Nagy at herts.ac.uk  Thu Oct 24 02:18:57 2013
From: A.Egri-Nagy at herts.ac.uk (Attila Egri-Nagy)
Date: Thu, 24 Oct 2013 12:18:57 +1100
Subject: [GAP Forum] D8 as a product of Q=D8/Center and its Center
Message-ID: <CAP=h6j2zyOC_8UnSFzByOKN9yO+JpgCh91t39ZyKZp0B9saP+g@mail.gmail.com>

Dear Ron,

Using the SgpDec pacakge (sgpdec.sf.net) you can construct subgroups
of the wreath product (called cascade products).
See Example 5 in http://arxiv.org/abs/1303.0091.

The package is still in development, so please let me know if you need
help installing/using it.

best wishes,
Attila

On Thu, Oct 24, 2013 at 12:07 PM, Sopsku <rrburns at cox.net> wrote:
> Dear Forum
>
> I am tryng to use GAP to "reconstruct" the group D8 as some sort of product
> of its quotient group Q=D8/Center(D8) and its Center(D8).
>
> gap> D8:=DihedralGroup(8); # or however best defined for this
> <pc group of size 8 with 3 generators>
> gap> ZD8:=Center(D8);
> Group([ f3 ])
> gap> Q:=D8/ZD8;
> Group([ f1, f2, <identity> of ... ])
> gap> StructureDescription(Q);
> "C2 x C2"
>
> I know it can't be direct product. I reorganized the Cayley Graph for D8 by
> grouping the cosets as nodes and and looking at the lines connecting the
> nodes. They cross and so a direct product will not do it. Verify this:
>
> gap> d:=DirectProduct(Q,ZD8);
> <pc group of size 8 with 3 generators>
> gap> StructureDescription(d);
> "C2 x C2 x C2"
>
> Not a direct product. See if I can make a semidirect product
>
> gap> A:=AutomorphismGroup(ZD8);
> <group of size 1 with 2 generators>
> gap> List(A,Order);
> [ 1 ]
>
> I don't see how to match up any orders and proceed from here.
>
> I would appreciate any help as how to use GAP functionality to construct
> this product Thank you for any help.
>       Ron
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum


From alexk at mcs.st-andrews.ac.uk  Thu Oct 24 10:30:26 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 24 Oct 2013 10:30:26 +0100
Subject: [GAP Forum] (no subject)
In-Reply-To: <1046585706.633278.1382518813615.JavaMail.root@gazi.edu.tr>
References: <1046585706.633278.1382518813615.JavaMail.root@gazi.edu.tr>
Message-ID: <FE0DF339-3A76-4B52-869F-2ED8721762C1@mcs.st-andrews.ac.uk>

Dear Ali Osman,

Please see http://www.gap-system.org/Faq/faq.html#5.4 about LogTo and SaveWorkspace. These two commands are quite different, and the usage depends on whether do you want to save the input and output or the full state of your GAP session. Saving a workspace, one will not be able to read it later in a different version of GAP, while LogTo produces just a text file with the history of inputs and outputs.

Hope this helps,
Alexander


On 23 Oct 2013, at 10:00, Ali Osman ASAR <aliasar at gazi.edu.tr> wrote:

> 
> 
> Dear GAP Foum, 
> I have a simple problem which I cannot overcome. I do not know how to save , where to save a GAP work. I would be grateful if someone could explain this by a  short example. (In GAP there is an example gap>a:=1; gap>Saveworkspace("savefile");true gap>quit. What is the value of "savefile" here? 
> Sincerely yours 
> A.O.Asar





From rrburns at cox.net  Thu Oct 24 21:25:37 2013
From: rrburns at cox.net (Sopsku)
Date: Thu, 24 Oct 2013 20:25:37 +0000 (UTC)
Subject: [GAP Forum] D8 as a product of Q=D8/Center and its Center
References: <loom.20131024T030134-180@post.gmane.org>
Message-ID: <loom.20131024T221529-186@post.gmane.org>

Sopsku <rrburns at ...> writes:
> 
> Dear Forum
> 
> I am tryng to use GAP to "reconstruct" the group D8 as some sort of product
> of its quotient group Q=D8/Center(D8) and its Center(D8).
> 
> gap> D8:=DihedralGroup(8); # or however best defined for this
> <pc group of size 8 with 3 generators>
> gap> ZD8:=Center(D8);
> Group([ f3 ])
> gap> Q:=D8/ZD8;
> Group([ f1, f2, <identity> of ... ])
> gap> StructureDescription(Q);
> "C2 x C2"
> 
> I know it can't be direct product. I reorganized the Cayley Graph for D8 by
> grouping the cosets as nodes and and looking at the lines connecting the
> nodes. They cross and so a direct product will not do it. Verify this:
> 
> gap> d:=DirectProduct(Q,ZD8);
> <pc group of size 8 with 3 generators>
> gap> StructureDescription(d);
> "C2 x C2 x C2"
> 
> Not a direct product. See if I can make a semidirect product
> 
> gap> A:=AutomorphismGroup(ZD8);
> <group of size 1 with 2 generators>
> gap> List(A,Order);
> [ 1 ]
> 
> I don't see how to match up any orders and proceed from here.
> 
> I would appreciate any help as how to use GAP functionality to construct 
> this product Thank you for any help.
>       Ron
> 

Dear Forum,

In my original pointing I made a mistake in stating the I could not
"reconstruct" the group D8 as some sort of product of its quotient group
Q=D8/Center(D8) and its Center(D8). In fact (since Q iso C2XC2 and
Center(D8) iso C2) this is simply done as follows:

gap> C2 := Group( (1,2) );;
gap> C2xC2 := Group( (1,3)(2,4), (1,2)(3,4) );;
gap> 
gap> A:=AutomorphismGroup(C2xC2);;
gap> L:=Elements(A);;
gap> List(L,Order);
[ 1, 2, 2, 3, 3, 2 ]
gap> phi:=GroupHomomorphismByImages(C2,A,[C2.1],[L[2]]);
[ (1,2) ] -> [ [ (1,3)(2,4), (1,2)(3,4) ] -> [ (1,4)(2,3), (1,2)(3,4) ] ]
gap> s:=SemidirectProduct(C2,phi,C2xC2);
Group([ (3,4)(5,6), (3,5)(4,6), (1,2)(5,6) ])
gap> StructureDescription(s);
"D8"

Which is what I wanted to see. As pointed out to me by Attila Egri-Nagy I
can also construct D8 as a wreath product from my C2's

gap> w:=WreathProduct(C2, C2);
Group([ (1,2), (3,4), (1,3)(2,4) ])
gap> StructureDescription(w);
"D8"

but this does not show D8/Center(D8) X Center(D8) as explicitly as the
semidirect product shows it.

I apologize for the mistake in my original posting and thank you all for
your consideration.
  Ron        





From bernhard.boehmler at googlemail.com  Sun Oct 27 17:56:18 2013
From: bernhard.boehmler at googlemail.com (Bernhard Boehmler)
Date: Sun, 27 Oct 2013 18:56:18 +0100
Subject: [GAP Forum] Question concerning the GAP package qpa and injective
 modules of quotients of path algebras
Message-ID: <CAD1scQZZBtBeqP1m+x5aRKqZ4ZHLBMA46am0ZiF24S+t7Gh=0Q@mail.gmail.com>

Dear GAP forum,

 I would like to test with the qpa package (qpa=quivers and path algebras),
whether a projective A-module is isomorphic to the dual of another
projective module (as modules).

 Here, A=kQ/I is a quotient of a path algebra by an admissible ideal I.

 I have projective A-modules P_1 and P_2 and its dual
I_2:=DualOfModule(P_2), but

 when I use the command IsomorphicModules(P_1,I_2), I get an error massage,
because I_2 is not an A-module, but an A^op ? module.

 Therefore, I would like to ask, if anybody knows, how to circumvent this
problem.

 Thank you very much.


 Kind regards,

 Bernhard

From lijr07 at gmail.com  Wed Oct 30 11:04:28 2013
From: lijr07 at gmail.com (Jianrong Li)
Date: Wed, 30 Oct 2013 13:04:28 +0200
Subject: [GAP Forum] represent elements of Weyl groups or affine Weyl groups
	in terms of matrics
Message-ID: <CABoaVnX-jgDpQVdt26+xQOxkeCR=81rEnMVgfqwosp7O1xNZ9g@mail.gmail.com>

Dear Forum,

Let s_1, ..., s_n be simple reflections. w=s_{i_1}...s_{i_k} be an element
of Weyl group. Is there some function in GAP which can produce the matrix
expression of w? Thank you very much.

Best wishes,
Jianrong.

From tendshumba at yahoo.com  Fri Nov  1 12:10:34 2013
From: tendshumba at yahoo.com (tendai shumba)
Date: Fri, 1 Nov 2013 05:10:34 -0700 (PDT)
Subject: [GAP Forum] Binary code generating function
Message-ID: <1383307834.65147.YahooMailNeo@web140104.mail.bf1.yahoo.com>

Dear Forum
I am trying to generate binary codes ?given a basis. I found :?
CodeGenBy:=function(codebasis)
return Subspace(GF(2)^Length(codebasis[1]),codebasis) works but it done not work?
for the empty basis codebasis:=[];
How can I make this to work?

Tendai Shumba

From oyvind.solberg at math.ntnu.no  Mon Nov  4 07:46:34 2013
From: oyvind.solberg at math.ntnu.no (Oeyvind Solberg)
Date: Mon, 4 Nov 2013 07:46:34 +0000 (UTC)
Subject: [GAP Forum] Question concerning the GAP package qpa and
	injective modules of quotients of path algebras
References: <CAD1scQZZBtBeqP1m+x5aRKqZ4ZHLBMA46am0ZiF24S+t7Gh=0Q@mail.gmail.com>
Message-ID: <loom.20131104T081947-390@post.gmane.org>

Bernhard Boehmler <bernhard.boehmler at ...> writes:

> 
> Dear GAP forum,
> 
>  I would like to test with the qpa package (qpa=quivers and path algebras),
> whether a projective A-module is isomorphic to the dual of another
> projective module (as modules).
> 
>  Here, A=kQ/I is a quotient of a path algebra by an admissible ideal I.
> 
>  I have projective A-modules P_1 and P_2 and its dual
> I_2:=DualOfModule(P_2), but
> 
>  when I use the command IsomorphicModules(P_1,I_2), I get an error massage,
> because I_2 is not an A-module, but an A^op ? module.
> 
>  Therefore, I would like to ask, if anybody knows, how to circumvent this
> problem.
> 
>  Thank you very much.
> 
>  Kind regards,
> 
>  Bernhard
> 
Dear Bernhard and the GAP Forum,
The vector space duality will induce a duality from mod A
to mod A^op. Even if  A  and  A^op are isomorphic,  A  and 
A^op  will be different objects in GAP. So if you want to
compare an (indecomposable) projective module and its dual,
one has to construct the indecomposable projective modules
over A^op, and then apply the duality. This can also be 
done directly with the command IndecInjectiveModules(). 

Alternatively, to check that a projective module is isomorphic 
to the dual of some projective module, this is the same as 
asking if the projective module also is injective. 

An example with a Nakayama algebra with four indecomposable 
projectives:

gap> A := NakayamaAlgebra(Rationals, [3,3,3,3]);
<Rationals[<quiver with 4 vertices and 4 arrows>]/
<two-sided ideal in <Rationals[<quiver with 4 vertices and 4 arrows>]>, (4
generators)>>
gap> P := IndecProjectiveModules(A);  
[ <[ 1, 1, 1, 0 ]>, <[ 0, 1, 1, 1 ]>, <[ 1, 0, 1, 1 ]>, <[ 1, 1, 0, 1 ]> ]
gap> Aop := OppositeAlgebra(A);
<Rationals[<quiver with 4 vertices and 4 arrows>]/
<two-sided ideal in <Rationals[<quiver with 4 vertices and 4 arrows>]>, (4
generators)>>
gap> Pop := IndecProjectiveModules(Aop);
[ <[ 1, 0, 1, 1 ]>, <[ 1, 1, 0, 1 ]>, <[ 1, 1, 1, 0 ]>, <[ 0, 1, 1, 1 ]> ]
gap> DPop := List(Pop, p -> DualOfModule(p));
[ <[ 1, 0, 1, 1 ]>, <[ 1, 1, 0, 1 ]>, <[ 1, 1, 1, 0 ]>, <[ 0, 1, 1, 1 ]> ]
gap> IsomorphicModules(P[1], DPop[1]);
false
gap> IsomorphicModules(P[1], DPop[2]);
false
gap> IsomorphicModules(P[1], DPop[3]);
true
gap> IsomorphicModules(P[1], DPop[4]);
false
gap> # or alternatively
gap> IsInjectiveModule(P[1]);
true

Best regards, Oeyvind. 



From caj21 at st-andrews.ac.uk  Sun Nov 10 19:54:30 2013
From: caj21 at st-andrews.ac.uk (Chris Jefferson)
Date: Sun, 10 Nov 2013 19:54:30 +0000
Subject: [GAP Forum] Naming of Primitive Groups
Message-ID: <527FE476.8080506@st-andrews.ac.uk>

After trying to track down some strange behavior in a program, I was 
surprised to find the names of the first two primitive groups of size 10:

gap> PrimitiveGroup(10, 1);
A(5)
gap> PrimitiveGroup(10, 2);
S(5)

These are, unsurprisingly, the same names as:

gap> PrimitiveGroup(5,4);
A(5)
gap> PrimitiveGroup(5,5);
S(5)

Out of curiosity, are these groups related in some non-obvious way, and 
is there any reason the names of the primitive groups are not unique?

Chris



From colva at mcs.st-and.ac.uk  Sun Nov 10 20:37:55 2013
From: colva at mcs.st-and.ac.uk (Colva Roney-Dougal)
Date: Sun, 10 Nov 2013 20:37:55 +0000
Subject: [GAP Forum] Naming of Primitive Groups
In-Reply-To: <527FE476.8080506@st-andrews.ac.uk>
References: <527FE476.8080506@st-andrews.ac.uk>
Message-ID: <FB355EDC-B65E-4679-858D-BAED0F5F5F65@mcs.st-and.ac.uk>

Hi Chris

They are isomorphic groups, so they have the same name. In both cases they?re the alternating and symmetric groups on 5 points; the ones of degree 5 are the natural action, the ones of degree 10 are the actions on unordered pairs. In general any group has multiple primitive actions. 

Best wishes

Colva

On 10 Nov 2013, at 19:54, Chris Jefferson <caj21 at st-andrews.ac.uk> wrote:

> After trying to track down some strange behavior in a program, I was surprised to find the names of the first two primitive groups of size 10:
> 
> gap> PrimitiveGroup(10, 1);
> A(5)
> gap> PrimitiveGroup(10, 2);
> S(5)
> 
> These are, unsurprisingly, the same names as:
> 
> gap> PrimitiveGroup(5,4);
> A(5)
> gap> PrimitiveGroup(5,5);
> S(5)
> 
> Out of curiosity, are these groups related in some non-obvious way, and is there any reason the names of the primitive groups are not unique?
> 
> Chris
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From sreedevimk at gmail.com  Sat Oct 26 19:03:15 2013
From: sreedevimk at gmail.com (Sreedevi Muthukumar)
Date: Sat, 26 Oct 2013 18:03:15 -0000
Subject: [GAP Forum] Issue with "Read" function - in GAP
Message-ID: <CAOu4GZ8ysYBLOpBf2bx5cbEzwvVwEF5iwQ+H2kLFYxTZpM7Deg@mail.gmail.com>

Dear All,

I'm a new GAP user and a student, I'm working with Grape package in GAP to
learn about graphs.

I tried to execute a "xxx.g"  file using "Read" function as given below in
two methods.

Please kindly check the methods I have tried and guide me to correct this
problem.


*Method 1: *

As Read("Path/filename.g"); function is used to read and execute set of
commands in GAP.

I created a file named "Symm_Star_3.g" to create a cayley graph.

*Symm_Star_3.g*
C := CayleyGraph(SymmetricGroup(3),[(1,2),(1,3)]);
Diameter(C);

After executing  the Read function I got the below error message.

gap>
Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
Error, Variable: 'CayleyGraph' must have a value
not in any function at line 1 of
C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g

*As CayleyGraph command is present in grape package , I invoked the grape
package as follows,then executed the .g file*

gap> LoadPackage("grape");
?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Loading  GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
true

gap>
Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
gap>

Now after invoking the grape package and then executing the Read function,
is not producing any output as shown above.

*Method 2:*

I tried to invoke the package directly from the .g file as follows.

*Symm_Star_3.g*
*
*
LoadPackage("grape");
C := CayleyGraph(SymmetricGroup(3),[(1,2),(1,3)]);
Diameter(C);


Now executing the Read function , is just invoking the package and not
executing the other commands in the .g file.

gap>
Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Loading  GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
gap>


Please guide me to correct this issue and help me to use "Read" function ,
to read a file with set of graph commands, after invoking Grape package.

Thanking you,
Sree Devi.

From sreedevimk at gmail.com  Thu Oct 31 03:12:02 2013
From: sreedevimk at gmail.com (Sreedevi Muthukumar)
Date: Wed, 30 Oct 2013 22:12:02 -0500
Subject: [GAP Forum] New GAP user - have few queries.
Message-ID: <CAOu4GZ-WfoYNzK+jnOGVvq97bB2x+q5+N_-OgMQ3VK+x-YSxKA@mail.gmail.com>

Dear All,

I'm a new GAP user and a student. I have few queries in GAP systems
software.
Could someone please point me to some links or documents or packages
available in GAP to perform the below computations in GAP.

( 1)  I'm looking for a way to use GAP to analyze simple cayley graphs like
                    Cycles,Toroids,Binary hypercube and Cayley graphs for
matrix groups.
      How to use GAP to do these computations.

(2) Is there a way to give the output of GAP computations to a graphic
package to          visually draw cayley graphs.

Thank you.

Sincerely,
Sree Devi.

From caj21 at st-andrews.ac.uk  Sun Nov 10 22:29:55 2013
From: caj21 at st-andrews.ac.uk (Chris Jefferson)
Date: Sun, 10 Nov 2013 22:29:55 +0000
Subject: [GAP Forum] Issue with "Read" function - in GAP
In-Reply-To: <CAOu4GZ8ysYBLOpBf2bx5cbEzwvVwEF5iwQ+H2kLFYxTZpM7Deg@mail.gmail.com>
References: <CAOu4GZ8ysYBLOpBf2bx5cbEzwvVwEF5iwQ+H2kLFYxTZpM7Deg@mail.gmail.com>
Message-ID: <528008E3.5050207@st-andrews.ac.uk>

The short answer is, your code is working as (I think) you expect, 
except when you call 'Read', GAP does not print out results after every 
statement, like it does in interactive mode.

So, you have to have a 'LoadPackage("grape")' either at the start of 
your .g file, or interactively (or both, it doesn't matter if you load a 
package twice).

GAP has read your file and run all the commands, you can see this by 
typing 'C' after your Read, like this:

gap> Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
gap> C;
rec( adjacencies := [ [ 3, 6 ] ], group := Group([ (1,4,5)(2,3,6), (1,3)(2,4)(5,6) ]), isGraph := true, isSimple := true, names := [ (), (2,3), (1,2), (1,2,3), (1,3,2), (1,3) ], order := 6,
   representatives := [ 1 ], schreierVector := [ -1, 2, 2, 1, 1, 1 ] )

If you want output from a file you read, then use the Print statement. For example, changing your file to:

LoadPackage("grape");
C := CayleyGraph(SymmetricGroup(3),[(1,2),(1,3)]);
Print("The Diameter is:", Diameter(C), "\n");

Gives me the output:

??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Loading  GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
The Diameter is:3


(The "\n" in the 'Print' Statement is a term used in many languages for "start a new line")


  On 26/10/13 19:03, Sreedevi Muthukumar wrote:
> Dear All,
>
> I'm a new GAP user and a student, I'm working with Grape package in GAP to
> learn about graphs.
>
> I tried to execute a "xxx.g"  file using "Read" function as given below in
> two methods.
>
> Please kindly check the methods I have tried and guide me to correct this
> problem.
>
>
> *Method 1: *
>
> As Read("Path/filename.g"); function is used to read and execute set of
> commands in GAP.
>
> I created a file named "Symm_Star_3.g" to create a cayley graph.
>
> *Symm_Star_3.g*
> C := CayleyGraph(SymmetricGroup(3),[(1,2),(1,3)]);
> Diameter(C);
>
> After executing  the Read function I got the below error message.
>
> gap>
> Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
> Error, Variable: 'CayleyGraph' must have a value
> not in any function at line 1 of
> C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g
>
> *As CayleyGraph command is present in grape package , I invoked the grape
> package as follows,then executed the .g file*
>
> gap> LoadPackage("grape");
> ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
> Loading  GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
> by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
> Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
> ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
> true
>
> gap>
> Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
> gap>
>
> Now after invoking the grape package and then executing the Read function,
> is not producing any output as shown above.
>
> *Method 2:*
>
> I tried to invoke the package directly from the .g file as follows.
>
> *Symm_Star_3.g*
> *
> *
> LoadPackage("grape");
> C := CayleyGraph(SymmetricGroup(3),[(1,2),(1,3)]);
> Diameter(C);
>
>
> Now executing the Read function , is just invoking the package and not
> executing the other commands in the .g file.
>
> gap>
> Read("C:/Users/Home/Desktop/Collage/Independent_Studies/Programs/Symm_Star_3.g");
> ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
> Loading  GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
> by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
> Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
> ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
> gap>
>
>
> Please guide me to correct this issue and help me to use "Read" function ,
> to read a file with set of graph commands, after invoking Grape package.
>
> Thanking you,
> Sree Devi.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From lijr07 at gmail.com  Mon Nov 11 08:52:03 2013
From: lijr07 at gmail.com (Jianrong Li)
Date: Mon, 11 Nov 2013 10:52:03 +0200
Subject: [GAP Forum] compute orbits
Message-ID: <CABoaVnXO7ui+rnu08LjGHTc6BSNPHgVN7xR5AuD5Ey-Aze7Oog@mail.gmail.com>

Dear all,

I am a new GAP user. I have a group generated by two elements e1, e2. e1,
e2 acts on a set U of lower triangular matrices in some way. Is there some
function in GAP that can compute the orbits of e1, e2? Thank you very much.

Best wishes,
Jianrong.

From bernhard.boehmler at googlemail.com  Mon Nov 11 13:26:13 2013
From: bernhard.boehmler at googlemail.com (Bernhard Boehmler)
Date: Mon, 11 Nov 2013 14:26:13 +0100
Subject: [GAP Forum] Compute Direct sum M:=M_1\oplus M_2 of modules and
	End(M) with GAP
Message-ID: <CAD1scQbeLETT=GXogY3qKiVjx8ROjZkYAKkSPju4eczsX1F89A@mail.gmail.com>

Dear GAP forum,

I am interested in computing End_A (M) for a finitely generated A-Module M.
Here, A is a finitely generated Algebra (which should not be assumed to be
necessarily an elementary algebra).

I tried the following example (thereby restricting the considerations to a
group algebra, which is in this special case an elementary algebra):

After having typed

k:=GF(3);;
G:=CyclicGroup(3);;
R:=GroupRing(k,G);;
f:=IsomorphismMatrixAlgebra(R);;
kG:=Image(f);;

in GAP, I would like to enter the kG-module M:=(kG) \oplus (k)
and compute End_{kG} (M) as a subalgebra of a full matrix algebra
with the aid of the GAP package MeatAxe (or other GAP-packages), but,
unfortunately, I wasn't able to find out, how to do that.

Therefore, I would be very thankful, if somebody was able to explain, how
to do this.

Thank you very much for your help.

Kind regards,
Bernhard Boehmler

From nehamakhijani at gmail.com  Tue Nov 12 16:11:44 2013
From: nehamakhijani at gmail.com (Neha Makhijani)
Date: Tue, 12 Nov 2013 11:11:44 -0500
Subject: [GAP Forum] Query - Character Table PSL(2,8) mod 2
Message-ID: <CAENqgLbk_Mh__WEkBBSC++TNb5Fyb=DsYDpSzWGgYrWDJrSYoA@mail.gmail.com>

How do I access the Brauer table of  PSL(2,8) mod 2 using GAP?


Thanks!
Neha

From Bill.Allombert at math.u-bordeaux1.fr  Tue Nov 12 17:13:09 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Tue, 12 Nov 2013 18:13:09 +0100
Subject: [GAP Forum] Query - Character Table PSL(2,8) mod 2
In-Reply-To: <CAENqgLbk_Mh__WEkBBSC++TNb5Fyb=DsYDpSzWGgYrWDJrSYoA@mail.gmail.com>
References: <CAENqgLbk_Mh__WEkBBSC++TNb5Fyb=DsYDpSzWGgYrWDJrSYoA@mail.gmail.com>
Message-ID: <20131112171309.GE8572@yellowpig>

On Tue, Nov 12, 2013 at 11:11:44AM -0500, Neha Makhijani wrote:
> How do I access the Brauer table of  PSL(2,8) mod 2 using GAP?

T:= CharacterTable("L2(8)") mod 2;
Display(T);

Cheers,
Bill.


From nehamakhijani at gmail.com  Tue Nov 12 17:19:11 2013
From: nehamakhijani at gmail.com (Neha Makhijani)
Date: Tue, 12 Nov 2013 12:19:11 -0500
Subject: [GAP Forum] Query - Character Table PSL(2,8) mod 2
In-Reply-To: <20131112171309.GE8572@yellowpig>
References: <CAENqgLbk_Mh__WEkBBSC++TNb5Fyb=DsYDpSzWGgYrWDJrSYoA@mail.gmail.com>
	<20131112171309.GE8572@yellowpig>
Message-ID: <CAENqgLaC6awpqvfqGdmyDAXPETBjE+vxF_caX7xChTDZVp3Ovg@mail.gmail.com>

thanks!


On Tue, Nov 12, 2013 at 12:13 PM, Bill Allombert <
Bill.Allombert at math.u-bordeaux1.fr> wrote:

> On Tue, Nov 12, 2013 at 11:11:44AM -0500, Neha Makhijani wrote:
> > How do I access the Brauer table of  PSL(2,8) mod 2 using GAP?
>
> T:= CharacterTable("L2(8)") mod 2;
> Display(T);
>
> Cheers,
> Bill.
>

From liveat1892 at gmail.com  Thu Nov 14 21:26:26 2013
From: liveat1892 at gmail.com (sam johnson)
Date: Thu, 14 Nov 2013 23:26:26 +0200
Subject: [GAP Forum] Need Help with first gap code
Message-ID: <CABFFSey++ZLURig-nPeNg7nc=pAcVBWbCFQ8AR3TcKNE7ra28g@mail.gmail.com>

Hey guys I'm new to this forum and i need help with my code. My code should
basically return the position of the maximum element in the list which is
quite easy the problem that it keeps giving me the following message and
I'm sure the logic of the code is correct.

Code:
whereismax := function(L)
    local x, maxpos;
    maxpos := 0;
    for x in [1..Size(L)-1]do
         if  L[x] > L[maxpos] then
            maxpos :=  x;
         fi;
    od;
    return maxpos;
end;


Error message:
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 1st choice method found for `[]' on 2 arguments called from
Size( L ) called from
<function "whereismax">( <arguments> )
 called from read-eval loop at line 40 of *stdin*

From benjamin.sambale at gmail.com  Thu Nov 14 21:40:35 2013
From: benjamin.sambale at gmail.com (Benjamin Sambale)
Date: Thu, 14 Nov 2013 22:40:35 +0100
Subject: [GAP Forum] Need Help with first gap code
In-Reply-To: <CABFFSey++ZLURig-nPeNg7nc=pAcVBWbCFQ8AR3TcKNE7ra28g@mail.gmail.com>
References: <CABFFSey++ZLURig-nPeNg7nc=pAcVBWbCFQ8AR3TcKNE7ra28g@mail.gmail.com>
Message-ID: <52854353.8020307@gmail.com>

A short answer: lists start with 1 in GAP, i.e. L[0] is not allowed.

Best,
Benjamin

Am 14.11.2013 22:26, schrieb sam johnson:
> Hey guys I'm new to this forum and i need help with my code. My code should
> basically return the position of the maximum element in the list which is
> quite easy the problem that it keeps giving me the following message and
> I'm sure the logic of the code is correct.
>
> Code:
> whereismax := function(L)
>      local x, maxpos;
>      maxpos := 0;
>      for x in [1..Size(L)-1]do
>           if  L[x] > L[maxpos] then
>              maxpos :=  x;
>           fi;
>      od;
>      return maxpos;
> end;
>
>
> Error message:
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 1st choice method found for `[]' on 2 arguments called from
> Size( L ) called from
> <function "whereismax">( <arguments> )
>   called from read-eval loop at line 40 of *stdin*
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From liveat1892 at gmail.com  Fri Nov 15 00:15:27 2013
From: liveat1892 at gmail.com (sam johnson)
Date: Fri, 15 Nov 2013 02:15:27 +0200
Subject: [GAP Forum] Ascending selection sort algorithm ERROR
Message-ID: <CABFFSew5_3g-4mdh94X7BAJzwFJivh75g5xZ-BNFEAsaK6p5LQ@mail.gmail.com>

Hey guys... I'm trying to write the code for and ascending order selection
sort algorithm and every time I try to read the function that I
implemented, GAP would just stop working no error messages no nothing so
it's difficult to determine the source of error. I need somone to tell me
whre did I go wrong with my code.

code:

*sortAscending := function(L)*
*     local x, i, max, hold;*
*     i := Size(L)-1;*

*     while i > 0 do*
*         max := L[i];*
*         x := i ;   *
*         while x > 0 do*
*             if L[x] > max  then*
*                  max := L[x];*
*             fi;*
*         od;*
*         hold := max;*
*         max := L[i];*
*         L[i] := hold;*
*         i := i -1;*
*    od;*
*    return L;*
*end; *

From gordon.royle at uwa.edu.au  Fri Nov 15 00:23:52 2013
From: gordon.royle at uwa.edu.au (Gordon Royle)
Date: Fri, 15 Nov 2013 08:23:52 +0800
Subject: [GAP Forum] Ascending selection sort algorithm ERROR
In-Reply-To: <CABFFSew5_3g-4mdh94X7BAJzwFJivh75g5xZ-BNFEAsaK6p5LQ@mail.gmail.com>
References: <CABFFSew5_3g-4mdh94X7BAJzwFJivh75g5xZ-BNFEAsaK6p5LQ@mail.gmail.com>
Message-ID: <59635B20-F5E7-48A0-B3D1-85198DC28A9B@uwa.edu.au>

This part is an infinite loop because x is not changed.

Anyway, surely you should just use Gap's sorting functionality.

On 15/11/2013, at 8:15 AM, sam johnson <liveat1892 at gmail.com<mailto:liveat1892 at gmail.com>> wrote:

*         while x > 0 do*
*             if L[x] > max  then*
*                  max := L[x];*
*             fi;*
*         od;*

Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>














From usopppp at gmail.com  Tue Nov 19 12:56:47 2013
From: usopppp at gmail.com (=?KOI8-R?B?98zBxMnNydIg+8nSz8vJyg==?=)
Date: Tue, 19 Nov 2013 16:56:47 +0400
Subject: [GAP Forum] groups comparison
Message-ID: <CALt2DL-ct5_5R5v_6gBeNDU5ZjbQy1iNGN=FG0GpQJAufYDi2w@mail.gmail.com>

I'm using cryst and crystcat packages and i want to compare two groups
g:=SpaceGroupIT(3,75);
gGens:=GeneratorsOfGroup(g);
gGens2:=[gGens[2], gGens[3], gGens[4], gGens[5]]
a:=Group(gGens);
b:=Group(gGens2);

I know, that they are the same groups, because gGens[2]*gGens[2]=gGens[1]

how can i check it OR how can i find all relations between generators (in
this case there is another one: gGens[2]^-1*gGens[3]*gGens[2]=gGens[4] )

From stefan at mcs.st-and.ac.uk  Tue Nov 19 13:34:21 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Tue, 19 Nov 2013 13:34:21 -0000 (UTC)
Subject: [GAP Forum] groups comparison
In-Reply-To: <CALt2DL-ct5_5R5v_6gBeNDU5ZjbQy1iNGN=FG0GpQJAufYDi2w@mail.gmail.com>
References: <CALt2DL-ct5_5R5v_6gBeNDU5ZjbQy1iNGN=FG0GpQJAufYDi2w@mail.gmail.com>
Message-ID: <submission.1VilRd-0007J1-Q2@mail-gap.mcs.st-and.ac.uk>


On Tue, November 19, 2013 12:56 pm, ???????? ??????? wrote:
> I'm using cryst and crystcat packages and i want to compare two groups
> g:=SpaceGroupIT(3,75);
> gGens:=GeneratorsOfGroup(g);
> gGens2:=[gGens[2], gGens[3], gGens[4], gGens[5]]
> a:=Group(gGens);
> b:=Group(gGens2);
>
> I know, that they are the same groups, because gGens[2]*gGens[2]=gGens[1]
>
> how can i check it OR how can i find all relations between generators (in
> this case there is another one: gGens[2]^-1*gGens[3]*gGens[2]=gGens[4] )

Unfortunately, at present the checks "a = b;" and "gGens[1] in b;"
fail due to a lack of available methods for your group:

gap> a = b;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 3rd choice method found for `Enumerator' on 1 arguments called from
Enumerator( D ) called from
[ ... ]
gap> gGens[1] in b;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 3rd choice method found for `Enumerator' on 1 arguments called from
Enumerator( D ) called from
[ ... ]

However what you can do is the following:

gap> First(b,g->g=gGens[1]);
[ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]

Since the result is not "fail", this tells you that gGens[1] is an
element of b.

Note that this may require some package --
try RCWA if it otherwise doesn't work for you.

Hope this helps,

    Stefan Kohl








From hulpke at me.com  Tue Nov 19 14:29:52 2013
From: hulpke at me.com (Alexander Hulpke)
Date: Tue, 19 Nov 2013 07:29:52 -0700
Subject: [GAP Forum] groups comparison
In-Reply-To: <submission.1VilRd-0007J1-Q2@mail-gap.mcs.st-and.ac.uk>
References: <CALt2DL-ct5_5R5v_6gBeNDU5ZjbQy1iNGN=FG0GpQJAufYDi2w@mail.gmail.com>
	<submission.1VilRd-0007J1-Q2@mail-gap.mcs.st-and.ac.uk>
Message-ID: <96EC82F2-361E-4467-8787-496CC0131E3A@me.com>


On Nov 19, 2013, at 6:34 AM, Stefan Kohl <stefan at mcs.st-and.ac.uk> wrote:

> Unfortunately, at present the checks "a = b;" and "gGens[1] in b;"
> fail due to a lack of available methods for your group:
> 
> gap> gGens[1] in b;
> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
> Error, no 3rd choice method found for `Enumerator' on 1 arguments called from
> Enumerator( D ) called from
> [ ... ]
> 
> However what you can do is the following:
> 
> gap> First(b,g->g=gGens[1]);
> [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]

I would not recommend use of such one-sided methods for infinite groups. If gGens[1] is not in b, but b is infinite (as the space groups are) this will never terminate.

What one could do (but currently is not implemented) is to first test membership in the (finite) point group quotient and then test membership in the translation group by linear algebra.

Best,

    Alexander Hulpke





From liveat1892 at gmail.com  Tue Nov 19 18:39:57 2013
From: liveat1892 at gmail.com (sam johnson)
Date: Tue, 19 Nov 2013 20:39:57 +0200
Subject: [GAP Forum] Extended Euclid Algorithm Need HELP
Message-ID: <CABFFSewgQK2spvyRXW=2R_pLRTzPELbOS5bv_s9SJK_SBvweeA@mail.gmail.com>

Hey guys ... I'm writing two algorithms for the extended euclidean
algorithm ( iterative & recursive). The iterative version works just fine
except that it gives false results for negative input. How can I modify?

code:

extEuclid := function(a,b)

      local x, y, u, v,m,n,r,q;
      x:=0;
      y:=1;
      u:=1;
      v:=0;
      while a>0 or a<0 do
               q := QuoInt(b,a);
               r :=  b mod a;
               m := x - u*q;
               n := y - v*q;
               b := a;
               a := r;
               x := u;
               y := v;
               u := m;
              v := n;
      od;
      return [x,y];
end;

Now, regarding the recursive version I understand the logic but  i have a
problem in implementing it (can't solve errors)

code:

extEuclidRecursive := function(a,b)
     local q, x, y, r;
          if b = 0 then
             return [1,0];
          fi;
          q := QuoInt(b,a);
           r := b mod a;
          [x,y] := extEuclidRecursive(b,r);
          return [x - q*y, y];
end;


I would appreciate it if the response was sooner rather than later. Thank
you for your time.

From haidaryouness at ymail.com  Tue Nov 19 19:35:23 2013
From: haidaryouness at ymail.com (Haidar Youness)
Date: Tue, 19 Nov 2013 11:35:23 -0800 (PST)
Subject: [GAP Forum] First GAP program
Message-ID: <1384889723.30520.YahooMailNeo@web160902.mail.bf1.yahoo.com>

Hi... My name is Jay and I'm new to this forum. And I'm writing my first GAP code; Basically I'm trying to find the number of a times a number "p" can be divided by a prime number "n" such that "p|n" is an integer. The program seems pretty trivial but every time it executes it keeps giving me zero regardless of the input. If somebody can just tell me where i went wrong with my code. Thank you. The code is as folows:


PowerofpDividingn := function(p,n)

? ? ? ?local x, count, ans;
? ? ? ?count :=0;

? ? ? ?for x in [1..p] do
? ? ? ? ? ? ans := p/n;
? ? ? ? ? ? if ans in Integers then
? ? ? ? ? ? ? ?count := count ?+ 1;
? ? ? ? ? ? fi;
? ? ? ? ? ? p := ans;?
? ? ? ?od;
? ? return count;
end;

From stefan at mcs.st-and.ac.uk  Tue Nov 19 19:44:03 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Tue, 19 Nov 2013 19:44:03 -0000 (UTC)
Subject: [GAP Forum] Extended Euclid Algorithm Need HELP
In-Reply-To: <CABFFSewgQK2spvyRXW=2R_pLRTzPELbOS5bv_s9SJK_SBvweeA@mail.gmail.com>
References: <CABFFSewgQK2spvyRXW=2R_pLRTzPELbOS5bv_s9SJK_SBvweeA@mail.gmail.com>
Message-ID: <submission.1VirDQ-0002ce-0M@mail-gap.mcs.st-and.ac.uk>


Sam Johnson asked:

> Hey guys ... I'm writing two algorithms for the extended euclidean
> algorithm ( iterative & recursive). The iterative version works just fine
> except that it gives false results for negative input. How can I modify?

The GAP Library already contains such function -- it is called Gcdex.

So there is no need to write your own code for this!

Hope this helps,

    Stefan Kohl

> code:
>
> extEuclid := function(a,b)
>
>       local x, y, u, v,m,n,r,q;
>       x:=0;
>       y:=1;
>       u:=1;
>       v:=0;
>       while a>0 or a<0 do
>                q := QuoInt(b,a);
>                r :=  b mod a;
>                m := x - u*q;
>                n := y - v*q;
>                b := a;
>                a := r;
>                x := u;
>                y := v;
>                u := m;
>               v := n;
>       od;
>       return [x,y];
> end;
>
> Now, regarding the recursive version I understand the logic but  i have a
> problem in implementing it (can't solve errors)
>
> code:
>
> extEuclidRecursive := function(a,b)
>      local q, x, y, r;
>           if b = 0 then
>              return [1,0];
>           fi;
>           q := QuoInt(b,a);
>            r := b mod a;
>           [x,y] := extEuclidRecursive(b,r);
>           return [x - q*y, y];
> end;
>
>
> I would appreciate it if the response was sooner rather than later. Thank
> you for your time.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From stefan at mcs.st-and.ac.uk  Tue Nov 19 19:53:50 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Tue, 19 Nov 2013 19:53:50 -0000 (UTC)
Subject: [GAP Forum] First GAP program
In-Reply-To: <1384889723.30520.YahooMailNeo@web160902.mail.bf1.yahoo.com>
References: <1384889723.30520.YahooMailNeo@web160902.mail.bf1.yahoo.com>
Message-ID: <submission.1VirMs-0002nF-Cz@mail-gap.mcs.st-and.ac.uk>


Haidar Youness asked:
> Hi... My name is Jay and I'm new to this forum. And I'm writing my first GAP code;
> Basically I'm trying to find the number of a times a number "p" can be divided by a
> prime number "n" such that "p|n" is an integer. The program seems pretty trivial but
> every time it executes it keeps giving me zero regardless of the input. If somebody can
> just tell me where i went wrong with my code. Thank you.

You can write your function as follows:

  PowerofpDividingn := function ( n, p )

    local  k;

    if IsZero(p) then return fail; fi;
    if IsZero(n) then return infinity; fi;
    k := 0;
    while IsZero(n mod p) do n := n/p; k := k + 1; od;
    return k;
  end;

Hope this helps,

    Stefan Kohl

> PowerofpDividingn := function(p,n)
>
> ? ? ? ?local x, count, ans;
> ? ? ? ?count :=0;
>
> ? ? ? ?for x in [1..p] do
> ? ? ? ? ? ? ans := p/n;
> ? ? ? ? ? ? if ans in Integers then
> ? ? ? ? ? ? ? ?count := count ?+ 1;
> ? ? ? ? ? ? fi;
> ? ? ? ? ? ? p := ans;?
> ? ? ? ?od;
> ? ? return count;
> end;
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From caj21 at st-andrews.ac.uk  Tue Nov 19 20:06:19 2013
From: caj21 at st-andrews.ac.uk (Chris Jefferson)
Date: Tue, 19 Nov 2013 20:06:19 +0000
Subject: [GAP Forum] First GAP program
In-Reply-To: <1384889723.30520.YahooMailNeo@web160902.mail.bf1.yahoo.com>
References: <1384889723.30520.YahooMailNeo@web160902.mail.bf1.yahoo.com>
Message-ID: <528BC4BB.3030006@st-andrews.ac.uk>

On 19/11/13 19:35, Haidar Youness wrote:
> Hi... My name is Jay and I'm new to this forum. And I'm writing my first GAP code; Basically I'm trying to find the number of a times a number "p" can be divided by a prime number "n" such that "p|n" is an integer. The program seems pretty trivial but every time it executes it keeps giving me zero regardless of the input. If somebody can just tell me where i went wrong with my code. Thank you. The code is as folows:
>
>
> PowerofpDividingn := function(p,n)
>
>         local x, count, ans;
>         count :=0;
>
>         for x in [1..p] do
>              ans := p/n;
>              if ans in Integers then
>                 count := count  + 1;
>              fi;
>              p := ans;
>         od;
>      return count;
> end;

Ignoring the fact that your program isn't very efficient, it also seems 
to work fine for me:

gap> PowerofpDividingn(12,2);
2
gap> PowerofpDividingn(108,3);
3

Could you give us the version of GAP you are using, and a full file 
which uses, and tests, your function, for sanity checking?

Chris


From neginyavari67 at yahoo.com  Thu Nov 28 09:13:47 2013
From: neginyavari67 at yahoo.com (Negin Yavari)
Date: Thu, 28 Nov 2013 09:13:47 +0000 (GMT)
Subject: [GAP Forum] Introducing a 2-Frobenius group
Message-ID: <1385630027.99263.YahooMailNeo@web171902.mail.ir2.yahoo.com>

Dear Forum,
?
??? According to the following text, I would like to introduce the group G in GAP:
?
?
"In the general linear group GL(4,2) and also in GL(4,3) there exists a Frobenius group E:=K : C of order 20 such that K acts fixed-point-freely on corresponding natural modules V_1 and V_2. Now?if we take G:=(V_1 \times V_2) . E with the natural action of E on direct factors, then G is a 2-Frobenius group.
?
?
?
?
Thanks alot in advance,
Negin?

From hatlam at gmail.com  Tue Dec  3 22:52:15 2013
From: hatlam at gmail.com (Ha T. Lam)
Date: Tue, 3 Dec 2013 17:52:15 -0500
Subject: [GAP Forum] Heisenberg group from the Polycyclic package
Message-ID: <CAFxJ0My_095PH1ZOEebT1r7qLUPH7b6DjdeD7phy8mPt-Kxing@mail.gmail.com>

Dear GAP forum,

I'm doing some computations with Heisenberg group and I'm using the method
HeisenbergPcpGroup(n) from the Polycyclic package. According to the manual,
I should get a Heisenberg group of 2n generators with Hirsch length 3n. I
do:

gap> HeisenbergPcpGroup(3);
Pcp-group with orders [ 0, 0, 0, 0, 0, 0, 0 ]

The Hirsch length here is 7, not 9. Is this a mistake in the manual? Can
you give me some reference of how these groups are generated by this
package?

Thank you for your help.

Ha T. Lam

From beick at tu-bs.de  Wed Dec  4 07:51:56 2013
From: beick at tu-bs.de (Bettina Eick)
Date: Wed, 4 Dec 2013 08:51:56 +0100 (CET)
Subject: [GAP Forum] Heisenberg group from the Polycyclic package
In-Reply-To: <CAFxJ0My_095PH1ZOEebT1r7qLUPH7b6DjdeD7phy8mPt-Kxing@mail.gmail.com>
References: <CAFxJ0My_095PH1ZOEebT1r7qLUPH7b6DjdeD7phy8mPt-Kxing@mail.gmail.com>
Message-ID: <alpine.LRH.2.02.1312040816590.6120@rzlogin01.rz.tu-bs.de>


Dear Ha T. Lam,

> I'm doing some computations with Heisenberg group and I'm using the method
> HeisenbergPcpGroup(n) from the Polycyclic package. According to the manual,
> I should get a Heisenberg group of 2n generators with Hirsch length 3n. I
> do:
>
> gap> HeisenbergPcpGroup(3);
> Pcp-group with orders [ 0, 0, 0, 0, 0, 0, 0 ]
>
> The Hirsch length here is 7, not 9. Is this a mistake in the manual? Can
> you give me some reference of how these groups are generated by this
> package?

It is indeed a mistake in the manual. The function HeisenbergPcpGroup(m)
returns the Heisenberg group on 2m generators; this has Hirsch length 
2m+1. To see some more details on how these groups are generated, you 
can do

gap> Print(HeisenbergPcpGroup);
function ( m )
     local  FLT, i;
     FLT := FromTheLeftCollector( 2 * m + 1 );
     for i  in [ 1 .. m ]  do
         SetConjugate( FLT, m + i, i, [ m + i, 1, 2 * m + 1, 1 ] );
     od;
     UpdatePolycyclicCollector( FLT );
     return PcpGroupByCollectorNC( FLT );
end

Thus HeisenbergPcpGroup(m) returns a group on 2m+1 polycyclic generators
g_1, ..., g_{2m+1} with conjugate relations

   g_{m+i}^g_i = g_{m+i} g_{2m+1} for 1 <= i <= m

Best wishes,

Bettina



From ulviye.cinar at metu.edu.tr  Wed Nov 27 12:19:49 2013
From: ulviye.cinar at metu.edu.tr (=?windows-1254?B?Qvz+cmEgx/1uYXI=?=)
Date: Wed, 27 Nov 2013 12:19:49 +0000
Subject: [GAP Forum] conjugate elements
Message-ID: <BLU168-W8540B4F66A33F724E93CBA0EF0@phx.gbl>

Hi,

I want to find all elements of a group that makes two specific elements
( that is I know they are conjugate by an element) conjugate?
Is there such an algorithm? 
I found the algorithm RepresentativeAction(g,x,y) which gives only one
element that makes x and y conjugate. Can I find all such elements?

Thank you,
Busra Guven
 		 	   		   		 	   		  

From stefan at mcs.st-and.ac.uk  Fri Dec  6 11:35:02 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Fri, 6 Dec 2013 11:35:02 -0000 (UTC)
Subject: [GAP Forum] conjugate elements
In-Reply-To: <BLU168-W8540B4F66A33F724E93CBA0EF0@phx.gbl>
References: <BLU168-W8540B4F66A33F724E93CBA0EF0@phx.gbl>
Message-ID: <submission.1VotgU-0008RR-S7@mail-gap.mcs.st-and.ac.uk>

Dear Busra Guven,

> I want to find all elements of a group that makes two specific elements
> ( that is I know they are conjugate by an element) conjugate?
> Is there such an algorithm?
> I found the algorithm RepresentativeAction(g,x,y) which gives only one
> element that makes x and y conjugate. Can I find all such elements?

Given a finite group G and elements g and h of G, the following function
returns a list of all elements x of G such that g^x = h:

AllConjugators := function ( G, g, h )
  return AsList(RightCoset(Centralizer(G,g),RepresentativeAction(G,g,h)));
end;

For example you can do the following:

gap> G := SymmetricGroup(8);;
gap> l := AllConjugators(G,(1,2,3,4,5)(6,7,8),(1,2,3)(4,5,6,7,8));
[ (1,4,7,2,5,8,3,6), (1,8,3,5,7,2,4,6), (1,4,7)(2,5,8)(3,6),
  (1,7,2,8,3,4,5,6), (1,8,2,4,6,3,5,7), (1,4,7,3,6,2,5,8), (1,6)(2,7)(3,8),
  (1,7)(2,8)(3,4,5,6), (1,8)(2,4,6)(3,5,7), (1,5,4,8,3,7,2,6), (1,6,3,8,2,7),
  (1,7,3,4,5,6,2,8), (1,5,4,8,2,6,3,7), (1,6,2,7,3,8), (1,5,4,8)(2,6)(3,7) ]
gap> List(l,g->(1,2,3,4,5)(6,7,8)^g);
[ (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8),
  (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8),
  (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8),
  (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8),
  (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8), (1,2,3)(4,5,6,7,8) ]

Hope this helps,

    Stefan Kohl

-----------------------------------------------------------------------------
http://www.gap-system.org/DevelopersPages/StefanKohl/
-----------------------------------------------------------------------------





From alexk at mcs.st-andrews.ac.uk  Fri Dec  6 16:03:02 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Fri, 6 Dec 2013 16:03:02 +0000
Subject: [GAP Forum] GAP 4.7.2 release announcement
Message-ID: <A0C35329-A607-4AEA-BCC5-DE4102F74574@mcs.st-andrews.ac.uk>

Dear GAP Forum,

We are glad to announce the next major release, GAP 4.7.2, which is 
now available for download at

	http://www.gap-system.org/Releases/

For an overview of changes introduced in GAP 4.7.2, including improved and
extended functionality, fixed bugs, 8 new and many substantially updated
packages, enter '?Changes between GAP 4.6 and GAP 4.7' in GAP 4.7.2 or see

	http://www.gap-system.org/Manuals/doc/changes/chap2.html

Among the alternative GAP distributions listed at

    http://www.gap-system.org/Download/#alternatives

BOB and the Windows installer already provide GAP 4.7.2, while the
rsync-based Linux binary distribution will be updated shortly.
Note that the URL of BOB has changed to 

	http://neunhoef.github.io/bob/

We encourage all users to upgrade to GAP 4.7.2. If you need any help 
or would like to report any problems, please do not hesitate to 
contact us at support at gap-system.org.

As a general remark, please note that we are regularly updating the
GAP distribution to include new versions of GAP packages, but we may not
announce each of them to the Forum. We use the Forum to announce updates
of the core GAP system, but we announce package updates there in general
only if they are really major or if they fix serious issues.

Wishing you fun and success using GAP,
The GAP Group



From mail at gbeyerle.de  Sun Dec  8 22:43:01 2013
From: mail at gbeyerle.de (Georg Beyerle)
Date: Sun, 08 Dec 2013 23:43:01 +0100
Subject: [GAP Forum] Root system of semi-simple Lie algebra G2
Message-ID: <52A4F5F5.8010909@gbeyerle.de>

Hello,

the following table of structure constants (see below) appears to define
a semi-simple Lie algebra. However, the call to RootSystem() fails:

   GAPInfo.Version = 4.6.4
   GAPInfo.Architecture = i586-suse-linux-gnu-gcc-default32
   Dimension( L ) = 14
   SemiSimpleType( L ) : G2
   Determinant( KillingMatrix( Basis( L ))) = 9618527719784448
   CartanSubalgebra( L ) = Algebra( Rationals, [ v.1, v.8 ] )
   #I  the Cartan subalgebra of <L> in not split
   RootSystem( L ) = fail

What am I missing?

Thanks
Georg


   Print( "GAPInfo.Version = ", GAPInfo.Version, "\n" );
   Print( "GAPInfo.Architecture = ", GAPInfo.Architecture, "\n" );
   SetInfoLevel( InfoAlgebra , 2 );
   T:= EmptySCTable( 14, 0, "antisymmetric" );;
   SetEntrySCTable( T, 1, 2, [  -1 , 3 , -1 , 10 ] );;
   SetEntrySCTable( T, 1, 3, [  1 , 2 , 1 , 9 ] );;
   SetEntrySCTable( T, 1, 4, [  1 , 5 , -1 , 12 ] );;
   SetEntrySCTable( T, 1, 5, [  -1 , 4 , -1 , 11 ] );;
   SetEntrySCTable( T, 1, 6, [  1 , 14 ] );;
   SetEntrySCTable( T, 1, 7, [  1 , 6 , 1 , 13 ] );;
   SetEntrySCTable( T, 1, 9, [  1 , 10 ] );;
   SetEntrySCTable( T, 1, 10, [  -1 , 9 ] );;
   SetEntrySCTable( T, 1, 11, [  1 , 12 ] );;
   SetEntrySCTable( T, 1, 12, [  -1 , 11 ] );;
   SetEntrySCTable( T, 1, 13, [  1 , 14 ] );;
   SetEntrySCTable( T, 1, 14, [  -2 , 6 , -2 , 13 ] );;
   SetEntrySCTable( T, 2, 3, [  -1 , 1 , -1 , 8 ] );;
   SetEntrySCTable( T, 2, 4, [  -1 , 6 , -1 , 13 ] );;
   SetEntrySCTable( T, 2, 5, [  -1 , 7 , -1 , 14 ] );;
   SetEntrySCTable( T, 2, 6, [  -1 , 11 ] );;
   SetEntrySCTable( T, 2, 7, [  1 , 5 , -1 , 12 ] );;
   SetEntrySCTable( T, 2, 8, [  -1 , 10 ] );;
   SetEntrySCTable( T, 2, 10, [  1 , 8 ] );;
   SetEntrySCTable( T, 2, 11, [  1 , 6 ] );;
   SetEntrySCTable( T, 2, 12, [  1 , 7 , 1 , 14 ] );;
   SetEntrySCTable( T, 2, 13, [  1 , 4 , 1 , 11 ] );;
   SetEntrySCTable( T, 2, 14, [  1 , 5 , -1 , 12 ] );;
   SetEntrySCTable( T, 3, 4, [  -1 , 7 ] );;
   SetEntrySCTable( T, 3, 5, [  -2 , 6 ] );;
   SetEntrySCTable( T, 3, 6, [  2 , 5 ] );;
   SetEntrySCTable( T, 3, 7, [  1 , 4 ] );;
   SetEntrySCTable( T, 3, 8, [  1 , 9 ] );;
   SetEntrySCTable( T, 3, 9, [  -1 , 8 ] );;
   SetEntrySCTable( T, 3, 11, [  1 , 7 , 1 , 14 ] );;
   SetEntrySCTable( T, 3, 12, [  -1 , 6 ] );;
   SetEntrySCTable( T, 3, 13, [  -1 , 5 ] );;
   SetEntrySCTable( T, 3, 14, [  -1 , 4 , -1 , 11 ] );;
   SetEntrySCTable( T, 4, 5, [  -1 , 8 ] );;
   SetEntrySCTable( T, 4, 6, [  1 , 9 ] );;
   SetEntrySCTable( T, 4, 7, [  -2 , 3 , -2 , 10 ] );;
   SetEntrySCTable( T, 4, 8, [  1 , 5 ] );;
   SetEntrySCTable( T, 4, 9, [  -1 , 6 ] );;
   SetEntrySCTable( T, 4, 10, [  1 , 7 ] );;
   SetEntrySCTable( T, 4, 12, [  -1 , 1 , -1 , 8 ] );;
   SetEntrySCTable( T, 4, 13, [  -1 , 2 , -1 , 9 ] );;
   SetEntrySCTable( T, 4, 14, [  1 , 3 , 1 , 10 ] );;
   SetEntrySCTable( T, 5, 6, [  -2 , 3 ] );;
   SetEntrySCTable( T, 5, 7, [  1 , 9 ] );;
   SetEntrySCTable( T, 5, 8, [  -1 , 4 ] );;
   SetEntrySCTable( T, 5, 9, [  -1 , 7 ] );;
   SetEntrySCTable( T, 5, 10, [  -1 , 6 ] );;
   SetEntrySCTable( T, 5, 11, [  -1 , 1 , -1 , 8 ] );;
   SetEntrySCTable( T, 5, 13, [  1 , 3 ] );;
   SetEntrySCTable( T, 5, 14, [  -1 , 2 , -1 , 9 ] );;
   SetEntrySCTable( T, 6, 7, [  1 , 8 ] );;
   SetEntrySCTable( T, 6, 8, [  -1 , 7 ] );;
   SetEntrySCTable( T, 6, 9, [  1 , 4 ] );;
   SetEntrySCTable( T, 6, 10, [  1 , 5 ] );;
   SetEntrySCTable( T, 6, 11, [  -1 , 2 ] );;
   SetEntrySCTable( T, 6, 12, [  1 , 3 ] );;
   SetEntrySCTable( T, 6, 14, [  1 , 1 ] );;
   SetEntrySCTable( T, 7, 8, [  1 , 6 ] );;
   SetEntrySCTable( T, 7, 9, [  1 , 5 ] );;
   SetEntrySCTable( T, 7, 10, [  -1 , 4 ] );;
   SetEntrySCTable( T, 7, 11, [  -1 , 3 , -1 , 10 ] );;
   SetEntrySCTable( T, 7, 12, [  -1 , 2 , -1 , 9 ] );;
   SetEntrySCTable( T, 7, 13, [  1 , 1 , 1 , 8 ] );;
   SetEntrySCTable( T, 8, 9, [  -2 , 10 ] );;
   SetEntrySCTable( T, 8, 10, [  2 , 9 ] );;
   SetEntrySCTable( T, 8, 11, [  1 , 12 ] );;
   SetEntrySCTable( T, 8, 12, [  -1 , 11 ] );;
   SetEntrySCTable( T, 8, 13, [  -1 , 7 , -1 , 14 ] );;
   SetEntrySCTable( T, 8, 14, [  1 , 6 , 1 , 13 ] );;
   SetEntrySCTable( T, 9, 10, [  -2 , 8 ] );;
   SetEntrySCTable( T, 9, 11, [  -1 , 6 , -1 , 13 ] );;
   SetEntrySCTable( T, 9, 12, [  -1 , 14 ] );;
   SetEntrySCTable( T, 9, 13, [  1 , 4 , 1 , 11 ] );;
   SetEntrySCTable( T, 9, 14, [  1 , 12 ] );;
   SetEntrySCTable( T, 10, 11, [  -1 , 14 ] );;
   SetEntrySCTable( T, 10, 12, [  1 , 6 , 1 , 13 ] );;
   SetEntrySCTable( T, 10, 13, [  1 , 5 , -1 , 12 ] );;
   SetEntrySCTable( T, 10, 14, [  1 , 11 ] );;
   SetEntrySCTable( T, 11, 12, [  2 , 1 , 2 , 8 ] );;
   SetEntrySCTable( T, 11, 13, [  -1 , 2 , -1 , 9 ] );;
   SetEntrySCTable( T, 11, 14, [  -1 , 10 ] );;
   SetEntrySCTable( T, 12, 13, [  1 , 3 , 1 , 10 ] );;
   SetEntrySCTable( T, 12, 14, [  -1 , 9 ] );;
   SetEntrySCTable( T, 13, 14, [  1 , 1 ] );;

   L := LieAlgebraByStructureConstants( Rationals, T );
   Print( "Dimension( L ) = ", Dimension( L ), "\n" );
   typ := SemiSimpleType( L );
   Print( "SemiSimpleType( L ) : ", typ, "\n" );
   detKM := Determinant( KillingMatrix( Basis( L )));
   Print( "Determinant( KillingMatrix( Basis( L ))) = ", detKM, "\n" );
   H := CartanSubalgebra( L );
   Print( "CartanSubalgebra( L ) = ", H, "\n" );
   R := RootSystem( L );
   Print( "RootSystem( L ) = ", R, "\n" );


From degraaf at science.unitn.it  Mon Dec  9 21:03:45 2013
From: degraaf at science.unitn.it (Willem de Graaf)
Date: Mon, 9 Dec 2013 22:03:45 +0100
Subject: [GAP Forum] Root system of semi-simple Lie algebra G2
In-Reply-To: <52A4F5F5.8010909@gbeyerle.de>
References: <52A4F5F5.8010909@gbeyerle.de>
Message-ID: <CAHQ8B2b9CL+BtwR-EDv-M2gdZE1UJV59TxB-j1TDVZwVuQy0Gg@mail.gmail.com>

Dear Georg,

The problem is that the Cartan subalgebra that has been computed is not
split over the rationals. It is split over Q(i).
However, GAP does not take advantage of that. Recently we have written
a package, called corelg, which does manage to compute the root system
in this case (http://www.science.unitn.it/~corelg/):

gap> L := LieAlgebraByStructureConstants( CF(4), T );
<Lie algebra of dimension 14 over GaussianRationals>
gap> RootSystem(L);
<root system of rank 2>

Best wishes,

Willem de Graaf


On Sun, Dec 8, 2013 at 11:43 PM, Georg Beyerle <mail at gbeyerle.de> wrote:

> Hello,
>
> the following table of structure constants (see below) appears to define
> a semi-simple Lie algebra. However, the call to RootSystem() fails:
>
>   GAPInfo.Version = 4.6.4
>   GAPInfo.Architecture = i586-suse-linux-gnu-gcc-default32
>   Dimension( L ) = 14
>   SemiSimpleType( L ) : G2
>   Determinant( KillingMatrix( Basis( L ))) = 9618527719784448
>   CartanSubalgebra( L ) = Algebra( Rationals, [ v.1, v.8 ] )
>   #I  the Cartan subalgebra of <L> in not split
>   RootSystem( L ) = fail
>
> What am I missing?
>
> Thanks
> Georg
>
>
>   Print( "GAPInfo.Version = ", GAPInfo.Version, "\n" );
>   Print( "GAPInfo.Architecture = ", GAPInfo.Architecture, "\n" );
>   SetInfoLevel( InfoAlgebra , 2 );
>   T:= EmptySCTable( 14, 0, "antisymmetric" );;
>   SetEntrySCTable( T, 1, 2, [  -1 , 3 , -1 , 10 ] );;
>   SetEntrySCTable( T, 1, 3, [  1 , 2 , 1 , 9 ] );;
>   SetEntrySCTable( T, 1, 4, [  1 , 5 , -1 , 12 ] );;
>   SetEntrySCTable( T, 1, 5, [  -1 , 4 , -1 , 11 ] );;
>   SetEntrySCTable( T, 1, 6, [  1 , 14 ] );;
>   SetEntrySCTable( T, 1, 7, [  1 , 6 , 1 , 13 ] );;
>   SetEntrySCTable( T, 1, 9, [  1 , 10 ] );;
>   SetEntrySCTable( T, 1, 10, [  -1 , 9 ] );;
>   SetEntrySCTable( T, 1, 11, [  1 , 12 ] );;
>   SetEntrySCTable( T, 1, 12, [  -1 , 11 ] );;
>   SetEntrySCTable( T, 1, 13, [  1 , 14 ] );;
>   SetEntrySCTable( T, 1, 14, [  -2 , 6 , -2 , 13 ] );;
>   SetEntrySCTable( T, 2, 3, [  -1 , 1 , -1 , 8 ] );;
>   SetEntrySCTable( T, 2, 4, [  -1 , 6 , -1 , 13 ] );;
>   SetEntrySCTable( T, 2, 5, [  -1 , 7 , -1 , 14 ] );;
>   SetEntrySCTable( T, 2, 6, [  -1 , 11 ] );;
>   SetEntrySCTable( T, 2, 7, [  1 , 5 , -1 , 12 ] );;
>   SetEntrySCTable( T, 2, 8, [  -1 , 10 ] );;
>   SetEntrySCTable( T, 2, 10, [  1 , 8 ] );;
>   SetEntrySCTable( T, 2, 11, [  1 , 6 ] );;
>   SetEntrySCTable( T, 2, 12, [  1 , 7 , 1 , 14 ] );;
>   SetEntrySCTable( T, 2, 13, [  1 , 4 , 1 , 11 ] );;
>   SetEntrySCTable( T, 2, 14, [  1 , 5 , -1 , 12 ] );;
>   SetEntrySCTable( T, 3, 4, [  -1 , 7 ] );;
>   SetEntrySCTable( T, 3, 5, [  -2 , 6 ] );;
>   SetEntrySCTable( T, 3, 6, [  2 , 5 ] );;
>   SetEntrySCTable( T, 3, 7, [  1 , 4 ] );;
>   SetEntrySCTable( T, 3, 8, [  1 , 9 ] );;
>   SetEntrySCTable( T, 3, 9, [  -1 , 8 ] );;
>   SetEntrySCTable( T, 3, 11, [  1 , 7 , 1 , 14 ] );;
>   SetEntrySCTable( T, 3, 12, [  -1 , 6 ] );;
>   SetEntrySCTable( T, 3, 13, [  -1 , 5 ] );;
>   SetEntrySCTable( T, 3, 14, [  -1 , 4 , -1 , 11 ] );;
>   SetEntrySCTable( T, 4, 5, [  -1 , 8 ] );;
>   SetEntrySCTable( T, 4, 6, [  1 , 9 ] );;
>   SetEntrySCTable( T, 4, 7, [  -2 , 3 , -2 , 10 ] );;
>   SetEntrySCTable( T, 4, 8, [  1 , 5 ] );;
>   SetEntrySCTable( T, 4, 9, [  -1 , 6 ] );;
>   SetEntrySCTable( T, 4, 10, [  1 , 7 ] );;
>   SetEntrySCTable( T, 4, 12, [  -1 , 1 , -1 , 8 ] );;
>   SetEntrySCTable( T, 4, 13, [  -1 , 2 , -1 , 9 ] );;
>   SetEntrySCTable( T, 4, 14, [  1 , 3 , 1 , 10 ] );;
>   SetEntrySCTable( T, 5, 6, [  -2 , 3 ] );;
>   SetEntrySCTable( T, 5, 7, [  1 , 9 ] );;
>   SetEntrySCTable( T, 5, 8, [  -1 , 4 ] );;
>   SetEntrySCTable( T, 5, 9, [  -1 , 7 ] );;
>   SetEntrySCTable( T, 5, 10, [  -1 , 6 ] );;
>   SetEntrySCTable( T, 5, 11, [  -1 , 1 , -1 , 8 ] );;
>   SetEntrySCTable( T, 5, 13, [  1 , 3 ] );;
>   SetEntrySCTable( T, 5, 14, [  -1 , 2 , -1 , 9 ] );;
>   SetEntrySCTable( T, 6, 7, [  1 , 8 ] );;
>   SetEntrySCTable( T, 6, 8, [  -1 , 7 ] );;
>   SetEntrySCTable( T, 6, 9, [  1 , 4 ] );;
>   SetEntrySCTable( T, 6, 10, [  1 , 5 ] );;
>   SetEntrySCTable( T, 6, 11, [  -1 , 2 ] );;
>   SetEntrySCTable( T, 6, 12, [  1 , 3 ] );;
>   SetEntrySCTable( T, 6, 14, [  1 , 1 ] );;
>   SetEntrySCTable( T, 7, 8, [  1 , 6 ] );;
>   SetEntrySCTable( T, 7, 9, [  1 , 5 ] );;
>   SetEntrySCTable( T, 7, 10, [  -1 , 4 ] );;
>   SetEntrySCTable( T, 7, 11, [  -1 , 3 , -1 , 10 ] );;
>   SetEntrySCTable( T, 7, 12, [  -1 , 2 , -1 , 9 ] );;
>   SetEntrySCTable( T, 7, 13, [  1 , 1 , 1 , 8 ] );;
>   SetEntrySCTable( T, 8, 9, [  -2 , 10 ] );;
>   SetEntrySCTable( T, 8, 10, [  2 , 9 ] );;
>   SetEntrySCTable( T, 8, 11, [  1 , 12 ] );;
>   SetEntrySCTable( T, 8, 12, [  -1 , 11 ] );;
>   SetEntrySCTable( T, 8, 13, [  -1 , 7 , -1 , 14 ] );;
>   SetEntrySCTable( T, 8, 14, [  1 , 6 , 1 , 13 ] );;
>   SetEntrySCTable( T, 9, 10, [  -2 , 8 ] );;
>   SetEntrySCTable( T, 9, 11, [  -1 , 6 , -1 , 13 ] );;
>   SetEntrySCTable( T, 9, 12, [  -1 , 14 ] );;
>   SetEntrySCTable( T, 9, 13, [  1 , 4 , 1 , 11 ] );;
>   SetEntrySCTable( T, 9, 14, [  1 , 12 ] );;
>   SetEntrySCTable( T, 10, 11, [  -1 , 14 ] );;
>   SetEntrySCTable( T, 10, 12, [  1 , 6 , 1 , 13 ] );;
>   SetEntrySCTable( T, 10, 13, [  1 , 5 , -1 , 12 ] );;
>   SetEntrySCTable( T, 10, 14, [  1 , 11 ] );;
>   SetEntrySCTable( T, 11, 12, [  2 , 1 , 2 , 8 ] );;
>   SetEntrySCTable( T, 11, 13, [  -1 , 2 , -1 , 9 ] );;
>   SetEntrySCTable( T, 11, 14, [  -1 , 10 ] );;
>   SetEntrySCTable( T, 12, 13, [  1 , 3 , 1 , 10 ] );;
>   SetEntrySCTable( T, 12, 14, [  -1 , 9 ] );;
>   SetEntrySCTable( T, 13, 14, [  1 , 1 ] );;
>
>   L := LieAlgebraByStructureConstants( Rationals, T );
>   Print( "Dimension( L ) = ", Dimension( L ), "\n" );
>   typ := SemiSimpleType( L );
>   Print( "SemiSimpleType( L ) : ", typ, "\n" );
>   detKM := Determinant( KillingMatrix( Basis( L )));
>   Print( "Determinant( KillingMatrix( Basis( L ))) = ", detKM, "\n" );
>   H := CartanSubalgebra( L );
>   Print( "CartanSubalgebra( L ) = ", H, "\n" );
>   R := RootSystem( L );
>   Print( "RootSystem( L ) = ", R, "\n" );
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From alexk at mcs.st-andrews.ac.uk  Mon Dec  9 21:43:33 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 9 Dec 2013 21:43:33 +0000
Subject: [GAP Forum] Root system of semi-simple Lie algebra G2
In-Reply-To: <CAHQ8B2b9CL+BtwR-EDv-M2gdZE1UJV59TxB-j1TDVZwVuQy0Gg@mail.gmail.com>
References: <52A4F5F5.8010909@gbeyerle.de>
	<CAHQ8B2b9CL+BtwR-EDv-M2gdZE1UJV59TxB-j1TDVZwVuQy0Gg@mail.gmail.com>
Message-ID: <6D38814C-986E-4BE2-910E-EC7A3C1BBAA0@mcs.st-andrews.ac.uk>

Dear Georg and all,

Just to add that CoReLG and three other packages extending GAP's
functionality for Lie algebras, namely LieRing, LiePRing and SLA,
are included in GAP 4.7.2 distribution which was announced on Friday,
and I'd like to encourage you to get CoReLG via upgrading to 
GAP 4.7.2 instead of trying to install it under GAP 4.6.4 which is 
dated May 2013.

Best wishes
Alexander





On 9 Dec 2013, at 21:03, Willem de Graaf <degraaf at science.unitn.it> wrote:

> Dear Georg,
> 
> The problem is that the Cartan subalgebra that has been computed is not
> split over the rationals. It is split over Q(i).
> However, GAP does not take advantage of that. Recently we have written
> a package, called corelg, which does manage to compute the root system
> in this case (http://www.science.unitn.it/~corelg/):
> 
> gap> L := LieAlgebraByStructureConstants( CF(4), T );
> <Lie algebra of dimension 14 over GaussianRationals>
> gap> RootSystem(L);
> <root system of rank 2>
> 
> Best wishes,
> 
> Willem de Graaf
> 
> 
> On Sun, Dec 8, 2013 at 11:43 PM, Georg Beyerle <mail at gbeyerle.de> wrote:
> 
>> Hello,
>> 
>> the following table of structure constants (see below) appears to define
>> a semi-simple Lie algebra. However, the call to RootSystem() fails:
>> 
>>  GAPInfo.Version = 4.6.4
>>  GAPInfo.Architecture = i586-suse-linux-gnu-gcc-default32
>>  Dimension( L ) = 14
>>  SemiSimpleType( L ) : G2
>>  Determinant( KillingMatrix( Basis( L ))) = 9618527719784448
>>  CartanSubalgebra( L ) = Algebra( Rationals, [ v.1, v.8 ] )
>>  #I  the Cartan subalgebra of <L> in not split
>>  RootSystem( L ) = fail
>> 
>> What am I missing?
>> 
>> Thanks
>> Georg
>> 
>> 
>>  Print( "GAPInfo.Version = ", GAPInfo.Version, "\n" );
>>  Print( "GAPInfo.Architecture = ", GAPInfo.Architecture, "\n" );
>>  SetInfoLevel( InfoAlgebra , 2 );
>>  T:= EmptySCTable( 14, 0, "antisymmetric" );;
>>  SetEntrySCTable( T, 1, 2, [  -1 , 3 , -1 , 10 ] );;
>>  SetEntrySCTable( T, 1, 3, [  1 , 2 , 1 , 9 ] );;
>>  SetEntrySCTable( T, 1, 4, [  1 , 5 , -1 , 12 ] );;
>>  SetEntrySCTable( T, 1, 5, [  -1 , 4 , -1 , 11 ] );;
>>  SetEntrySCTable( T, 1, 6, [  1 , 14 ] );;
>>  SetEntrySCTable( T, 1, 7, [  1 , 6 , 1 , 13 ] );;
>>  SetEntrySCTable( T, 1, 9, [  1 , 10 ] );;
>>  SetEntrySCTable( T, 1, 10, [  -1 , 9 ] );;
>>  SetEntrySCTable( T, 1, 11, [  1 , 12 ] );;
>>  SetEntrySCTable( T, 1, 12, [  -1 , 11 ] );;
>>  SetEntrySCTable( T, 1, 13, [  1 , 14 ] );;
>>  SetEntrySCTable( T, 1, 14, [  -2 , 6 , -2 , 13 ] );;
>>  SetEntrySCTable( T, 2, 3, [  -1 , 1 , -1 , 8 ] );;
>>  SetEntrySCTable( T, 2, 4, [  -1 , 6 , -1 , 13 ] );;
>>  SetEntrySCTable( T, 2, 5, [  -1 , 7 , -1 , 14 ] );;
>>  SetEntrySCTable( T, 2, 6, [  -1 , 11 ] );;
>>  SetEntrySCTable( T, 2, 7, [  1 , 5 , -1 , 12 ] );;
>>  SetEntrySCTable( T, 2, 8, [  -1 , 10 ] );;
>>  SetEntrySCTable( T, 2, 10, [  1 , 8 ] );;
>>  SetEntrySCTable( T, 2, 11, [  1 , 6 ] );;
>>  SetEntrySCTable( T, 2, 12, [  1 , 7 , 1 , 14 ] );;
>>  SetEntrySCTable( T, 2, 13, [  1 , 4 , 1 , 11 ] );;
>>  SetEntrySCTable( T, 2, 14, [  1 , 5 , -1 , 12 ] );;
>>  SetEntrySCTable( T, 3, 4, [  -1 , 7 ] );;
>>  SetEntrySCTable( T, 3, 5, [  -2 , 6 ] );;
>>  SetEntrySCTable( T, 3, 6, [  2 , 5 ] );;
>>  SetEntrySCTable( T, 3, 7, [  1 , 4 ] );;
>>  SetEntrySCTable( T, 3, 8, [  1 , 9 ] );;
>>  SetEntrySCTable( T, 3, 9, [  -1 , 8 ] );;
>>  SetEntrySCTable( T, 3, 11, [  1 , 7 , 1 , 14 ] );;
>>  SetEntrySCTable( T, 3, 12, [  -1 , 6 ] );;
>>  SetEntrySCTable( T, 3, 13, [  -1 , 5 ] );;
>>  SetEntrySCTable( T, 3, 14, [  -1 , 4 , -1 , 11 ] );;
>>  SetEntrySCTable( T, 4, 5, [  -1 , 8 ] );;
>>  SetEntrySCTable( T, 4, 6, [  1 , 9 ] );;
>>  SetEntrySCTable( T, 4, 7, [  -2 , 3 , -2 , 10 ] );;
>>  SetEntrySCTable( T, 4, 8, [  1 , 5 ] );;
>>  SetEntrySCTable( T, 4, 9, [  -1 , 6 ] );;
>>  SetEntrySCTable( T, 4, 10, [  1 , 7 ] );;
>>  SetEntrySCTable( T, 4, 12, [  -1 , 1 , -1 , 8 ] );;
>>  SetEntrySCTable( T, 4, 13, [  -1 , 2 , -1 , 9 ] );;
>>  SetEntrySCTable( T, 4, 14, [  1 , 3 , 1 , 10 ] );;
>>  SetEntrySCTable( T, 5, 6, [  -2 , 3 ] );;
>>  SetEntrySCTable( T, 5, 7, [  1 , 9 ] );;
>>  SetEntrySCTable( T, 5, 8, [  -1 , 4 ] );;
>>  SetEntrySCTable( T, 5, 9, [  -1 , 7 ] );;
>>  SetEntrySCTable( T, 5, 10, [  -1 , 6 ] );;
>>  SetEntrySCTable( T, 5, 11, [  -1 , 1 , -1 , 8 ] );;
>>  SetEntrySCTable( T, 5, 13, [  1 , 3 ] );;
>>  SetEntrySCTable( T, 5, 14, [  -1 , 2 , -1 , 9 ] );;
>>  SetEntrySCTable( T, 6, 7, [  1 , 8 ] );;
>>  SetEntrySCTable( T, 6, 8, [  -1 , 7 ] );;
>>  SetEntrySCTable( T, 6, 9, [  1 , 4 ] );;
>>  SetEntrySCTable( T, 6, 10, [  1 , 5 ] );;
>>  SetEntrySCTable( T, 6, 11, [  -1 , 2 ] );;
>>  SetEntrySCTable( T, 6, 12, [  1 , 3 ] );;
>>  SetEntrySCTable( T, 6, 14, [  1 , 1 ] );;
>>  SetEntrySCTable( T, 7, 8, [  1 , 6 ] );;
>>  SetEntrySCTable( T, 7, 9, [  1 , 5 ] );;
>>  SetEntrySCTable( T, 7, 10, [  -1 , 4 ] );;
>>  SetEntrySCTable( T, 7, 11, [  -1 , 3 , -1 , 10 ] );;
>>  SetEntrySCTable( T, 7, 12, [  -1 , 2 , -1 , 9 ] );;
>>  SetEntrySCTable( T, 7, 13, [  1 , 1 , 1 , 8 ] );;
>>  SetEntrySCTable( T, 8, 9, [  -2 , 10 ] );;
>>  SetEntrySCTable( T, 8, 10, [  2 , 9 ] );;
>>  SetEntrySCTable( T, 8, 11, [  1 , 12 ] );;
>>  SetEntrySCTable( T, 8, 12, [  -1 , 11 ] );;
>>  SetEntrySCTable( T, 8, 13, [  -1 , 7 , -1 , 14 ] );;
>>  SetEntrySCTable( T, 8, 14, [  1 , 6 , 1 , 13 ] );;
>>  SetEntrySCTable( T, 9, 10, [  -2 , 8 ] );;
>>  SetEntrySCTable( T, 9, 11, [  -1 , 6 , -1 , 13 ] );;
>>  SetEntrySCTable( T, 9, 12, [  -1 , 14 ] );;
>>  SetEntrySCTable( T, 9, 13, [  1 , 4 , 1 , 11 ] );;
>>  SetEntrySCTable( T, 9, 14, [  1 , 12 ] );;
>>  SetEntrySCTable( T, 10, 11, [  -1 , 14 ] );;
>>  SetEntrySCTable( T, 10, 12, [  1 , 6 , 1 , 13 ] );;
>>  SetEntrySCTable( T, 10, 13, [  1 , 5 , -1 , 12 ] );;
>>  SetEntrySCTable( T, 10, 14, [  1 , 11 ] );;
>>  SetEntrySCTable( T, 11, 12, [  2 , 1 , 2 , 8 ] );;
>>  SetEntrySCTable( T, 11, 13, [  -1 , 2 , -1 , 9 ] );;
>>  SetEntrySCTable( T, 11, 14, [  -1 , 10 ] );;
>>  SetEntrySCTable( T, 12, 13, [  1 , 3 , 1 , 10 ] );;
>>  SetEntrySCTable( T, 12, 14, [  -1 , 9 ] );;
>>  SetEntrySCTable( T, 13, 14, [  1 , 1 ] );;
>> 
>>  L := LieAlgebraByStructureConstants( Rationals, T );
>>  Print( "Dimension( L ) = ", Dimension( L ), "\n" );
>>  typ := SemiSimpleType( L );
>>  Print( "SemiSimpleType( L ) : ", typ, "\n" );
>>  detKM := Determinant( KillingMatrix( Basis( L )));
>>  Print( "Determinant( KillingMatrix( Basis( L ))) = ", detKM, "\n" );
>>  H := CartanSubalgebra( L );
>>  Print( "CartanSubalgebra( L ) = ", H, "\n" );
>>  R := RootSystem( L );
>>  Print( "RootSystem( L ) = ", R, "\n" );
>> 
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From eyesha313 at gmail.com  Thu Dec 12 18:38:36 2013
From: eyesha313 at gmail.com (Eye_sha Khan)
Date: Thu, 12 Dec 2013 23:38:36 +0500
Subject: [GAP Forum] question
Message-ID: <CAJHDBAp4_GMs-Zi42+Dh4QtedX1bq6_jeCtH8Q-xb19ggftJOA@mail.gmail.com>

we have to find the order of the group.we have permutation [
(1,3,6),(2,4,12),(7),(8,9,10),(11),(0,5, ?)] second permutation is
[(0, ?,12),(1,11,6),(2,5,4),(3),(7,10,8),(9)]
and third permutation is [(0, ?),(1,12),(2,6),(7,11),(3,4),(5),(8),(9,10)]
;but we cannot write any symbol for infinity in Gap;please tell us which
symbol we should write in GAP;
regards

From mathieu.dutour at gmail.com  Thu Dec 12 21:38:03 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Thu, 12 Dec 2013 22:38:03 +0100
Subject: [GAP Forum] question
In-Reply-To: <CAJHDBAp4_GMs-Zi42+Dh4QtedX1bq6_jeCtH8Q-xb19ggftJOA@mail.gmail.com>
References: <CAJHDBAp4_GMs-Zi42+Dh4QtedX1bq6_jeCtH8Q-xb19ggftJOA@mail.gmail.com>
Message-ID: <CADm_tePJ4cV95TgsrncVbh7Y3+vBHQW1m3LuX+ux3RtpvKyndg@mail.gmail.com>

What you should do is number the N elements you are permuting
on from 1 to N.

So, in your case:
0 ----> 1
1 -----> 2
.
.
.
12 -----> 13
Infinity ------> 14.

That way you can use existing Gap commands.
That translation business is absolutely necessary
in order to use GAP.

  Mathieu

On Thursday, December 12, 2013, Eye_sha Khan wrote:

> we have to find the order of the group.we have permutation [
> (1,3,6),(2,4,12),(7),(8,9,10),(11),(0,5, ?)] second permutation is
> [(0, ?,12),(1,11,6),(2,5,4),(3),(7,10,8),(9)]
> and third permutation is [(0, ?),(1,12),(2,6),(7,11),(3,4),(5),(8),(9,10)]
> ;but we cannot write any symbol for infinity in Gap;please tell us which
> symbol we should write in GAP;
> regards
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org <javascript:;>
> http://mail.gap-system.org/mailman/listinfo/forum
>

From mnarde01 at mail.bbk.ac.uk  Fri Dec 13 11:31:30 2013
From: mnarde01 at mail.bbk.ac.uk (Michele Nardella)
Date: Fri, 13 Dec 2013 11:31:30 +0000
Subject: [GAP Forum] Group Actions In GAP
Message-ID: <CADPxvHnAwxnyv1cAvK6DJEmxN124e8BLK56pEi3SPfYhszTZsw@mail.gmail.com>

Dear Subscribers to the GAP Forum,

I am an undergraduate student and taking my first class in Group Theory.
I would like to obtain
a) the permutation cycles of the faces of a truncated octahedron induced by
the action of its rotation group (S_4); and
b) the orbits of its faces;

To generate S_4 in GAP is the easiest part.
By I do not know, how to specify the domain, \Omega, and \mu which is
defined to be "a  function compatible with the group arithmetic." (
http://www.gap-system.org/Manuals/doc/ref/chap41.html).

Since a truncated octahedron  is made of 8 regular hexagons and 6 squares,
would I be correct in specifying the domain as
gap>dom:=[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14]];
where 1..8 are the labels of the hexagonal faces and 9..14 are the label of
the squared faces?

Concerning the method \mu, GAP manual specifies many different options
ranging from paragraph 41.2-1 to 41.2-15. I have no idea which one apply to
my case.
Would you be so kind to give to me an hint?
Moreover, I will really appreciate if you can suggest to me some reference
so that I can understand a good portion of the other methods with the
constraint that I am an undergraduate student

Thank you very much,

Michele

From Bill.Allombert at math.u-bordeaux1.fr  Fri Dec 13 12:14:53 2013
From: Bill.Allombert at math.u-bordeaux1.fr (Bill Allombert)
Date: Fri, 13 Dec 2013 13:14:53 +0100
Subject: [GAP Forum] Group Actions In GAP
In-Reply-To: <CADPxvHnAwxnyv1cAvK6DJEmxN124e8BLK56pEi3SPfYhszTZsw@mail.gmail.com>
References: <CADPxvHnAwxnyv1cAvK6DJEmxN124e8BLK56pEi3SPfYhszTZsw@mail.gmail.com>
Message-ID: <20131213121453.GF22267@yellowpig>

On Fri, Dec 13, 2013 at 11:31:30AM +0000, Michele Nardella wrote:
> Dear Subscribers to the GAP Forum,
> 
> I am an undergraduate student and taking my first class in Group Theory.
> I would like to obtain
> a) the permutation cycles of the faces of a truncated octahedron induced by
> the action of its rotation group (S_4); and
> b) the orbits of its faces;
> 
> To generate S_4 in GAP is the easiest part.
> By I do not know, how to specify the domain, \Omega, and \mu which is
> defined to be "a  function compatible with the group arithmetic." (
> http://www.gap-system.org/Manuals/doc/ref/chap41.html).

I really suggest you do the computation by hand, and then to do it using
GAP when you have a clear picture of the concept involved.
S_4 is a small group, so the computation is easy.

Cheers,
Bill.


From vlad at vladikoff.com  Mon Dec 16 22:34:59 2013
From: vlad at vladikoff.com (vlad at vladikoff.com)
Date: Mon, 16 Dec 2013 16:34:59 -0600
Subject: [GAP Forum] Speed up loading, minimize workspace file
Message-ID: <d86527122330e9349f6cca8f4dec95f3@vladikoff.com>

Hello,


I'm looking for a way to speed up GAP loading.
How can I do this? Or how can I minimize my workspace file?

I'm assuming that unloading certain packages and components might help, 
but I'm not sure how to do that. Should I just move them out of the 
`pkg` directory?

Thanks!
Vlad.


From alexk at mcs.st-andrews.ac.uk  Tue Dec 17 13:10:26 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Tue, 17 Dec 2013 13:10:26 +0000
Subject: [GAP Forum] Speed up loading, minimize workspace file
In-Reply-To: <d86527122330e9349f6cca8f4dec95f3@vladikoff.com>
References: <d86527122330e9349f6cca8f4dec95f3@vladikoff.com>
Message-ID: <58E3C491-A269-4BB6-8136-F9FD58BF16BB@mcs.st-andrews.ac.uk>

Hello Vlad,

On 16 Dec 2013, at 22:34, vlad at vladikoff.com wrote:

> Hello,
> 
> I'm looking for a way to speed up GAP loading.
> How can I do this? Or how can I minimize my workspace file?

Using the workspace is the recommended way to speed it up. 

On my machine, the workspace created with the BOB installer
( http://neunhoef.github.io/bob/ ) occupies 38 MB for 32-bit
mode and 67 MB for 64-bit mode. Are you interested in 
squeezing it even further? Is this a network installation, or
slow machine, or anything else which motivates your question?

> I'm assuming that unloading certain packages and components might help, but I'm not sure how to do that. Should I just move them out of the `pkg` directory?

Those packages which are not loaded at startup, they do not 
make big use of the workspace (only meta-data will be loaded). 
Also, some packages are required to run GAP, and some extend 
it significantly, and some depend on others, so one should be 
careful. It's easy to break the system without any significant
gain in loading time.

Hope this helps
Alexander






From l18981040 at gmail.com  Thu Dec 19 13:53:55 2013
From: l18981040 at gmail.com (Chiang-En Chen)
Date: Thu, 19 Dec 2013 21:53:55 +0800
Subject: [GAP Forum] The command "IsIdentical" can not work.
Message-ID: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>

My GAP version is 4.6.5. When I performed the command   "IsIdentical( 1, 1
);" (this is an example in the section 27.10 of the manual ), it can not
work. The information of error is

gap>  IsIdentical( 1, 1 );
Error, Variable: 'IsIdentical' must have a value
not in any function at line 1 of *stdin*

Thank for reading.

From mathieu.dutour at gmail.com  Thu Dec 19 13:58:21 2013
From: mathieu.dutour at gmail.com (Mathieu Dutour)
Date: Thu, 19 Dec 2013 14:58:21 +0100
Subject: [GAP Forum] The command "IsIdentical" can not work.
In-Reply-To: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
References: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
Message-ID: <CADm_teNNkeDiChbcZt2Z7CLadXN3S-h2Oc8SyS8FBsySnzW8sw@mail.gmail.com>

Well, the function "IsIdentical" simply does not exist.
GAP is a functional language. The function themselves
are variables.

But if you want you have:
gap> IsIdenticalObj(1,1);
true

or
gap> 1=1;
true

I am not sure of the difference between both.

  Mathieu


On Thu, Dec 19, 2013 at 2:53 PM, Chiang-En Chen <l18981040 at gmail.com> wrote:

> My GAP version is 4.6.5. When I performed the command   "IsIdentical( 1, 1
> );" (this is an example in the section 27.10 of the manual ), it can not
> work. The information of error is
>
> gap>  IsIdentical( 1, 1 );
> Error, Variable: 'IsIdentical' must have a value
> not in any function at line 1 of *stdin*
>
> Thank for reading.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From stefan at mcs.st-and.ac.uk  Thu Dec 19 15:22:57 2013
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Thu, 19 Dec 2013 15:22:57 -0000 (UTC)
Subject: [GAP Forum] The command "IsIdentical" can not work.
In-Reply-To: <CADm_teNNkeDiChbcZt2Z7CLadXN3S-h2Oc8SyS8FBsySnzW8sw@mail.gmail.com>
References: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
	<CADm_teNNkeDiChbcZt2Z7CLadXN3S-h2Oc8SyS8FBsySnzW8sw@mail.gmail.com>
Message-ID: <submission.1VtfRB-0007jz-Md@mail-gap.mcs.st-and.ac.uk>

On Thu, December 19, 2013 1:58 pm, Mathieu Dutour wrote:
> Well, the function "IsIdentical" simply does not exist.
> GAP is a functional language. The function themselves
> are variables.
>
> But if you want you have:
> gap> IsIdenticalObj(1,1);
> true
>
> or
> gap> 1=1;
> true
>
> I am not sure of the difference between both.

The difference between "=" and "IsIdenticalObj" is just the one between
"equal" and "the same", where "the same" is understood as "referring to the
same bytes in memory". -- For example:

gap> list1 := [1,2,3];;
gap> list2 := list1;;
gap> IsIdenticalObj(list1,list2);
true
gap> list1[2] := 17;
17
gap> list2; # changing list1 changed list2 as well, since it is THE SAME object
[ 1, 17, 3 ]
gap> list2 := ShallowCopy(list1); # make a copy, i.e. create another equal object
[ 1, 17, 3 ]
gap> list1 = list2; # list1 and list2 are still equal ...
true
gap> IsIdenticalObj(list1,list2); # ... but no longer identical
false
gap> list1[2] := 50; # now changing list1 does not change list2
50
gap> list2;
[ 1, 17, 3 ]

Hope this helps,

    Stefan Kohl

> On Thu, Dec 19, 2013 at 2:53 PM, Chiang-En Chen <l18981040 at gmail.com> wrote:
>
>> My GAP version is 4.6.5. When I performed the command   "IsIdentical( 1, 1
>> );" (this is an example in the section 27.10 of the manual ), it can not
>> work. The information of error is
>>
>> gap>  IsIdentical( 1, 1 );
>> Error, Variable: 'IsIdentical' must have a value
>> not in any function at line 1 of *stdin*
>>
>> Thank for reading.
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>



From roberto.radina at tiscali.it  Thu Dec 19 17:39:56 2013
From: roberto.radina at tiscali.it (=?iso-8859-1?Q?Roberto_R=E0dina?=)
Date: Thu, 19 Dec 2013 18:39:56 +0100
Subject: [GAP Forum] Speed up loading, minimize workspace file
References: <d86527122330e9349f6cca8f4dec95f3@vladikoff.com>
Message-ID: <998B3D79765846CEB1F8DA0CA3E80333@carnia>

> I'm looking for a way to speed up GAP loading.
> How can I do this? Or how can I minimize my workspace file?

On my (old) machine, GAP472, with a 38 MB workspace,  starts in 15 seconds 
the first time I load it. And in only 2 seconds if I "quit;"and reload it 
again because, I suppose, it is chached in RAM.
If I reload GAP with a DIFFERENT workspace, the time is again 2 seconds, so 
the time to load the workspace is about 0 seconds. So minimize the workspace 
will not help.

If I start GAP with a workspace but without the "-l" option, it starts in 5 
seconds (three times faster) the first time and still 2 seconds on reloads.

I don't know what changes without the "-l" option. Surely the online help 
(e.g.: gap> ?group) does not work.

Times may vary +/- 50%, I reported mean times.

Roberto 



From alexk at mcs.st-andrews.ac.uk  Thu Dec 19 18:35:41 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 19 Dec 2013 18:35:41 +0000
Subject: [GAP Forum] The command "IsIdentical" can not work.
In-Reply-To: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
References: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
Message-ID: <41BE1ACE-475F-4B3A-8A33-9AD549CCB97E@mcs.st-andrews.ac.uk>

In GAP 4.6.5 section 27.10 is "Obtaining LaTeX Representations of Objects"
and it has no such example. OTOH, IsIdenticalObj is documented there in 
Section 12.5-1 IsIdenticalObj - just to make it sure that you're looking 
at the right manual, to avoid further controversies.

Best wishes
Alexander





On 19 Dec 2013, at 13:53, Chiang-En Chen <l18981040 at gmail.com> wrote:

> My GAP version is 4.6.5. When I performed the command   "IsIdentical( 1, 1
> );" (this is an example in the section 27.10 of the manual ), it can not
> work. The information of error is
> 
> gap>  IsIdentical( 1, 1 );
> Error, Variable: 'IsIdentical' must have a value
> not in any function at line 1 of *stdin*
> 
> Thank for reading.
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum



From alexk at mcs.st-andrews.ac.uk  Thu Dec 19 20:27:35 2013
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 19 Dec 2013 20:27:35 +0000
Subject: [GAP Forum] The command "IsIdentical" can not work.
In-Reply-To: <41BE1ACE-475F-4B3A-8A33-9AD549CCB97E@mcs.st-andrews.ac.uk>
References: <CALpLja5SMS1pc2vGYWSADbwO+WbZ8x60MGiVUFxNo+V34meE3A@mail.gmail.com>
	<41BE1ACE-475F-4B3A-8A33-9AD549CCB97E@mcs.st-andrews.ac.uk>
Message-ID: <70A258CF-8BC9-4360-B2C9-C39CC5813A13@mcs.st-andrews.ac.uk>

P.S. I've just checked what google returns for "IsIdentical( 1, 1 );"
and the 1st hit is http://www.gap-system.org/Gap3/Manual3/C027S010.htm
and at the bottom of the page it is stated that this is GAP 3.4.4, April 1997
so this is likely where the question comes from.

You might be interested to look at http://www.gap-system.org/Faq/faq.html#3.2
"Where do I find a manual?" from GAP F.A.Q. The manual is supplied with
the system, and is a part of your installation. You may search in it very
efficiently from the GAP command line. Try, for example, to enter

?SetHelpViewer 

to see how this works and to read about further customisation dependently
on which format you'd prefer.

Hope this helps
Alexander


On 19 Dec 2013, at 18:35, Alexander Konovalov <alexk at mcs.st-andrews.ac.uk> wrote:

> In GAP 4.6.5 section 27.10 is "Obtaining LaTeX Representations of Objects"
> and it has no such example. OTOH, IsIdenticalObj is documented there in 
> Section 12.5-1 IsIdenticalObj - just to make it sure that you're looking 
> at the right manual, to avoid further controversies.
> 
> Best wishes
> Alexander
> 
> 
> 
> 
> 
> On 19 Dec 2013, at 13:53, Chiang-En Chen <l18981040 at gmail.com> wrote:
> 
>> My GAP version is 4.6.5. When I performed the command   "IsIdentical( 1, 1
>> );" (this is an example in the section 27.10 of the manual ), it can not
>> work. The information of error is
>> 
>> gap>  IsIdentical( 1, 1 );
>> Error, Variable: 'IsIdentical' must have a value
>> not in any function at line 1 of *stdin*
>> 
>> Thank for reading.
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
> 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum