From hulpke at math.colostate.edu  Fri Jan  4 19:35:13 2008
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri Jan  4 19:36:00 2008
Subject: [GAP Forum] Cartesian Group Direct Product
In-Reply-To: <BAY116-F389196E09F49D16582DCFDD14C0@phx.gbl>
References: <BAY116-F389196E09F49D16582DCFDD14C0@phx.gbl>
Message-ID: <45807BA7-83C3-4FCD-985D-B9A01256CDEA@math.colostate.edu>

Dear Paul Hjelmsted, Dear GAP-Forum,

> The problem with this is that it merely seems to shuffle between the  
> non-Cartesian
> form of the permutations, that is, for example, sending (123) to  
> (567) (Second Embedding) or merely leaving at at (123) (First  
> Embedding) but I may be doing something wrong.
>
> I am not getting anything Cartesian-wise. Perhaps I must leave D4  
> (actually called Dihedral(8)),
> as a pc-group and not a perm group?
>
> After I get this right, I need to generate the CycleIndex, and then  
> expand it in a manner you indicated, to get the full Polya  
> Polynomial, whose coefficients will be useful to me (especially to  
> find how many octads there are under D8 X S3 (Dihedral(16) X  
> Symmetric(3)) and other issues
>
> I need these generators for D4 X S3:
>
> (0,3,6,9)(1,4,7,10)(2,5,8,11)
> (0,4,8)(1,5,9)(2,6,10)(3,7,11)
> (1,7)(3,9)(5,11)
> (1,11)(2,10)(3,9)(4,8)(5,7)
>
> Or something with the same meaning

OK. You want a different representation for the direct product. GAP  
gives you by default the intransitive action (which has smaller  
degree), you would prefer the transitive product action.

The easiest way to construct this group is to let the intransitive  
direct product act on the cartesian product of the domains:

gap> d4:=DihedralGroup(IsPermGroup,8);
Group([ (1,2,3,4), (2,4) ])
gap> s3:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> d:=DirectProduct(d4,s3);
Group([ (1,2,3,4), (2,4), (5,6,7), (5,6) ])
gap> cart:=Cartesian([1..4],[5..7]);
[ [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ],
   [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ] ]
gap> hom:=ActionHomomorphism(d,cart,OnTuples,"surjective");
<action epimorphism>
gap> prod:=Image(hom);
Group([ (1,4,7,10)(2,5,8,11)(3,6,9,12), (4,10)(5,11)(6,12),
   (1,2,3)(4,5,6)(7,8,9)(10,11,12), (1,2)(4,5)(7,8)(10,11) ])


Up to labelling (which is due to the arrangement of the pairs in  
`cart') these are the generators you listed. You can use the map `hom'  
to go back to the intransitive direct product and use its  
decomposition functions.


Best wishes,

     Alexander Hulpke

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


From phjelmstad at msn.com  Sat Jan  5 18:05:33 2008
From: phjelmstad at msn.com (PAUL HJELMSTAD)
Date: Sat Jan  5 18:06:28 2008
Subject: [GAP Forum] Cartesian Group Direct Product
In-Reply-To: <45807BA7-83C3-4FCD-985D-B9A01256CDEA@math.colostate.edu>
Message-ID: <BAY116-F3980C429D7625EC9D7C0C4D14D0@phx.gbl>

Dear Alexander Hulpke, Dear GAP-Forum,

Thanks! I realized after I sent my last message, that I was not 
understanding the meaning of "Cartesian" correctly, but I see you understood 
what I meant. Someone else called what I am looking for the "cross-product" 
representation, or what you call the transitive product representation.

Finding the CycleIndex should be relatively easy here, but expanding to the 
Polya Polynomial
has proved difficult, merely because of a problem with variables. Thanks

PGH


>From: Alexander Hulpke <hulpke@math.colostate.edu>
>To: PAUL HJELMSTAD <phjelmstad@msn.com>
>CC: GAP Forum <forum@gap-system.org>
>Subject: Re: [GAP Forum] Cartesian Group Direct Product
>Date: Fri, 4 Jan 2008 12:35:13 -0700
>
>Dear Paul Hjelmsted, Dear GAP-Forum,
>
>>The problem with this is that it merely seems to shuffle between the  
>>non-Cartesian
>>form of the permutations, that is, for example, sending (123) to  (567) 
>>(Second Embedding) or merely leaving at at (123) (First  Embedding) but I 
>>may be doing something wrong.
>>
>>I am not getting anything Cartesian-wise. Perhaps I must leave D4  
>>(actually called Dihedral(8)),
>>as a pc-group and not a perm group?
>>
>>After I get this right, I need to generate the CycleIndex, and then  
>>expand it in a manner you indicated, to get the full Polya  Polynomial, 
>>whose coefficients will be useful to me (especially to  find how many 
>>octads there are under D8 X S3 (Dihedral(16) X  Symmetric(3)) and other 
>>issues
>>
>>I need these generators for D4 X S3:
>>
>>(0,3,6,9)(1,4,7,10)(2,5,8,11)
>>(0,4,8)(1,5,9)(2,6,10)(3,7,11)
>>(1,7)(3,9)(5,11)
>>(1,11)(2,10)(3,9)(4,8)(5,7)
>>
>>Or something with the same meaning
>
>OK. You want a different representation for the direct product. GAP  gives 
>you by default the intransitive action (which has smaller  degree), you 
>would prefer the transitive product action.
>
>The easiest way to construct this group is to let the intransitive  direct 
>product act on the cartesian product of the domains:
>
>gap> d4:=DihedralGroup(IsPermGroup,8);
>Group([ (1,2,3,4), (2,4) ])
>gap> s3:=SymmetricGroup(3);
>Sym( [ 1 .. 3 ] )
>gap> d:=DirectProduct(d4,s3);
>Group([ (1,2,3,4), (2,4), (5,6,7), (5,6) ])
>gap> cart:=Cartesian([1..4],[5..7]);
>[ [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ],
>   [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ] ]
>gap> hom:=ActionHomomorphism(d,cart,OnTuples,"surjective");
><action epimorphism>
>gap> prod:=Image(hom);
>Group([ (1,4,7,10)(2,5,8,11)(3,6,9,12), (4,10)(5,11)(6,12),
>   (1,2,3)(4,5,6)(7,8,9)(10,11,12), (1,2)(4,5)(7,8)(10,11) ])
>
>
>Up to labelling (which is due to the arrangement of the pairs in  `cart') 
>these are the generators you listed. You can use the map `hom'  to go back 
>to the intransitive direct product and use its  decomposition functions.
>
>
>Best wishes,
>
>     Alexander Hulpke
>
>-- Colorado State University, Department of Mathematics,
>Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
>email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
>http://www.math.colostate.edu/~hulpke
>
>


From phjelmstad at msn.com  Tue Jan 15 02:04:05 2008
From: phjelmstad at msn.com (PAUL HJELMSTAD)
Date: Tue Jan 15 02:04:43 2008
Subject: FW: [GAP Forum] Cartesian Group Direct Product
Message-ID: <BAY116-W3973CD1F75D7977BA3CBB1D1470@phx.gbl>


Dear GAP-Forum:
 
I also found the Cycle Index and Polya Polynomial of the Group generated by all the primes coprime to 24 (Totient). (1,5,7,11,13,17,19,23) Here are my results. My question is, what is the Group-theoretical name for this? (Something
like D8.2 X S3, having order 192?)
 
G:= Group( [ (1,2,3,4,5,6,7,8), (1,3)(2,6)(5,7), (1,5)(3,7), (1,7)(2,6)(3,5),  ( 9,10), ( 9,10,11) ] );
 
(Convert to Cartesian...)
 
Cycle Index:
1/192*x_1^24+1/96*x_1^12*x_2^6+1/64*x_1^8*x_2^8+1/24*x_1^6*x_2^9+1/32*x_1^4*x_\2^10+1/8*x_1^2*x_2^11+5/48*x_2^12+1/96*x_3^8+1/48*x_3^4*x_6^2+1/6*x_4^6+1/12*x\_3^2*x_6^3+5/96*x_6^4+1/6*x_8^3+1/12*x_12^2+1/12*x_24
 
Polya:
x_1^24+x_1^23+7*x_1^22+23*x_1^21+97*x_1^20+294*x_1^19+870*x_1^18+2051*x_1^17+4\272*x_1^16+7352*x_1^15+10980*x_1^14+13790*x_1^13+15008*x_1^12+13790*x_1^11+109\80*x_1^10+7352*x_1^9+4272*x_1^8+2051*x_1^7+870*x_1^6+294*x_1^5+97*x_1^4+23*x_1\^3+7*x_1^2+x_1+1
 
 
Thanks
 
PGH
 


To: phjelmstad@msn.comCC: forum@gap-system.org; hulpke@math.colostate.eduSubject: Re: [GAP Forum] Cartesian Group Direct ProductFrom: Paul.Hjelmstad@allianzlife.comDate: Sun, 6 Jan 2008 16:06:22 -0600Dear Alexander Hulpke, Dear GAP-Forum, Works great. The relabelling was confusing, but that is because the permutation for S3 permutes the origin, so to speak, using (5,6), but it doesn't matter, I get the correct CycleIndex and expanding it out is easy, now that I know what to do. This is the Polya Polynomials I get for D8 X S3 and C8 X C3 respectively, I believe they are correct: x^24+x^23+9*x^22+31*x^21+151*x^20+496*x^19+1553*x^18+3777*x^17+8028*x^16+13981\ *x^15+21042*x^14+26516*x^13+28898*x^12+26516*x^11+21042*x^10+13981*x^9+8028*x^\ 8+3777*x^7+1553*x^6+496*x^5+151*x^4+31*x^3+9*x^2+x+1 x^24+x^23+12*x^22+85*x^21+446*x^20+1771*x^19+5620*x^18+14421*x^17+30667*x^16+5\ 4484*x^15+81752*x^14+104006*x^13+112720*x^12+104006*x^11+81752*x^10+54484*x^9+\ 30667*x^8+14421*x^7+5620*x^6+1771*x^5+446*x^4+85*x^3+12*x^2+x+1 Paul HjelmstadITS Enterprise Security763-582-6547 (x46547)Paul_Hjelmstad@allianzlife.com 



'PAUL HJELMSTAD' <phjelmstad@msn.com> 01/05/2008 12:05 PM 





To
hulpke@math.colostate.edu 


cc
forum@gap-system.org 


Subject
Re: [GAP Forum] Cartesian Group Direct Product




Dear Alexander Hulpke, Dear GAP-Forum,Thanks! I realized after I sent my last message, that I was not understanding the meaning of 'Cartesian' correctly, but I see you understood what I meant. Someone else called what I am looking for the 'cross-product' representation, or what you call the transitive product representation.Finding the CycleIndex should be relatively easy here, but expanding to the Polya Polynomialhas proved difficult, merely because of a problem with variables. ThanksPGH>From: Alexander Hulpke <hulpke@math.colostate.edu>>To: PAUL HJELMSTAD <phjelmstad@msn.com>>CC: GAP Forum <forum@gap-system.org>>Subject: Re: [GAP Forum] Cartesian Group Direct Product>Date: Fri, 4 Jan 2008 12:35:13 -0700>>Dear Paul Hjelmsted, Dear GAP-Forum,>>>The problem with this is that it merely seems to shuffle between the  >>non-Cartesian>>form of the permutations, that is, for example, sending (123) to  (567) >>(Second Embedding) or merely leaving at at (123) (First  Embedding) but I >>may be doing something wrong.>>>>I am not getting anything Cartesian-wise. Perhaps I must leave D4  >>(actually called Dihedral(8)),>>as a pc-group and not a perm group?>>>>After I get this right, I need to generate the CycleIndex, and then  >>expand it in a manner you indicated, to get the full Polya  Polynomial, >>whose coefficients will be useful to me (especially to  find how many >>octads there are under D8 X S3 (Dihedral(16) X  Symmetric(3)) and other >>issues>>>>I need these generators for D4 X S3:>>>>(0,3,6,9)(1,4,7,10)(2,5,8,11)>>(0,4,8)(1,5,9)(2,6,10)(3,7,11)>>(1,7)(3,9)(5,11)>>(1,11)(2,10)(3,9)(4,8)(5,7)>>>>Or something with the same meaning>>OK. You want a different representation for the direct product. GAP  gives >you by default the intransitive action (which has smaller  degree), you >would prefer the transitive product action.>>The easiest way to construct this group is to let the intransitive  direct >product act on the cartesian product of the domains:>>gap> d4:=DihedralGroup(IsPermGroup,8);>Group([ (1,2,3,4), (2,4) ])>gap> s3:=SymmetricGroup(3);>Sym( [ 1 .. 3 ] )>gap> d:=DirectProduct(d4,s3);>Group([ (1,2,3,4), (2,4), (5,6,7), (5,6) ])>gap> cart:=Cartesian([1..4],[5..7]);>[ [ 1, 5 ], [ 1, 6 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ],>   [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 4, 7 ] ]>gap> hom:=ActionHomomorphism(d,cart,OnTuples,'surjective');><action epimorphism>>gap> prod:=Image(hom);>Group([ (1,4,7,10)(2,5,8,11)(3,6,9,12), (4,10)(5,11)(6,12),>   (1,2,3)(4,5,6)(7,8,9)(10,11,12), (1,2)(4,5)(7,8)(10,11) ])>>>Up to labelling (which is due to the arrangement of the pairs in  `cart') >these are the generators you listed. You can use the map `hom'  to go back >to the intransitive direct product and use its  decomposition functions.>>>Best wishes,>>     Alexander Hulpke>>-- Colorado State University, Department of Mathematics,>Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA>email: hulpke@math.colostate.edu, Phone: ++1-970-4914288>http://www.math.colostate.edu/~hulpke>>

CONFIDENTIALITY NOTICE: The information in this message, and any files transmitted with it, is confidential, may be legally privileged, and intended only for the use of the individual(s) named above. Be aware that the use of any confidential or personal information may be restricted by state and federal privacy laws. If you are not the intended recipient, do not further disseminate this message. If this message was received in error, please notify the sender and delete it. 
From megha.iitd at gmail.com  Tue Jan 15 10:24:17 2008
From: megha.iitd at gmail.com (Megha Gupta)
Date: Tue Jan 15 10:24:53 2008
Subject: [GAP Forum] related to matrices
Message-ID: <1447f9270801150224v7e7eff4dy90ffdf49894d1777@mail.gmail.com>

Dear Gap Forum,

Given invertible matrices A, B, C having determinant 1 and entries from
integers i.e. from SL(3,Z). Is it possible to check whether A can be written
as a product of powers of matrices B, C and their inverses?

Cheers
Megha
From alice at maths.uwa.edu.au  Wed Jan 16 07:53:08 2008
From: alice at maths.uwa.edu.au (Alice Niemeyer)
Date: Wed Jan 16 07:54:06 2008
Subject: [GAP Forum] GAP related Research Jobs at Perth Western Australia
Message-ID: <478DB7E4.60003@maths.uwa.edu.au>


Hi everyone,

the following jobs are available at UWA in Perth.
At the very least one of the appointments will be for
algorithms for group theory and these algorithms
are usually developed and implemented in GAP.

Cheers,
Alice Niemeyer.

> > RESEARCH ASSOCIATE POSITIONS  (REF: 2139)
> > SCHOOL OF MATHEMATICS AND STATISTICS, UNIVERSITY OF WESTERN AUSTRALIA
> > 
> > 2 x 3 year appointments
> > 1 x 2 year appointment
> > with further employment dependent on funding
> > and demand for the research programs.
> > Salary Range:  Level A  $48,905 - $66,367 p.a. - minimum starting salary
> > for appointee with PhD will be $61,827 p.a.
> > Closing date:  Friday, 29 February 2008
> > 
> > Full details available at:
> > 
> > https://www.his.admin.uwa.edu.au/jobvacs/external/academic/doc/doc1089925.RTF 
> > 
> > 
> > 
> > Three positions are available in the research group in Groups and
> > Combinatorics led by Professor Cheryl E. Praeger and including Dr Alice
> > Niemeyer, Associate Professors Cai Heng Li and Gordon Royle and Dr
> > Michael Giudici.  Appointees are expected to conduct research within the
> > research programs of Praeger's ARC Federation Fellowship Grant ?Group
> > actions: combinatorics, geometry and computation? and/or Niemeyer and
> > Praeger's ARC Discovery Grant ?Groups: statistics, structure and
> > algorithms?.  At least one successful applicant will work in the area of
> > computational group theory and at least one will work in the area of
> > permutation groups and algebraic combinatorics.
> > 
> > A PhD (or near-completion) in a relevant field is essential.  Beyond
> > technical strength, we seek persons who get excited about achieving an
> > outcome to join our focussed research teams.  For further information
> > regarding any of these positions please email Cheryl Praeger or Alice
> > Niemeyer at   mathsjobs@maths.uwa.edu.au.
> > 
> > Application Details: Applicants must address the selection criteria.
> > Written applications quoting the reference number, personal contact
> > details, qualifications and experience, along with contact details of
> > three referees should be sent to Director, Human Resources, The
> > University of Western Australia, M350, 35 Stirling Highway, Crawley WA
> > 6009 or emailed to jobs@uwa.edu.au by the closing date.
> > 


-- 
=*=*=*=*=*=*=*=*=*=*=*=M=*=*=*=*M*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
Alice C. Niemeyer     =@\___)  =@\     School of Mathematics & Statistics
alice@maths.uwa.edu.au  \_ (    ( \    University of Western Australia
+61-8-6488 3890         .| .|  .|_(\_) Nedlands,  WA 6009,   Australia.
=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
      WWW:      http://www.maths.uwa.edu.au/~alice/

From jaijinenedra at yahoo.co.in  Mon Jan 21 08:49:46 2008
From: jaijinenedra at yahoo.co.in (Vivek Jain)
Date: Mon Jan 21 08:50:23 2008
Subject: [GAP Forum] transversals
Message-ID: <876717.63223.qm@web8708.mail.in.yahoo.com>

How can we determine all the right transversals with identity of a subgroup in a finite group using GAP?


Vivek Kumar Jain 

Dept. of Mathematics

Univ. of Allahabad

Allahabad-211002

India

       
---------------------------------
 Bollywood, fun, friendship, sports and more. You name it,  we have it.
From dkahrobaei at CityTech.Cuny.Edu  Fri Jan 18 16:27:08 2008
From: dkahrobaei at CityTech.Cuny.Edu (Delaram Kahrobaei)
Date: Mon Jan 21 10:31:57 2008
Subject: [GAP Forum] Group Theory and Theoretical Computer Science Conference
Message-ID: <47908D0C0200009F000009F9@email1.citytech.cuny.edu>

May 2nd 2008
Interdisciplinary Research in Logic, Group Theory, and Theoretical Computer Science Conference at CUNY
The Second Conference for Women in Mathematics (New York)
All interested members of the mathematical community are invited to attend.

Speakers will include
Moira Chas (Stony Brook University)
Natasha Dobrinen (University of Denver)
Olga Kharlampovich (McGill University) 
Gretchen Ostheimer (Hofstra University)
Jennifer Taback (Bowdoin College)
Carol Wood (Wesleyan University)

Discussion Panel
Jane Gilman (Rutgers University)
Linda Keen (Lehman College and The Graduate Center (CUNY) (Tentative)
Estela Rojas (NYC College of Technology (CUNY))
Gretchen Ostheimer (Hofstra University)
Christina Sormani (Lehman College and The Graduate Center (CUNY))

This will be the second meeting of the New York Women in Mathematics Network supported by NSF.

There will be a poster session for women PhD students. To apply please contact one of the organizers
Victoria Gitman (vgitman@nylogic.org) or Delaram Kahrobaei(dkahrobaei@citytech.cuny.edu).

Further details of the meeting are available at:
http://www.nywimn.net


Delaram Kahrobaei, Ph.D.
Assistant Professor in Mathematics
E-mail: DKahrobaei@CityTech.CUNY.edu
Tel: +1.718.260.5384
Fax: +1.718.254.8537
Cel: +1.646.318.8520
Webpage: http://websupport1.citytech.cuny.edu/Faculty/dkahrobaei/
Address:    Mathematics Department (Namm 707), New York City College of Technology (CUNY), 300 Jay Street, Brooklyn, NY 11201

From l.h.soicher at qmul.ac.uk  Wed Jan 23 20:44:39 2008
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Wed Jan 23 20:45:52 2008
Subject: [GAP Forum] Announcing the Circle Package
Message-ID: <20080123204439.GA15610@maths.qmul.ac.uk>

Dear Forum Members,

It is my pleasure to announce the newly accepted Circle package for GAP,
by Alexander Konovalov and Panagiotis Soules. This package provides
functionality to compute in the adjoint groups of associative rings.

The Circle package homepage is

http://www.cs.st-andrews.ac.uk/~alexk/circle.htm

where you can download the package and also find HTML and PDF
documentation. 

Sincerely,
Leonard Soicher
(on behalf of the GAP Council)

From gerhard.hiss at math.rwth-aachen.de  Fri Jan 25 16:31:43 2008
From: gerhard.hiss at math.rwth-aachen.de (Gerhard Hiss)
Date: Fri Jan 25 16:32:14 2008
Subject: [GAP Forum] Wedderga
Message-ID: <hiss-1080125173143.A0213916@sirius.math.rwth-aachen.de>

Dear Members of the GAP forum,

it is my pleasure to announce the new GAP package Wedderga by 
Osnel Broche Cristo, Alexander Konovalov, Aurora Olivieri, 
Gabriela Olteanu, and Angel del Rio. 

Wedderga contains routines to compute the Wedderburn decomposition 
of a group algebra of a finite group over abelian number fields and over 
finite fields. Wedderga also contains functions to compute the primitive 
central idempotents of group algebras, and to construct crossed products.

Wedderga homepages are

	http://www.um.es/adelrio/wedderga.htm

and

	http://www.cs.st-andrews.ac.uk/~alexk/wedderga.htm,

where you can download the package and its documentation.

Sincerely,

Gerhard Hiss
January 25, 200


--
Gerhard Hiss, Lehrstuhl D fuer Mathematik, RWTH Aachen, 52056 Aachen
Tel.: (+49) (0) 241 / 80-94543



From armahg at gmail.com  Fri Jan 25 21:56:58 2008
From: armahg at gmail.com (George Armah)
Date: Fri Jan 25 21:57:36 2008
Subject: [GAP Forum] Cross Compiling GAP for Mac OS X
Message-ID: <479A5B2A.8070009@gmail.com>

Hello,

I am trying to build a universal gap binary for Mac OS X.

To get started I ran the following to try and test what the results of a 
cross compilation would be
./configure --build=i686-apple-darwin8 --with-arch=apple 
--host=powerpc-apple-darwin8

and got the following error:
checking unaligned access... configure: error: cannot run test program 
while cross compiling
See `config.log' for more details.
make: *** [bin/powerpc-apple-darwin8-gcc/Makefile] Error 1

Is there a way to disable the above test? Am I doing this completely wrong?
Any and all advice is welcome.

Thanks in advance,

George Armah.

p.s. I am an undergraduate Math & C.S. major and am using GAP and the 
kbmag package to learn about the Automatic structures of
Coxeter groups.

From ndroock1 at gmail.com  Sun Jan 27 10:39:58 2008
From: ndroock1 at gmail.com (Nilo de Roock)
Date: Sun Jan 27 10:40:18 2008
Subject: [GAP Forum] gap and Windows Vista
Message-ID: <fe34b49e0801270239k6b75751cla42f15ea77f1bab7@mail.gmail.com>

forum,

I am aware this is not a math related gap question but I don't know
where else to go.

The command c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap works fine on
XP but generates the following error message on Vista: gap: sorry,
options must not be grouped '-L:'.


<screencopy>
Vista:
C:\gap4r4\bin>gapw95 -L: "c:/gap4r4/bin/ws.gap"
gap: sorry, options must not be grouped '-L:'.
usage: gap [OPTIONS] [FILES]
       run the Groups, Algorithms and Programming system, Version 4.4.10
       use '-h' option to get help.

gap: Press <Enter> to end program

C:\gap4r4\bin>
</screencopy>


<screencopy>
XP: ( behaviour is as expected ).
C:\gap4r4\bin>c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap
GAP4, Version: 4.4.10 of 02-Oct-2007, i686-pc-cygwin-gcc
Components:  small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0,
             small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10 0.2,
             id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10 0.1,
             trans 1.0, prim 2.1  loaded.
Packages:    AClib 1.1, Polycyclic 2.2, Alnuth 2.2.5, CrystCat 1.1.2,
             Cryst 4.1.5, AutPGrp 1.2, CRISP 1.3.1, CTblLib 1.1.3,
             TomLib 1.1.2, FactInt 1.5.2, GAPDoc 1.1, FGA 1.1.0.1,
             IRREDSOL 1.1.2, LAGUNA 3.4, Sophus 1.23, Polenta 1.2.7,
             ResClasses 2.5.3  loaded.
gap>
</screencopy>

-- 
kind regards / met vriendelijke groet,
nilo de roock

From resteban at mat.upv.es  Sun Jan 27 14:18:05 2008
From: resteban at mat.upv.es (Ramon Esteban)
Date: Sun Jan 27 14:18:38 2008
Subject: [GAP Forum] gap and Windows Vista
In-Reply-To: <fe34b49e0801270239k6b75751cla42f15ea77f1bab7@mail.gmail.com>
References: <fe34b49e0801270239k6b75751cla42f15ea77f1bab7@mail.gmail.com>
Message-ID: <20080127141805.GA8823@upvnet.upv.es>

Dear Nilo, dear forum,

I see you are writing '-L:' in the Vista command line  and '-L' in the
XP command line. Have you tried to delete the ':' in the Vista
version?

I have not tried the Vista version, so I cannot tell you more.

Best regards,
-- 
Ramon <resteban@mat.upv.es>

Clau p?blica PGP/Llave p?blica PGP/Clef publique PGP/PGP public key:
         http://www.rediris.es/cert/servicios/keyserver/
         http://ttt.upv.es/~resteban/resteban.pgp
Nou tel?fon/Nuevo tel?fono/Nouveau t?l?phone/New phone: (+34)963877007 x76676

* Nilo de Roock <ndroock1@gmail.com> [080127 12:48]:
> forum,
> 
> I am aware this is not a math related gap question but I don't know
> where else to go.
> 
> The command c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap works fine on
> XP but generates the following error message on Vista: gap: sorry,
> options must not be grouped '-L:'.
> 
> 
> <screencopy>
> Vista:
> C:\gap4r4\bin>gapw95 -L: "c:/gap4r4/bin/ws.gap"
> gap: sorry, options must not be grouped '-L:'.
> usage: gap [OPTIONS] [FILES]
>        run the Groups, Algorithms and Programming system, Version 4.4.10
>        use '-h' option to get help.
> 
> gap: Press <Enter> to end program
> 
> C:\gap4r4\bin>
> </screencopy>
> 
> 
> <screencopy>
> XP: ( behaviour is as expected ).
> C:\gap4r4\bin>c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap
> GAP4, Version: 4.4.10 of 02-Oct-2007, i686-pc-cygwin-gcc
> Components:  small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0,
>              small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10 0.2,
>              id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10 0.1,
>              trans 1.0, prim 2.1  loaded.
> Packages:    AClib 1.1, Polycyclic 2.2, Alnuth 2.2.5, CrystCat 1.1.2,
>              Cryst 4.1.5, AutPGrp 1.2, CRISP 1.3.1, CTblLib 1.1.3,
>              TomLib 1.1.2, FactInt 1.5.2, GAPDoc 1.1, FGA 1.1.0.1,
>              IRREDSOL 1.1.2, LAGUNA 3.4, Sophus 1.23, Polenta 1.2.7,
>              ResClasses 2.5.3  loaded.
> gap>
> </screencopy>
> 
> -- 
> kind regards / met vriendelijke groet,
> nilo de roock
> 
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

From ndroock1 at gmail.com  Sun Jan 27 20:08:43 2008
From: ndroock1 at gmail.com (Nilo de Roock)
Date: Sun Jan 27 20:10:04 2008
Subject: [GAP Forum] gap and Windows Vista
In-Reply-To: <20080127141805.GA8823@upvnet.upv.es>
References: <fe34b49e0801270239k6b75751cla42f15ea77f1bab7@mail.gmail.com>
	<20080127141805.GA8823@upvnet.upv.es>
Message-ID: <fe34b49e0801271208m5d016372l2e944ae4f2248354@mail.gmail.com>

Thank you very much, Ramon!

It must have been the 'copy / paste'-ing from one vmware XP machine to
another vmware Vista machine, that got it ( me ) mixed up. A
non-problem but nevertheless solved.

kind regards,
nilo


2008/1/27, Ramon Esteban <resteban@mat.upv.es>:
> Dear Nilo, dear forum,
>
> I see you are writing '-L:' in the Vista command line  and '-L' in the
> XP command line. Have you tried to delete the ':' in the Vista
> version?
>
> I have not tried the Vista version, so I cannot tell you more.
>
> Best regards,
> --
> Ramon <resteban@mat.upv.es>
>
> Clau p?blica PGP/Llave p?blica PGP/Clef publique PGP/PGP public key:
>          http://www.rediris.es/cert/servicios/keyserver/
>          http://ttt.upv.es/~resteban/resteban.pgp
> Nou tel?fon/Nuevo tel?fono/Nouveau t?l?phone/New phone: (+34)963877007 x76676
>
> * Nilo de Roock <ndroock1@gmail.com> [080127 12:48]:
> > forum,
> >
> > I am aware this is not a math related gap question but I don't know
> > where else to go.
> >
> > The command c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap works fine on
> > XP but generates the following error message on Vista: gap: sorry,
> > options must not be grouped '-L:'.
> >
> >
> > <screencopy>
> > Vista:
> > C:\gap4r4\bin>gapw95 -L: "c:/gap4r4/bin/ws.gap"
> > gap: sorry, options must not be grouped '-L:'.
> > usage: gap [OPTIONS] [FILES]
> >        run the Groups, Algorithms and Programming system, Version 4.4.10
> >        use '-h' option to get help.
> >
> > gap: Press <Enter> to end program
> >
> > C:\gap4r4\bin>
> > </screencopy>
> >
> >
> > <screencopy>
> > XP: ( behaviour is as expected ).
> > C:\gap4r4\bin>c:/gap4r4/bin/gapw95 -L c:/gap4r4/bin/ws.gap
> > GAP4, Version: 4.4.10 of 02-Oct-2007, i686-pc-cygwin-gcc
> > Components:  small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0,
> >              small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10 0.2,
> >              id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10 0.1,
> >              trans 1.0, prim 2.1  loaded.
> > Packages:    AClib 1.1, Polycyclic 2.2, Alnuth 2.2.5, CrystCat 1.1.2,
> >              Cryst 4.1.5, AutPGrp 1.2, CRISP 1.3.1, CTblLib 1.1.3,
> >              TomLib 1.1.2, FactInt 1.5.2, GAPDoc 1.1, FGA 1.1.0.1,
> >              IRREDSOL 1.1.2, LAGUNA 3.4, Sophus 1.23, Polenta 1.2.7,
> >              ResClasses 2.5.3  loaded.
> > gap>
> > </screencopy>
> >
> > --
> > kind regards / met vriendelijke groet,
> > nilo de roock
> >
> > _______________________________________________
> > Forum mailing list
> > Forum@mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>

From bob.heffernan at gmail.com  Tue Jan 29 14:50:59 2008
From: bob.heffernan at gmail.com (Robert Heffernan)
Date: Tue Jan 29 14:51:23 2008
Subject: [GAP Forum] question
Message-ID: <6d9a83e90801290650leeb5326p2e44582f228827fc@mail.gmail.com>

Hi,

I've written a (very naive) function to test if two groups are
isoclinic.  However, it will sometimes return true and sometimes false
for the same two groups & I'm not sure why this is happening.

The code is below.  I would be very grateful for any suggestions,

thank you,
Bob Heffernan

# Code to test if two groups G and H are isoclinic.
# we want:
#   i) an isomorphism phi1 from G/Z(G) -> H/Z(H)
#  ii) an isomorphism phi2 from G' -> H'
# st. if
#  a) (g1Z(G))phi1=h1Z(H); and
#  b) (g2Z(G))phi1=h2Z(H)
# then
#  c) ([g1,g2])phi2 = [h1,h2]

# returns true if G~H
IsIsoclinic := function(G,H)
  local DG,DH,ZG,ZH,GZG,HZH,phi1,phi2,elG,piG,piH,g1,g2,g1p,g2p,h1,h2;
  G:=Image(IsomorphismPcGroup(G));
  H:=Image(IsomorphismPcGroup(H));

  DG:=DerivedSubgroup(G);
  DH:=DerivedSubgroup(H);
  ZG:=Centre(G);
  ZH:=Centre(H);

  GZG:=FactorGroup(G,ZG);
  HZH:=FactorGroup(H,ZH);

  phi1:=IsomorphismGroups(GZG,HZH);
  if phi1=fail then return false; fi;
  phi2:=IsomorphismGroups(DG,DH);
  if phi2=fail then return false; fi;

  elG:=Elements(G);

  piG:=NaturalHomomorphismByNormalSubgroup(G,ZG);
  piH:=NaturalHomomorphismByNormalSubgroup(H,ZH);

  for g1 in elG do
    for g2 in elG do
      g1p:=Image(phi1, Image(piG, g1));
      g2p:=Image(phi1, Image(piG, g2));
      h1:=PreImagesRepresentative(piH, g1p);
      h2:=PreImagesRepresentative(piH, g2p);
      if not(Image(phi2, Comm(g1,g2))=Comm(h1,h2)) then return false; fi;
    od;
  od;
  return true;
end;

From reichard at maths.uwa.edu.au  Wed Jan 30 00:25:47 2008
From: reichard at maths.uwa.edu.au (Sven Reichard)
Date: Wed Jan 30 00:26:14 2008
Subject: [GAP Forum] question
In-Reply-To: <6d9a83e90801290650leeb5326p2e44582f228827fc@mail.gmail.com>
References: <6d9a83e90801290650leeb5326p2e44582f228827fc@mail.gmail.com>
Message-ID: <479FC40B.4060308@maths.uwa.edu.au>

Bob,

according to your definition you need to find two group isomorphisms which satisfy certain 
properties in relation to each other. For both phi1 and phi2, there may be several 
candidates. GAP normally uses random methods for certain tasks, so IsomorphismGroups is 
not guaranteed to return the same isomorphism each time it is called.

If for a certain choice of phi1 and phi2 your properties are fulfilled you can be sure the 
groups are isoclinic. However, if for one choice they are not fulfilled it does not mean 
they are not isoclinic; we might just have picked the wrong set of isomorphisms. You need 
to somehow show that for any choice of phi1 and phi2, a) and b) do not necessarily imply c).

Hope this helps.
Sven.



Robert Heffernan wrote:
> Hi,
> 
> I've written a (very naive) function to test if two groups are
> isoclinic.  However, it will sometimes return true and sometimes false
> for the same two groups & I'm not sure why this is happening.
> 
> The code is below.  I would be very grateful for any suggestions,
> 
> thank you,
> Bob Heffernan
> 
> # Code to test if two groups G and H are isoclinic.
> # we want:
> #   i) an isomorphism phi1 from G/Z(G) -> H/Z(H)
> #  ii) an isomorphism phi2 from G' -> H'
> # st. if
> #  a) (g1Z(G))phi1=h1Z(H); and
> #  b) (g2Z(G))phi1=h2Z(H)
> # then
> #  c) ([g1,g2])phi2 = [h1,h2]
> 
> # returns true if G~H
> IsIsoclinic := function(G,H)
>   local DG,DH,ZG,ZH,GZG,HZH,phi1,phi2,elG,piG,piH,g1,g2,g1p,g2p,h1,h2;
>   G:=Image(IsomorphismPcGroup(G));
>   H:=Image(IsomorphismPcGroup(H));
> 
>   DG:=DerivedSubgroup(G);
>   DH:=DerivedSubgroup(H);
>   ZG:=Centre(G);
>   ZH:=Centre(H);
> 
>   GZG:=FactorGroup(G,ZG);
>   HZH:=FactorGroup(H,ZH);
> 
>   phi1:=IsomorphismGroups(GZG,HZH);
>   if phi1=fail then return false; fi;
>   phi2:=IsomorphismGroups(DG,DH);
>   if phi2=fail then return false; fi;
> 
>   elG:=Elements(G);
> 
>   piG:=NaturalHomomorphismByNormalSubgroup(G,ZG);
>   piH:=NaturalHomomorphismByNormalSubgroup(H,ZH);
> 
>   for g1 in elG do
>     for g2 in elG do
>       g1p:=Image(phi1, Image(piG, g1));
>       g2p:=Image(phi1, Image(piG, g2));
>       h1:=PreImagesRepresentative(piH, g1p);
>       h2:=PreImagesRepresentative(piH, g2p);
>       if not(Image(phi2, Comm(g1,g2))=Comm(h1,h2)) then return false; fi;
>     od;
>   od;
>   return true;
> end;

-- 
Sven Reichard
School of Mathematics and Statistics
The University of Western Australia
35 Stirling Highway
Crawley 6009
Western Australia

>

From rollandj at uwm.edu  Sun Feb  3 00:29:51 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sun Feb  3 00:29:55 2008
Subject: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
Message-ID: <47A50AFF.9030408@uwm.edu>

Hello, all!

I am trying to install GAP on an iBook 900 MHz running Mac OS 10.4.11 
with 640 MB of RAM.

I have a basic GAP install compiled. The problem is getting all the 
packages configured (or otherwise installed).

The packages are installed in the directory /usr/local/lib/gap4r4/pkg/. 
Inside this directory, there is a shell script InstPackages.sh; I am 
attaching a copy of InstPackages.sh.

When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh, I get 
the error message "tcsh: ./InstPackages.sh: Command not found." (I am 
running tcsh as my default shell.)

Can someone help me trouble-shoot the package installation process?

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>
-------------- next part --------------
#!/usr/bin/sh 

# $Id: InstPackages.sh,v 1.7 2006/12/06 17:07:16 gap Exp $

# You need 'gzip', GNU 'tar', a C compiler, sed, pdftex to run this.
# Copy the current merged package archive to the 'pkg' subdirectory of
# your GAP installation.
# Then start this script (or do it step by step with cut and paste) inside
# this 'pkg' subdirectory.

# Frank L?beck, Frank.Luebeck@Math.RWTH-Aachen.De for questions and complaints.

# Note, that this isn't and is not intended to be a sophisticated script.
# Even if it doesn't work completely automatically for you, you may get 
# an idea what to do for a complete installation of GAP.

# first unpack the merged package archive inside the 'pkg' subdirectory:
# tar xpzvf packages-*.tar.gz

cd ace
./configure ../..
make
cd ..

cd anupq
./configure ../..
# on Linux with gmp in standard place and with GAP 4.3 gap.sh script
# in standard path as: gap  just do: make  (otherwise check installation
# instructions - configure output gives hints)
make
cd ..

# You may not want a writable directory here! In this case substitute
# the directories 'datagens' and 'dataword' by links to somewhere else.
cd atlasrep
chmod 1777 datagens dataword
cd ..

# Installation of Carat produces a lot of data, maybe you want to leave 
# this out until a user complains.
# It is not possible to move around compiled binaries because these have the
# path to some data files burned in.
cd carat
tar xzpf carat-2.0.tar.gz
rm -f bin
ln -s carat-2.0/bin bin
cd carat-2.0/functions
# Install the include Gmp first.
# (If you have already Gmp on your system, you can delete the file
# gmp-4.1.2.tar.gz and delete the target 'Gmp' from the target 'ALL' in
# carat-2.0/Makefile.)
tar xzpf gmp-4.1.2.tar.gz
cd ..
make TOPDIR=`pwd` Links
# Note that Gmp may use processor specific code, so this step may not be ok
# for a network installation if you want to use the package on older computers
# as well.
make TOPDIR=`pwd` Gmp
# And now the actual Carat programs.
make TOPDIR=`pwd` CFLAGS=`-O2`
cd ../..


cd cohomolo
./configure 
cd standalone/progs.d
cp makefile.orig makefile
cd ../..
make 
cd ..

# create dynamic library with EDIM kernel module
cd edim
make clean
unsetenv LANG
unsetenv LC_ALL
./configure
make
cd ..

cd example
./configure ../..
make
cd ..

cd fplsa
./configure ../..
make CC="gcc -O2 "
cd doc
tex manual
tex manual
makeindex manual
tex manual
cd ../..

cd grape
./configure ../..
make 
cd ..


cd guava*
./configure ../..
make
cd ..

cd kbmag
make clean
./configure ../..
make COPTS="-O2 -g"
cd ..

# nq needs 'gmp' the GNU multi precision integer package, it is contained in
# the 'carat' package installed above (you can use another installation
# of 'gmp', adjust the argument -I... and -L... below accordingly)
cd nq
setenv COPTS "-I../../carat/carat/include -L../../carat/carat/lib"
./configure
make
unsetenv COPTS
cd ..

# openmath
cd openmath
cd OMCv1.3c/src
./configure
make
cd ../..
./configure ../..
make
cd ..

#  see the pargap documentation how to use this 
#  (in particular, user needs procgroup file)
#  [more complicated to include EDIM kernel module ...]
cd pargap
./configure ../..
make 
cp bin/pargap.sh ../../bin/
cd ..
rm -f ALLPKG

# For XGap the following shared libraries of the X window system must be 
# installed on your machine together with the development files (header 
# files and so on):
# 
#   libXaw.so, libXmu.so, libXt.so, libXext.so, libX11.so, libSM.so, libICE.so
# 
# In addition you need on XFree Version >= 4:
# 
#   libXpm.so
#
# If you  miss one of  these under Linux you  can usually just  install some
# more packages of your favorite distribution. The development files usually
# come in some package with "dev" in its name.
cd xgap
./configure
make 
rm -f ../../bin/xgap.sh
cp bin/xgap.sh ../../bin/
cd ..



From justin at mac.com  Sun Feb  3 01:13:43 2008
From: justin at mac.com (Justin C. Walker)
Date: Sun Feb  3 01:14:35 2008
Subject: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
In-Reply-To: <47A50AFF.9030408@uwm.edu>
References: <47A50AFF.9030408@uwm.edu>
Message-ID: <1A6B71F0-9028-4F9B-90A7-5CFE2C6C217C@mac.com>

Dear Jeffrey, Forum:

On Feb 2, 2008, at 16:29 , Jeffrey Rolland wrote:

> I am trying to install GAP on an iBook 900 MHz running Mac OS  
> 10.4.11 with 640 MB of RAM.
>
> I have a basic GAP install compiled. The problem is getting all the  
> packages configured (or otherwise installed).
>
> The packages are installed in the directory /usr/local/lib/gap4r4/ 
> pkg/. Inside this directory, there is a shell script  
> InstPackages.sh; I am attaching a copy of InstPackages.sh.
>
> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh,  
> I get the error message "tcsh: ./InstPackages.sh: Command not  
> found." (I am running tcsh as my default shell.)
>
> Can someone help me trouble-shoot the package installation process?

[[Added in proof :-} I just noticed that script begins with the  
string "#!/usr/bin/sh".  This actually may be the problem (the shells  
on Mac OS X are usually in "/bin").  Try changing that to "#!/bin/ 
sh".  If that doesn't fix it, read on.]


 From the error message you get ("not found"), it appears that the  
problem is not with the installation script.  Typically, shells on  
Unix-like systems find executable commands with the help of a "shell  
variable" called PATH.  This gives a list of directories in which the  
shell should look if you type a command that does not begin with a "/".

In addition, files that are to be executed must be marked as executable.

You can determine which of these might be the problem as follows.

It may be that your PATH is not set up to let you execute commands in  
the current directory.  Type the following

% echo $PATH

You should see a string of pathnames interspersed with ':'s.  Look at  
this string and see if you see ":.:" (in the middle), ".:" (at the  
beginning), or ":." (at the end).  If it's there, your problem is  
probably that the script is not marked to be executed.  If it is not  
there, you can modify your path variable, but the easiest way to fix  
your problem may be to execute the command using the full path name:

% /usr/local/lib/gap4r4/pkg/InstPackages.sh

To see if the file is executable, type

% ls -l InstPackages.sh

The latter assumes you are in the directory containing that file.   
You might see something like the following:

% ls -l /bin/sh
-r-xr-xr-x   1 root  wheel  1068844 Apr 24  2007 /bin/sh
% ls -l /etc/motd
-rw-r--r--   1 root  wheel  19 Jul  1  2006 /etc/motd

The first case is an executable, and the row of letters at the  
beginning has 'x's; the second is not executable and does not have  
'x's.  Your file should have 'x's.  If it does not, you can do one of  
two things.  You can execute this as a shell script:

% sh InstPackages.sh

or you can mark this as executable:

% chmod +x InstPackages.sh

I hope this helps (not knowing how familiar you are with command-line  
and Unixy operations, I erred on the chatty side).

Justin

--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
-----------
If it weren't for carbon-14, I wouldn't date at all.
-----------


From hulpke at mac.com  Sun Feb  3 01:15:50 2008
From: hulpke at mac.com (Alexander Hulpke)
Date: Sun Feb  3 01:16:55 2008
Subject: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
In-Reply-To: <47A50AFF.9030408@uwm.edu>
References: <47A50AFF.9030408@uwm.edu>
Message-ID: <9CF7DA53-B536-42DA-97E3-1D706B5A0500@mac.com>

Dear Jeffrey Rolland,

> The packages are installed in the directory /usr/local/lib/gap4r4/ 
> pkg/. Inside this directory, there is a shell script  
> InstPackages.sh; I am attaching a copy of InstPackages.sh.
>
> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh, I  
> get the error message "tcsh: ./InstPackages.sh: Command not  
> found." (I am running tcsh as my default shell.)

The error is prompted by the fact that the script wants to run using  
`sh' at `/usr/bin/sh', while under OSX sh sits under `/bin/sh'.
You could edit this first line of InstallPackages.sh, tough you might  
get similar errors from other packages.

Alternatively you could link sh under /usr/bin:

cd /usr/bin
sudo ln -s /bin/sh .

Again the package installations themselves might hang on some similar  
path or library issues.

(E.g. for installing XGAP you must install X11 and the X11SDK which  
might not be installed by default, you can find them on the  
installation disk for Tiger.)

Best,

     Alexander Hulpke
>

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


From rollandj at uwm.edu  Sun Feb  3 02:18:59 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sun Feb  3 02:19:16 2008
Subject: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
In-Reply-To: <1A6B71F0-9028-4F9B-90A7-5CFE2C6C217C@mac.com>
References: <47A50AFF.9030408@uwm.edu>
	<1A6B71F0-9028-4F9B-90A7-5CFE2C6C217C@mac.com>
Message-ID: <47A52493.1090809@uwm.edu>

Justin C. Walker wrote:
> Dear Jeffrey, Forum:
> 
> On Feb 2, 2008, at 16:29 , Jeffrey Rolland wrote:
> 
>> I am trying to install GAP on an iBook 900 MHz running Mac OS 10.4.11 
>> with 640 MB of RAM.
>>
>> I have a basic GAP install compiled. The problem is getting all the 
>> packages configured (or otherwise installed).
>>
>> The packages are installed in the directory 
>> /usr/local/lib/gap4r4/pkg/. Inside this directory, there is a shell 
>> script InstPackages.sh; I am attaching a copy of InstPackages.sh.
>>
>> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh, I 
>> get the error message "tcsh: ./InstPackages.sh: Command not found." (I 
>> am running tcsh as my default shell.)
>>
>> Can someone help me trouble-shoot the package installation process?
> 
> [[Added in proof :-} I just noticed that script begins with the string 
> "#!/usr/bin/sh".  This actually may be the problem (the shells on Mac OS 
> X are usually in "/bin").  Try changing that to "#!/bin/sh".  If that 
> doesn't fix it, read on.]

<snip>

> Justin

Justin,

Thanks so much for the reply!

It appears the /usr/bin/sh vs. /bin/sh thing was it. (Obviously, I do 
zero shell scriping :)) It's running now (and it appears it will be 
running for some time).

If I have any more problems, I'll email again, but that was it for now.

Thanks again.

Sincerely,
-- 
Jeffrey Rolland
<rollandj@uwm.edu>


From rollandj at uwm.edu  Sun Feb  3 02:21:12 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sun Feb  3 02:21:16 2008
Subject: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
In-Reply-To: <9CF7DA53-B536-42DA-97E3-1D706B5A0500@mac.com>
References: <47A50AFF.9030408@uwm.edu>
	<9CF7DA53-B536-42DA-97E3-1D706B5A0500@mac.com>
Message-ID: <47A52518.9070802@uwm.edu>

Alexander Hulpke wrote:
> Dear Jeffrey Rolland,
> 
>> The packages are installed in the directory 
>> /usr/local/lib/gap4r4/pkg/. Inside this directory, there is a shell 
>> script InstPackages.sh; I am attaching a copy of InstPackages.sh.
>>
>> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh, I 
>> get the error message "tcsh: ./InstPackages.sh: Command not found." (I 
>> am running tcsh as my default shell.)
> 
> The error is prompted by the fact that the script wants to run using 
> `sh' at `/usr/bin/sh', while under OSX sh sits under `/bin/sh'.
> You could edit this first line of InstallPackages.sh, tough you might 
> get similar errors from other packages.

<snip>

> Best,
> 
>     Alexander Hulpke

Alexander,

Thanks so much for your reply!

The /usr/bin/sh vs. /bin/sh thing appears to have been it. It's running 
now - yay!

If I have any futher problems, I'll email again, but that was it for now.

Thanks again.

Sincerely,
-- 
Jeffrey Rolland
<rollandj@uwm.edu>

From graham.ellis at nuigalway.ie  Sun Feb  3 20:08:37 2008
From: graham.ellis at nuigalway.ie (Ellis, Grahamj)
Date: Sun Feb  3 20:11:41 2008
Subject: [GAP Forum] De Brun Workshop On Computational Algebra
References: <7BC4FCB2B695D64CBF525CEC6437532701BA33D1@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33D2@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33D3@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33D4@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33D5@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33D6@EVS1.ac.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA33DA@EVS1.ac.nuigalway.ie>
Message-ID: <7BC4FCB2B695D64CBF525CEC6437532701BA33E9@EVS1.ac.nuigalway.ie>

First de Brun Workshop on Computational Algebra
===================================

The De Brun Centre at NUI Galway (http://hamilton.nuigalway.ie/DeBrunCentre) will run a series of workshops on computational algebra over the next few years. The first of these

(http://hamilton.nuigalway.ie/DeBrunCentre/FirstWorkshop/poster/FirstWorkshop.html)

will be held at the National University of Ireland, Galway, from 21 July to August 1, 2008.

The workshop, at which we expect to have approximately 40 participants, will consist of four morning lecture courses by

Gerhard Hiss (Aachen)
John McKay (Concordia)
Mike Stillman (Cornell)
Bernd Sturmfels (Berkeley).

and a full programme of afternoon lectures on recent research in computational algebra. The organizers encourage workshop participants to submit abstracts for contributed talks. 

The workshop is supported by Science Foundation Ireland and there is some funding available to assist graduate students, postdocs (and possibly others).

For registration details see http://hamilton.nuigalway.ie/DeBrunCentre/FirstWorkshop/poster/FirstWorkshopDetails.html .

The organizers,

Graham Ellis
Goetz Pfeiffer

From l.h.soicher at qmul.ac.uk  Wed Feb  6 14:20:37 2008
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Wed Feb  6 14:21:11 2008
Subject: [GAP Forum] Announcing the RDS Package
Message-ID: <20080206142037.GA6732@maths.qmul.ac.uk>

Dear Forum Members,

It is my pleasure to announce the newly accepted RDS package for GAP,
by Marc Roeder. This package is for finding relative difference sets in
(not necessarily abelian) groups. In addition, there is functionality for
constructing resulting block designs and for analyzing projective planes.

The RDS package can be downloaded from 

http://www.maths.nuigalway.ie/~roeder/rds.shtml

where you can also find HTML and PDF documentation. 

Sincerely,
Leonard Soicher
(on behalf of the GAP Council)

From rollandj at uwm.edu  Fri Feb  8 17:39:48 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Fri Feb  8 17:39:34 2008
Subject: [GAP Forum] Compute Homotopy Groups with GAP?
Message-ID: <47AC93E4.6060008@uwm.edu>

Hello, all!

I am a newbie to GAP.

I have used the module HAP to compute group homologies for a certain 
group - the binary icosahedral group, P, aka SL(2,5) and the Poincare 
group - to great success. HAP correctly tells me H_n(P) is Z_120 for n 
congruent to 3 mod 4.

I am interested, however, not in the space BP, but the space BP+, the 
result of applying Quillen's Plus Construction to BP with respect to P. 
Of course, this makes BP+ simply connected; moreover, it leaves the 
homology groups of BP+ unchanged from those of BP.

But now, by Hurewitz Theorem, pi_3(BP+) = H_3(BP+) = H_3(BP) = Z_120. 
So, BP+ is no longer aspherical.

What I would like is a way of computing pi_4(BP+) through pi_8(BP+) - 
without "building my own nails" (as one of the professors at my school 
accuses me of doing all to often), that is, by getting GAP or some other 
source to do it for me (I have bigger fish to fry).

If this beyond GAP's present capabilities, knowing that would be a plus.

If anyone knows of a reference for this in the literature, I would be 
eternally grateful.

Thank you in advance for any assistance you can provide.

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

From rollandj at uwm.edu  Fri Feb  8 21:42:53 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Fri Feb  8 21:43:03 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz]
Message-ID: <47ACCCDD.1010508@uwm.edu>

Hello, again, all!

Thanks so much for your help with the package install script.

It turns out that the install script crashed on the "nq" ("Nilpotent 
Quotient") package. The problem appears to be that one of the files 
attempts to include the "malloc.h" library, but this package has been 
replaced by the "stdlib.h" package on Mac Os X.

I tried just changing the inclusion, but the script appears to run cvs 
to download the source files.

Has anyone had any success getting this package to compile on Mac OS X? 
I am running Tiger (OS 10.4.11) on an iBook G3 900 MHz with 640 MB of RAM.

Thanks in advance for any assistance you can provide.

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

-------- Original Message --------
Subject: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900 MHz
Date: Sat, 02 Feb 2008 20:21:12 -0600
From: Jeffrey Rolland <rollandj@uwm.edu>
To: forum@gap-system.org
References: <47A50AFF.9030408@uwm.edu> 
<9CF7DA53-B536-42DA-97E3-1D706B5A0500@mac.com>

Alexander Hulpke wrote:
> Dear Jeffrey Rolland,
> 
>> The packages are installed in the directory 
>> /usr/local/lib/gap4r4/pkg/. Inside this directory, there is a shell 
>> script InstPackages.sh; I am attaching a copy of InstPackages.sh.
>>
>> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh, I 
>> get the error message "tcsh: ./InstPackages.sh: Command not found." (I 
>> am running tcsh as my default shell.)
> 
> The error is prompted by the fact that the script wants to run using 
> `sh' at `/usr/bin/sh', while under OSX sh sits under `/bin/sh'.
> You could edit this first line of InstallPackages.sh, tough you might 
> get similar errors from other packages.

<snip>

> Best,
> 
>     Alexander Hulpke

Alexander,

Thanks so much for your reply!

The /usr/bin/sh vs. /bin/sh thing appears to have been it. It's running
now - yay!

If I have any futher problems, I'll email again, but that was it for now.

Thanks again.

Sincerely,
-- 
Jeffrey Rolland
<rollandj@uwm.edu>

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

-- 
--
Jeffrey Rolland
<rollandj@uwm.edu>

From rollandj at uwm.edu  Fri Feb  8 21:57:44 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Fri Feb  8 21:57:24 2008
Subject: [GAP Forum] Use GAP to Compute Hom(G1, G2)?
Message-ID: <47ACD058.70703@uwm.edu>

Hello, all!

I am a newbie to GAP.

I am trying to compute the set of all homomorphisms from a group G1 
[which is the semi-direct product of the integeres Z with the binary 
icosahedral group P (also known as SL(2,5) and the Poincare group)] to 
the group P (the Poincare group again) - Hom(G1, P). This sort of 
problem seems right up GAP's alley.

I have a presentatiion for G1: <z, s, t| s^3(st)^(-2), t^5(st^(-2), 
zs(s^2ts^2t^3z)^(-1), zt(s^5ts^2tz)^(-1)>. (The first two relators 
recreate the Poincare group; the second two relators give the 
consequences for sliding the "z" past the "s" and the "t", 
respectively.) The group G1 satisfies the short exact sequence 1 -> P -> 
G1 -> Z - 1; it is the only group (other than ZxP) to do so (up to 
congruence).

If anyone can help me compute this set of homomorphisms from G1 to P, I 
would greatly appreciate it.

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

From rollandj at uwm.edu  Fri Feb  8 22:10:18 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Fri Feb  8 22:09:57 2008
Subject: [GAP Forum] Compute Homotopy Groups with GAP?
In-Reply-To: <7BC4FCB2B695D64CBF525CEC6437532701BA3431@EVS1.ac.nuigalway.ie>
References: <47AC93E4.6060008@uwm.edu>
	<7BC4FCB2B695D64CBF525CEC6437532701BA3431@EVS1.ac.nuigalway.ie>
Message-ID: <47ACD34A.2010909@uwm.edu>

Ellis, Grahamj wrote:
> Jeffrey Roland wrote:
>> I am interested, however, not in the space BP, but the space BP+, the
>> result of applying Quillen's Plus Construction to BP with respect to P.
>> Of course, this makes BP+ simply connected; moreover, it leaves the
>> homology groups of BP+ unchanged from those of BP.
> 
> Hi Jeffrey,
>  
> There is no method in HAP for computing the homotopy groups of BP+. The main focus (as yet) in HAP is on homology of BP.
>  
>  One place to look for ideas is the KENZO package by Francis Ssergereart at Grenoble. It uses simplicial groups and sets to model homotopy types with main focus on simply connected spaces.I don't think it will answer you problem directly though.
>  
> All the best,
>  
> Graham

Dear Graham,

Thanks so much for your input.

I have tried finding KENZO on the net, but all of the links to it that I 
have found appear to be broken. I will keep trying. Hopefully, once I 
find it, it will be able to answer my question.

Sincerely,
-- 
Jeffrey Rolland
<rollandj@uwm.edu>

From hulpke at math.colostate.edu  Fri Feb  8 22:37:27 2008
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Fri Feb  8 22:38:40 2008
Subject: [GAP Forum] Use GAP to Compute Hom(G1, G2)?
In-Reply-To: <47ACD058.70703@uwm.edu>
References: <47ACD058.70703@uwm.edu>
Message-ID: <C708016C-A0CA-475E-9C5E-73D3F4015A36@math.colostate.edu>

Dear GAP Forum,

Jeffrey Rolland asked:

> I am trying to compute the set of all homomorphisms from a group G1  
> [which is the semi-direct product of the integeres Z with the binary  
> icosahedral group P (also known as SL(2,5) and the Poincare group)]  
> to the group P (the Poincare group again) - Hom(G1, P). This sort of  
> problem seems right up GAP's alley.
>
> I have a presentatiion for G1: <z, s, t| s^3(st)^(-2), t^5(st^(-2),  
> zs(s^2ts^2t^3z)^(-1), zt(s^5ts^2tz)^(-1)>.

The easiest seems to be to find all quotients of G1 that are  
isomorphic to a subgroup of SL(2,5). (There is some redundancy in this  
and for bigger cases other methods would be better. However in this  
case everything else is far more work for the user.)

gap> f:=FreeGroup("z","s","t");
<free group on the generators [ z, s, t ]>
gap> AssignGeneratorVariables(f);
#I  Assigned the global variables [ z, s, t ]
gap> rels:=[ s^3*t^-1*s^-1*t^-1*s^-1, t^4*s^-1*t^-1*s^-1,  
z*s*z^-1*t^-3*s^-2*t^-1*s^-2,
   z*t*z^-1*t^-1*s^-2*t^-1*s^-5 ];
[ s^3*t^-1*s^-1*t^-1*s^-1, t^4*s^-1*t^-1*s^-1,  
z*s*z^-1*t^-3*s^-2*t^-1*s^-2,
   z*t*z^-1*t^-1*s^-2*t^-1*s^-5 ]
gap> G1:=f/rels;
<fp group on the generators [ z, s, t ]>

Careful: This group has no quotient isomorphic to A_5 and thus cannot  
have SL(2,5) as quotient. So its probably not the group you want.

Now create SL(2,5) as permutation group (more efficient than matrix  
form):

gap> P:=SL(2,5);
SL(2,5)
gap> P:=Image(IsomorphismPermGroup(P));
Group([ (1,2,4,8)(3,6,9,5)(7,12,13,17)(10,14,11,15)(16,20,21,24) 
(18,22,19,23),
   (1,3,7)(2,5,10)(4,9,13)(6,11,8)(12,16,20)(14,18,22)(15,19,23) 
(17,21,24) ])

All subgroups (careful: Only up to conjugacy. We will get  
homomorphisms only up to conjugacy as well!)
s:=List(ConjugacyClassesSubgroups(P),Representative);
gap> List(s,Size);
[ 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 120 ]

Now for each subgroup find the epimorphisms, together they are all  
homomorphisms:
gap> q:=List(s,i->GQuotients(G1,i));
[ [ [ z, s, t ] -> [ (), (), () ] ],
   [ [ z, s, t ] -> [ (1,4)(2,8)(3,9)(5,6)(7,13)(10,11)(12,17)(14,15) 
(16,
             21)(18,19)(20,24)(22,23), (), () ] ],
   [ [ z, s, t ] -> [ (1,3,7)(2,5,10)(4,9,13)(6,11,8)(12,16,20) 
(14,18,22)(15,
             19,23)(17,21,24), (), () ] ],
   [ [ z, s, t ] -> [ (1,2,4,8)(3,6,9,5)(7,12,13,17)(10,14,11,15) 
(16,20,21,
             24)(18,22,19,23), (), () ] ],
   [ [ z, s, t ] -> [ (3,13,23,21,15)(5,11,20,19,12)(6,10,24,18,17) 
(7,22,16,14,
             9), (), () ] ],
   [ [ z, s, t ] -> [ (1,9,7,4,3,13)(2,6,10,8,5,11)(12,21,20,17,16,24) 
(14,19,
             22,15,18,23), (), () ] ], [  ],
   [ [ z, s, t ] -> [ (1,4)(2,8)(3,7,23,16,15,9,13,22,21,14) 
(5,10,20,18,12,6,
             11,24,19,17), (), () ] ], [  ], [  ], [  ], [  ] ]
gap> List(q,Length);
[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0 ]


Again, this is for the presentation you gave which I think is not the  
group you want. In any case these are the commands you need in GAP.

Best,

    Alexander Hulpke







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


From justin at mac.com  Sat Feb  9 00:25:20 2008
From: justin at mac.com (Justin Walker)
Date: Sat Feb  9 00:25:41 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900
	MHz]
In-Reply-To: <47ACCCDD.1010508@uwm.edu>
References: <47ACCCDD.1010508@uwm.edu>
Message-ID: <82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>

Dear Jeffrey and Forum,

On Feb 8, 2008, at 1:42 PM, Jeffrey Rolland wrote:

> Has anyone had any success getting this package to compile on Mac OS  
> X? I am running Tiger (OS 10.4.11) on an iBook G3 900 MHz with 640  
> MB of RAM.

I have in the past had luck with the following egregious hack:
  $ sudo touch /usr/include/malloc.h

This creates an empty 'malloc.h' that the compiler will find.  This  
should satisfy it, and since this file is unnecessary (at least on Mac  
OS X, and, I think, on many modern systems :-}), the fact that it  
provides no content should pass unnoticed.

As I say, I have tried it in the past and it's worked, but that is no  
guarantee.

Regards,

Justin

--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Absorption of Federal Funds
--------
Men are from Earth.
Women are from Earth.
    Deal with it.
--------



From alexander.konovalov at gmail.com  Sat Feb  9 01:29:47 2008
From: alexander.konovalov at gmail.com (Alexander Konovalov)
Date: Sat Feb  9 01:30:04 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900
	MHz]
In-Reply-To: <47ACCCDD.1010508@uwm.edu>
References: <47ACCCDD.1010508@uwm.edu>
Message-ID: <0CE8C5E1-9101-485D-B13A-FAB7A4D0FFF5@gmail.com>

Dear Jeffrey,

I put some notes how to install some GAP packages on Mac OS X here:

http://www.cs.st-andrews.ac.uk/~alexk/gap/pkgmacos.txt

Hope that they may help in your situation.

Best wishes,
Alexander


On 8 Feb 2008, at 21:42, Jeffrey Rolland wrote:

> Hello, again, all!
>
> Thanks so much for your help with the package install script.
>
> It turns out that the install script crashed on the "nq" ("Nilpotent  
> Quotient") package. The problem appears to be that one of the files  
> attempts to include the "malloc.h" library, but this package has  
> been replaced by the "stdlib.h" package on Mac Os X.
>
> I tried just changing the inclusion, but the script appears to run  
> cvs to download the source files.
>
> Has anyone had any success getting this package to compile on Mac OS  
> X? I am running Tiger (OS 10.4.11) on an iBook G3 900 MHz with 640  
> MB of RAM.
>
> Thanks in advance for any assistance you can provide.
>
> Sincerely,
> --
> Jeffrey Rolland
> <rollandj@uwm.edu>
>
> -------- Original Message --------
> Subject: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900  
> MHz
> Date: Sat, 02 Feb 2008 20:21:12 -0600
> From: Jeffrey Rolland <rollandj@uwm.edu>
> To: forum@gap-system.org
> References: <47A50AFF.9030408@uwm.edu> <9CF7DA53-B536-42DA-97E3-1D706B5A0500@mac.com 
> >
>
> Alexander Hulpke wrote:
>> Dear Jeffrey Rolland,
>>> The packages are installed in the directory /usr/local/lib/gap4r4/ 
>>> pkg/. Inside this directory, there is a shell script  
>>> InstPackages.sh; I am attaching a copy of InstPackages.sh.
>>>
>>> When I cd to /usr/local/lib/gap4r4/pkg/ and run ./InstPackages.sh,  
>>> I get the error message "tcsh: ./InstPackages.sh: Command not  
>>> found." (I am running tcsh as my default shell.)
>> The error is prompted by the fact that the script wants to run  
>> using `sh' at `/usr/bin/sh', while under OSX sh sits under `/bin/sh'.
>> You could edit this first line of InstallPackages.sh, tough you  
>> might get similar errors from other packages.
>
> <snip>
>
>> Best,
>>    Alexander Hulpke
>
> Alexander,
>
> Thanks so much for your reply!
>
> The /usr/bin/sh vs. /bin/sh thing appears to have been it. It's  
> running
> now - yay!
>
> If I have any futher problems, I'll email again, but that was it for  
> now.
>
> Thanks again.
>
> Sincerely,
> -- 
> Jeffrey Rolland
> <rollandj@uwm.edu>
>
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
> -- 
> --
> Jeffrey Rolland
> <rollandj@uwm.edu>
>
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum

From rollandj at uwm.edu  Sat Feb  9 01:31:24 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sat Feb  9 01:31:05 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook
	900 MHz]
In-Reply-To: <82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>
References: <47ACCCDD.1010508@uwm.edu>
	<82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>
Message-ID: <47AD026C.2040100@uwm.edu>

Justin Walker wrote:
> Dear Jeffrey and Forum,
> 
> On Feb 8, 2008, at 1:42 PM, Jeffrey Rolland wrote:
> 
>> Has anyone had any success getting this package to compile on Mac OS 
>> X? I am running Tiger (OS 10.4.11) on an iBook G3 900 MHz with 640 MB 
>> of RAM.
> 
> I have in the past had luck with the following egregious hack:
>  $ sudo touch /usr/include/malloc.h
> 
> This creates an empty 'malloc.h' that the compiler will find.  This 
> should satisfy it, and since this file is unnecessary (at least on Mac 
> OS X, and, I think, on many modern systems :-}), the fact that it 
> provides no content should pass unnoticed.
> 
> As I say, I have tried it in the past and it's worked, but that is no 
> guarantee.
> 
> Regards,
> 
> Justin

<snip>

Justin,

Thanks, that took care of the the malloc.h problem.

Now, I have a new problem. Make complains that it can't find a certain 
file in the carat directory:

(cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/lib 
-DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o relations.o 
word.o system.o time.o addgen.o tails.o eliminate.o engel.o glimt.o 
instances.o presentation.o mem.o pcarith.o collect.o combicol.o 
trmetab.o gap.o -L. -o nq -lgmp -static
/usr/bin/ld: can't locate file for: -lcrt0.o
collect2: ld returned 1 exit status
make[1]: *** [nq] Error 1
make: *** [compile] Error 2

The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.

Any suggestions/

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

From rollandj at uwm.edu  Sat Feb  9 01:37:07 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sat Feb  9 01:37:04 2008
Subject: [GAP Forum] Use GAP to Compute Hom(G1, G2)?
In-Reply-To: <C708016C-A0CA-475E-9C5E-73D3F4015A36@math.colostate.edu>
References: <47ACD058.70703@uwm.edu>
	<C708016C-A0CA-475E-9C5E-73D3F4015A36@math.colostate.edu>
Message-ID: <47AD03C3.9030606@uwm.edu>


Alexander Hulpke wrote:
> Dear GAP Forum,
> 
> Jeffrey Rolland asked:
> 
>> I am trying to compute the set of all homomorphisms from a group G1 
>> [which is the semi-direct product of the integeres Z with the binary 
>> icosahedral group P (also known as SL(2,5) and the Poincare group)] to 
>> the group P (the Poincare group again) - Hom(G1, P). This sort of 
>> problem seems right up GAP's alley.
>>
>> I have a presentatiion for G1: <z, s, t| s^3(st)^(-2), t^5(st^(-2), 
>> zs(s^2ts^2t^3z)^(-1), zt(s^5ts^2tz)^(-1)>.
> 
> The easiest seems to be to find all quotients of G1 that are isomorphic 
> to a subgroup of SL(2,5). (There is some redundancy in this and for 
> bigger cases other methods would be better. However in this case 
> everything else is far more work for the user.)

<snip>

> Careful: This group has no quotient isomorphic to A_5 and thus cannot 
> have SL(2,5) as quotient. So its probably not the group you want.

<snip>

> Best,
> 
>    Alexander Hulpke

<snip>

Prof. Hulpke,

Oops! You are right. I actually want all homomorhphisms to Out(P) = Z_2. 
I know you can just send z from the Z in G1 to 1 in Z_2 and the s and t 
from the P in G1 to 0 in Z_2, but I needed to know if there were any 
other homs. Sorry, it's been a long time since I looked at this, and I 
forgot what I needed. I put this on the back burner until I realized GAP 
may be able to do this.

At any rate, your post should give me what I need. Thanks.

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

From dima at ntu.edu.sg  Sat Feb  9 06:33:24 2008
From: dima at ntu.edu.sg (Dmitrii Pasechnik)
Date: Sat Feb  9 06:34:19 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook
	900 MHz]
In-Reply-To: <47AD026C.2040100@uwm.edu>
Message-ID: <C3D36A34.4AE4%dima@ntu.edu.sg>

Dear Jeffrey and Forum,

On 2/9/08 9:31 AM, "Jeffrey Rolland" <rollandj@uwm.edu> wrote:
[...]
> 
> Now, I have a new problem. Make complains that it can't find a certain
> file in the carat directory:
> 
> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/lib
> -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o relations.o
> word.o system.o time.o addgen.o tails.o eliminate.o engel.o glimt.o
> instances.o presentation.o mem.o pcarith.o collect.o combicol.o
> trmetab.o gap.o -L. -o nq -lgmp -static
> /usr/bin/ld: can't locate file for: -lcrt0.o
> collect2: ld returned 1 exit status
> make[1]: *** [nq] Error 1
> make: *** [compile] Error 2
> 
> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.

this could be due to GMP built with wrong options.
I have had problems using GPM supplied within carat, until I switched to GMP
supplied by fink (do you use fink? www.finkproject.org).

You'd comment out building Gmp in carat's top makefile, and add
-I/sw/include to the CFLAGS there.
Then everything builds fine.

Anyhow, it's certainly better to have out-of-package-tree installation of
GPM on your system, be it the fink's one or other, for GMP is used by lots
of software around...

HTH,
Dmitrii

> 
> Any suggestions/
> 
> Sincerely,
> --
> Jeffrey Rolland
> <rollandj@uwm.edu>

-- 
Dima Pasechnik
http://www.ntu.edu.sg/home/dima/



From maasiru at yahoo.com  Sat Feb  9 16:11:22 2008
From: maasiru at yahoo.com (muniru asiru)
Date: Sat Feb  9 16:11:46 2008
Subject: [GAP Forum] cubic equations
Message-ID: <409319.59515.qm@web53306.mail.re2.yahoo.com>

Dear Forum,

Please assist me in programming Gap to find x(rational
number) and y(integer number) so that
(y-1)x^3+yx^2+(y+1)x-y=0,  y<>1.

The only solutions I got is (x,y)=(1/2,3).  Could
anyone help find others?

Thanks

maasiru


      ____________________________________________________________________________________
Never miss a thing.  Make Yahoo your home page. 
http://www.yahoo.com/r/hs

From nikos.ap at gmail.com  Sat Feb  9 19:45:57 2008
From: nikos.ap at gmail.com (Nikos Apostolakis)
Date: Sat Feb  9 19:47:03 2008
Subject: [GAP Forum] Re: cubic equations
In-Reply-To: <409319.59515.qm@web53306.mail.re2.yahoo.com>
Message-ID: <87y79thq16.fsf@knotter.earthlink.net>


On Sat, Feb 09, 2008 at 08:11:22AM -0800, thus spake muniru asiru:
> Dear Forum,
> 
> Please assist me in programming Gap to find x(rational
> number) and y(integer number) so that
> (y-1)x^3+yx^2+(y+1)x-y=0,  y<>1.
> 
> The only solutions I got is (x,y)=(1/2,3).  Could
> anyone help find others?
> 

Two more solutions are (1,0) and (56/103, - 418488) if there is an other
solution with x > 0 the denominator of x is larger than 1000.  

I used maxima to symbolicaly solve the equation to get that the general 
solution is 

[y = (x^3-x)/(x^3 + x^2 + x -1)]

then still using maxima we substitute x = m/n to get:

y = (m*n^2 - m^3)/(n^3 - m*n^2 - m^2*n - m^3)

Then using Gap (since this is Gap forum ;)) I did:

Filtered(Cartesian([1..1000], [1..1000]), x -> IsInt((x[1]*x[2]^2-x[1]^3)/(x[2]^3-x[1]*x[2]^2-x[1]^2*x[2]-x[1]^3)));;
List(last, x -> x[1]/x[2]);;
Collected(last); #==> [ [ 1/2, 500 ], [ 56/103, 9 ], [ 1, 1000 ] ]

Of course the above is a quick"brute force" approach.  Perhaps there is a more
elegant way.

HTH,
Nikos

> Thanks
> 
> maasiru
> 


From justin at mac.com  Sat Feb  9 22:35:36 2008
From: justin at mac.com (Justin C. Walker)
Date: Sat Feb  9 22:36:36 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook	900
	MHz]
In-Reply-To: <47AD026C.2040100@uwm.edu>
References: <47ACCCDD.1010508@uwm.edu>
	<82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>
	<47AD026C.2040100@uwm.edu>
Message-ID: <0B80D81F-3F80-4BFB-AB53-6B08B1771028@mac.com>


On Feb 8, 2008, at 17:31 , Jeffrey Rolland wrote:

> Justin Walker wrote:
>> Dear Jeffrey and Forum,
>> On Feb 8, 2008, at 1:42 PM, Jeffrey Rolland wrote:
>>> Has anyone had any success getting this package to compile on Mac  
>>> OS X? I am running Tiger (OS 10.4.11) on an iBook G3 900 MHz with  
>>> 640 MB of RAM.
>> I have in the past had luck with the following egregious hack:
>>  $ sudo touch /usr/include/malloc.h
>> This creates an empty 'malloc.h' that the compiler will find.   
>> This should satisfy it, and since this file is unnecessary (at  
>> least on Mac OS X, and, I think, on many modern systems :-}), the  
>> fact that it provides no content should pass unnoticed.
>> As I say, I have tried it in the past and it's worked, but that is  
>> no guarantee.
>> Regards,
>> Justin
>
> <snip>
>
> Justin,
>
> Thanks, that took care of the the malloc.h problem.
>
> Now, I have a new problem. Make complains that it can't find a  
> certain file in the carat directory:
>
> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/ 
> lib -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o  
> relations.o word.o system.o time.o addgen.o tails.o eliminate.o  
> engel.o glimt.o instances.o presentation.o mem.o pcarith.o  
> collect.o combicol.o trmetab.o gap.o -L. -o nq -lgmp -static
> /usr/bin/ld: can't locate file for: -lcrt0.o
> collect2: ld returned 1 exit status
> make[1]: *** [nq] Error 1
> make: *** [compile] Error 2
>
> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.

I've reproduced this on my system.  I really don't think this is a  
'gmp' issue, and I would not (yet) start fooling around with fink or  
MacPorts.  The problem seems more basic: the fact that "-lcrt0.o" is  
the issue means (to me, at least) that the tool chain is really  
confused.

In the future, please include this information, since it will help  
diagnose this kind of problem:
  - hardware platform (processor, if known)
  - OS
  - OS version
  - GAP version and (if it's about a package) package version

I am running on a Mac Pro (Dual Quad Xeon, 3GHz), Mac OS X 10.4.11.

I tried this with Gap 4.4.10, and nq 2.2.

I find that my locally-built GMP is built as a 64-bit library, while  
nq is built 32-bit.  I think that is the problem (GMP seems to insist  
on 64-bit builds if it's possible).

Let us know what the above information is, and whether you built GMP  
yourself (and if not, where it came from).

Justin

--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Enhancement of the Director's Income
--------
When LuteFisk is outlawed,
Only outlaws will have LuteFisk
--------



From rollandj at uwm.edu  Sun Feb 10 03:33:44 2008
From: rollandj at uwm.edu (Jeffrey Rolland)
Date: Sun Feb 10 03:33:28 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook
	900 MHz]
In-Reply-To: <0B80D81F-3F80-4BFB-AB53-6B08B1771028@mac.com>
References: <47ACCCDD.1010508@uwm.edu>
	<82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>
	<47AD026C.2040100@uwm.edu>
	<0B80D81F-3F80-4BFB-AB53-6B08B1771028@mac.com>
Message-ID: <47AE7098.4000709@uwm.edu>

Justin C. Walker wrote:
> 
> On Feb 8, 2008, at 17:31 , Jeffrey Rolland wrote:

<snip>

Justin,
>>
>> Thanks, that took care of the the malloc.h problem.
>>
>> Now, I have a new problem. Make complains that it can't find a certain 
>> file in the carat directory:
>>
>> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
>> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/lib 
>> -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o relations.o 
>> word.o system.o time.o addgen.o tails.o eliminate.o engel.o glimt.o 
>> instances.o presentation.o mem.o pcarith.o collect.o combicol.o 
>> trmetab.o gap.o -L. -o nq -lgmp -static
>> /usr/bin/ld: can't locate file for: -lcrt0.o
>> collect2: ld returned 1 exit status
>> make[1]: *** [nq] Error 1
>> make: *** [compile] Error 2
>>
>> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.
> 
> I've reproduced this on my system.  I really don't think this is a 'gmp' 
> issue, and I would not (yet) start fooling around with fink or 
> MacPorts.  The problem seems more basic: the fact that "-lcrt0.o" is the 
> issue means (to me, at least) that the tool chain is really confused.
> 
> In the future, please include this information, since it will help 
> diagnose this kind of problem:
>  - hardware platform (processor, if known)
>  - OS
>  - OS version
>  - GAP version and (if it's about a package) package version
> 
> I am running on a Mac Pro (Dual Quad Xeon, 3GHz), Mac OS X 10.4.11.
> 
> I tried this with Gap 4.4.10, and nq 2.2.
> 
> I find that my locally-built GMP is built as a 64-bit library, while nq 
> is built 32-bit.  I think that is the problem (GMP seems to insist on 
> 64-bit builds if it's possible).
> 
> Let us know what the above information is, and whether you built GMP 
> yourself (and if not, where it came from).
> 
> Justin

<snip>

Justin (et. al),

Thanks for the response.

My info is

Hardware: Apple iBook G3 900 MHz
OS and Version: Mac OS X 10.4.11
GAP: 4.4.9
NQ Version: 2.2

GMP Version (Long Edition): OK, here's where it gets embarassing. I 
*had* tried to compile GMP myself a while ago, but it failed some 
checks, so I never install it (I forgot this until your post :( ). I 
just redownloaded it and compiled it, and I installed it before I did a 
"make check" :( - but when I did eventually do a "make check", it passed 
all tests this time :) So, to make a long story short, I am using 
version 4.2.2.

GMP Version (Short Edition): 4.2.2

I have not tried recomiling NQ since installing GMP.

Please let me know if there is any additional information you require. 
Thank you in advance for any assistance you can provide.

Sincerely,
--
Jeffrey Rolland
<rollandj@uwm.edu>

From dima at ntu.edu.sg  Sun Feb 10 06:17:53 2008
From: dima at ntu.edu.sg (Dmitrii Pasechnik)
Date: Sun Feb 10 06:20:21 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook
	900 MHz]
In-Reply-To: <0B80D81F-3F80-4BFB-AB53-6B08B1771028@mac.com>
Message-ID: <C3D4B811.4B00%dima@ntu.edu.sg>

Dear Justin,

On 2/10/08 6:35 AM, "Justin C. Walker" <justin@mac.com> wrote:
[...]
>> Now, I have a new problem. Make complains that it can't find a
>> certain file in the carat directory:
>> 
>> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
>> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/
>> lib -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o
>> relations.o word.o system.o time.o addgen.o tails.o eliminate.o
>> engel.o glimt.o instances.o presentation.o mem.o pcarith.o
>> collect.o combicol.o trmetab.o gap.o -L. -o nq -lgmp -static
>> /usr/bin/ld: can't locate file for: -lcrt0.o
>> collect2: ld returned 1 exit status
>> make[1]: *** [nq] Error 1
>> make: *** [compile] Error 2
>> 
>> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.
> 
> I've reproduced this on my system.  I really don't think this is a
> 'gmp' issue, 
well, the problem evidently lies in the way carat builds gpm library. Hence
it IS a gmp issue :)

I don't see why we really should discuss buidling gmp in this forum,
especially as there are well-known ways to avoid messing around with this on
the particular platform we talk about, e.g. to use fink.
Otherwise you are of course right that the tool chain gets confused here.
But it's gmp's toolchain...

> and I would not (yet) start fooling around with fink or
> MacPorts.  
without one of them, developing "generic" unix soft, such as gap, on a Mac
becomes a major pain, that's why it's not "fooling around", but rather a
very reasonable thing to do.

Cheers,
Dmitrii


From justin at mac.com  Sun Feb 10 21:26:14 2008
From: justin at mac.com (Justin C. Walker)
Date: Sun Feb 10 21:27:22 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook	900
	MHz]
In-Reply-To: <47AE7098.4000709@uwm.edu>
References: <47ACCCDD.1010508@uwm.edu>
	<82A1F8A3-B98F-4E5A-A750-F7534062B0B4@mac.com>
	<47AD026C.2040100@uwm.edu>
	<0B80D81F-3F80-4BFB-AB53-6B08B1771028@mac.com>
	<47AE7098.4000709@uwm.edu>
Message-ID: <53BF5AC5-1CD6-4EBE-B980-E50CCE7691CC@mac.com>

Dear Jeffrey and Forum,

On Feb 9, 2008, at 19:33 , Jeffrey Rolland wrote:
> Justin C. Walker wrote:
>> On Feb 8, 2008, at 17:31 , Jeffrey Rolland wrote:
>>> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
>>> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/ 
>>> carat/lib -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o  
>>> relations.o word.o system.o time.o addgen.o tails.o eliminate.o  
>>> engel.o glimt.o instances.o presentation.o mem.o pcarith.o  
>>> collect.o combicol.o trmetab.o gap.o -L. -o nq -lgmp -static
>>> /usr/bin/ld: can't locate file for: -lcrt0.o
>>> collect2: ld returned 1 exit status
>>> make[1]: *** [nq] Error 1
>>> make: *** [compile] Error 2
>>>
>>> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.
>> I've reproduced this on my system.  I really don't think this is a  
>> 'gmp' issue, and I would not (yet) start fooling around with fink  
>> or MacPorts.  The problem seems more basic: the fact that "- 
>> lcrt0.o" is the issue means (to me, at least) that the tool chain  
>> is really confused.
>> In the future, please include this information, since it will help  
>> diagnose this kind of problem:
>>  - hardware platform (processor, if known)
>>  - OS
>>  - OS version
>>  - GAP version and (if it's about a package) package version
>> I am running on a Mac Pro (Dual Quad Xeon, 3GHz), Mac OS X 10.4.11.
>> I tried this with Gap 4.4.10, and nq 2.2.
>> I find that my locally-built GMP is built as a 64-bit library,  
>> while nq is built 32-bit.  I think that is the problem (GMP seems  
>> to insist on 64-bit builds if it's possible).
>> Let us know what the above information is, and whether you built  
>> GMP yourself (and if not, where it came from).
>

> Hardware: Apple iBook G3 900 MHz

This pretty much eliminates the "64-bit" answer :-}

> OS and Version: Mac OS X 10.4.11
> GAP: 4.4.9
> NQ Version: 2.2
>
> GMP Version (Long Edition): OK, here's where it gets embarassing.

No need to be too embarrassed; many of us have been in the same boat  
at times :-}

> GMP Version (Short Edition): 4.2.2
>
> I have not tried recomiling NQ since installing GMP.

I would do that (I rebuilt GMP on my system, forcing it to 32 bits,  
and the 'nq' build completed).

If that doesn't work, post the results of

  file $XXX/libgmp*
  ar x $XXX/libgmp.a fscanf.o
  file fscanf.o
  rm fscanf.o

(XXX = path to the libraries).

Hope that helps.

Justin

--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Enhancement of the Director's Income
--------
Experience is what you get
   when you don't get what you want.
--------

From justin at mac.com  Sun Feb 10 22:04:59 2008
From: justin at mac.com (Justin C. Walker)
Date: Sun Feb 10 22:05:52 2008
Subject: [Fwd: Re: [GAP Forum] Help Configuring GAP Packages on iBook 900
	MHz]
In-Reply-To: <C3D4B811.4B00%dima@ntu.edu.sg>
References: <C3D4B811.4B00%dima@ntu.edu.sg>
Message-ID: <92D1167C-F527-4108-87E2-417B8D48ED28@mac.com>

Dear Dimitrii,

On Feb 9, 2008, at 22:17 , Dmitrii Pasechnik wrote:

> Dear Justin,
>
> On 2/10/08 6:35 AM, "Justin C. Walker" <justin@mac.com> wrote:
> [...]
>>> Now, I have a new problem. Make complains that it can't find a
>>> certain file in the carat directory:
>>>
>>> (cd src; make GNU_MP_LIB=. GNU_MP_INC=.)
>>> gcc -O3 -DLONGLONG -I../../carat/carat/include -L../../carat/carat/
>>> lib -DVERSION='"2.0 January 2003"' nq.o consistency.o pc.o
>>> relations.o word.o system.o time.o addgen.o tails.o eliminate.o
>>> engel.o glimt.o instances.o presentation.o mem.o pcarith.o
>>> collect.o combicol.o trmetab.o gap.o -L. -o nq -lgmp -static
>>> /usr/bin/ld: can't locate file for: -lcrt0.o
>>> collect2: ld returned 1 exit status
>>> make[1]: *** [nq] Error 1
>>> make: *** [compile] Error 2
>>>
>>> The file isn't in /usr/local/lib/gap4r4/pkg/carat/carat-2.0/lib.
>>
>> I've reproduced this on my system.  I really don't think this is a
>> 'gmp' issue,
> well, the problem evidently lies in the way carat builds gpm  
> library. Hence
> it IS a gmp issue :)
>
> I don't see why we really should discuss buidling gmp in this forum,
> especially as there are well-known ways to avoid messing around  
> with this on
> the particular platform we talk about, e.g. to use fink.
> Otherwise you are of course right that the tool chain gets confused  
> here.
> But it's gmp's toolchain...
>
>> and I would not (yet) start fooling around with fink or
>> MacPorts.
> without one of them, developing "generic" unix soft, such as gap,  
> on a Mac
> becomes a major pain, that's why it's not "fooling around", but  
> rather a
> very reasonable thing to do.

I wasn't trying to provoke a discussion on the issue of fink/macports  
(and I'm not disagreeing that fink and macports are good ways to deal  
with Unix software on Mac OS X).  I wanted to isolate what was going  
wrong for Jeffrey.

For someone not familiar with software development, tackling the job  
of installing either of these schemes can be daunting.  Throwing that  
into the mix at the start didn't seem like the right approach.

It may be that it works out to be a GMP issue, but for now, my  
concern is getting to the bottom of a specific failure.

In my case, the problem seems to be related to differences between 64- 
bit and 32-bit toolchains (and the fact that I had a 64-bit GMP and a  
32-bit nq).  I'm not sure yet what is wrong in Jeffrey's case.

Justin

--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Enhancement of the Director's Income
--------
When LuteFisk is outlawed,
Only outlaws will have LuteFisk
--------



From gordon at csse.uwa.edu.au  Mon Feb 11 17:34:57 2008
From: gordon at csse.uwa.edu.au (Gordon Royle)
Date: Mon Feb 11 17:36:07 2008
Subject: [GAP Forum] Two Guava Questions...
Message-ID: <CF3D74BD-D5D9-45C1-8DCA-DFC99CE92C9C@csse.uwa.edu.au>

Hi..

I have two Guava questions... I have never used it before, so I am  
working from scratch.

(1) Leon's code..

I installed a new copy of GAP and compiled the C code for Leon's  
automorphism group stuff following the instructions.

However if I start GAP and LoadPackage("guava") from any location  
OTHER than $GAPROOT then I get a message "C code not compiled"

(2)  Generator Matrices

When I create a code with GeneratorMatCode, it seems to go away and  
precompute a whole pile of stuff taking perhaps minutes to enter a  
code.. what is it doing at this point? Is there a way of making it  
"lazy" so that it only computes things when and if they are asked for...

Thanks

Gordon

--
Associate Professor Gordon Royle
School of Computer Science & Software Engineering / School of  
Mathematics & Statistics
University of Western Australia
http://people.csse.uwa.edu.au/gordon





From wdjoyner at gmail.com  Mon Feb 11 17:57:59 2008
From: wdjoyner at gmail.com (David Joyner)
Date: Mon Feb 11 17:58:23 2008
Subject: [GAP Forum] Two Guava Questions...
In-Reply-To: <CF3D74BD-D5D9-45C1-8DCA-DFC99CE92C9C@csse.uwa.edu.au>
References: <CF3D74BD-D5D9-45C1-8DCA-DFC99CE92C9C@csse.uwa.edu.au>
Message-ID: <8cf963450802110957m33350d19k4b06479cc6b67efb@mail.gmail.com>

On Feb 11, 2008 12:34 PM, Gordon Royle <gordon@csse.uwa.edu.au> wrote:
> Hi..
>
> I have two Guava questions... I have never used it before, so I am
> working from scratch.
>
> (1) Leon's code..
>
> I installed a new copy of GAP and compiled the C code for Leon's
> automorphism group stuff following the instructions.
>
> However if I start GAP and LoadPackage("guava") from any location
> OTHER than $GAPROOT then I get a message "C code not compiled"

I'm not sure if this should be viewed as a bug or not. It it a problem
for you? It has never been a problem for me.

>
> (2)  Generator Matrices
>
> When I create a code with GeneratorMatCode, it seems to go away and
> precompute a whole pile of stuff taking perhaps minutes to enter a
> code.. what is it doing at this point? Is there a way of making it
> "lazy" so that it only computes things when and if they are asked for...

Some commands have faster method implemented - such as
RandomLinearCode. For most commands, though, it searches some tables
and tries to get estimates for the parameters.  I think that is the
part that takes the most time. Removing that would, I think,
require a significant amount of programming.


>
> Thanks

Thanks for trying out GUAVA! Hope this helps.

>
> Gordon
>
> --
> Associate Professor Gordon Royle
> School of Computer Science & Software Engineering / School of
> Mathematics & Statistics
> University of Western Australia
> http://people.csse.uwa.edu.au/gordon
>
>
>
>
>
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From wdjoyner at gmail.com  Mon Feb 11 18:43:49 2008
From: wdjoyner at gmail.com (David Joyner)
Date: Mon Feb 11 18:44:33 2008
Subject: [GAP Forum] Two Guava Questions...
In-Reply-To: <CF3D74BD-D5D9-45C1-8DCA-DFC99CE92C9C@csse.uwa.edu.au>
References: <CF3D74BD-D5D9-45C1-8DCA-DFC99CE92C9C@csse.uwa.edu.au>
Message-ID: <8cf963450802111043u368923cfv1aceb08779dc7a1b@mail.gmail.com>

A follow-up to my previous reply.

Cen Tjhai (a GUAVA co-developer) reminded me off-list that
GeneratorMatCodeNC does exactly what Gordon was asking for.
It's undocumented though (and I'd forgotten about it). so I'll try
to remember to fix that in the next release of GUAVA.

Thanks CJ!

On Feb 11, 2008 12:34 PM, Gordon Royle <gordon@csse.uwa.edu.au> wrote:
> Hi..
>
> I have two Guava questions... I have never used it before, so I am
> working from scratch.
>
> (1) Leon's code..
>
> I installed a new copy of GAP and compiled the C code for Leon's
> automorphism group stuff following the instructions.
>
> However if I start GAP and LoadPackage("guava") from any location
> OTHER than $GAPROOT then I get a message "C code not compiled"
>
> (2)  Generator Matrices
>
> When I create a code with GeneratorMatCode, it seems to go away and
> precompute a whole pile of stuff taking perhaps minutes to enter a
> code.. what is it doing at this point? Is there a way of making it
> "lazy" so that it only computes things when and if they are asked for...
>
> Thanks
>
> Gordon
>
> --
> Associate Professor Gordon Royle
> School of Computer Science & Software Engineering / School of
> Mathematics & Statistics
> University of Western Australia
> http://people.csse.uwa.edu.au/gordon
>
>
>
>
>
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

From kohl at mathematik.uni-stuttgart.de  Tue Feb 12 13:02:53 2008
From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl)
Date: Tue Feb 12 13:04:33 2008
Subject: [GAP Forum] cubic equations
In-Reply-To: <409319.59515.qm@web53306.mail.re2.yahoo.com>
References: <409319.59515.qm@web53306.mail.re2.yahoo.com>
Message-ID: <47B198FD.3060707@mathematik.uni-stuttgart.de>

Dear Forum,

Muniru Asiru asked:

> Please assist me in programming Gap to find x(rational
> number) and y(integer number) so that
> (y-1)x^3+yx^2+(y+1)x-y=0,  y<>1.
> 
> The only solutions I got is (x,y)=(1/2,3).  Could
> anyone help find others?

A general remark in advance: It is well-known that there is no general
algorithm for computing the set of solutions of a diophantine equation,
or even only for deciding whether there is a solution at all.

However, now let's turn to Muniru Asiru's particular equation:

He asks for rational zeros of a certain family of cubic polynomials
with integer coefficients.

For approximating zeros of polynomials with integer coefficients,
GAP provides a function ContinuedFractionApproximationOfRoot( P, n ).
As the name suggests, this function computes the n-th continued fraction
approximation of some real zero of the polynomial P.

     As an example, let's compute the 20th continued fraction
     approximation of the third root of 2:

     gap> x := Indeterminate(Integers);; SetName(x,"x");
     gap> ContinuedFractionApproximationOfRoot(x^3-2,20);
     1348776323/1070524477
     gap> last^3-2;
     1671371601/1226845304290527628130119333

There is also another function ContinuedFractionExpansionOfRoot( P, n ),
which computes the first n terms of the corresponding continued fraction
expansions.

     As an example, let's compute the first 20 terms of the
     continued fraction expansion of the third root of 2:

     gap> ContinuedFractionExpansionOfRoot(x^3-2,20);
     [ 1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3 ]

Both of these functions require that the leading coefficient of P is
positive, that P(0) is negative and that P has only one positive real zero.
These conditions are satisfied for Muniru Asiru's polynomial if y > 1,
and they are satisfied for its additive inverse if y < 0.

Now note that the continued fraction expansion of a rational number stops
after a finite number of terms.

Given this, we can start to look for solutions.

First we enter Muniru Asiru's family of polynomials:

gap> x := Indeterminate(Integers);; SetName(x,"x");
gap> pol := y -> (y-1)*x^3+y*x^2+(y+1)*x-y;;

Then we look for solutions with y > 1 ...

gap> Filtered([1..500000],
 >              y->Length(ContinuedFractionExpansionOfRoot(pol(y),10)) < 10);
[ 3 ]
gap> ContinuedFractionExpansionOfRoot(pol(3),10);
[ 0, 2 ]
gap> ContinuedFractionApproximationOfRoot(pol(3),10);
1/2

... and obtain the solution (1/2,3).

Next we look for solutions with y < 0 ...

gap> Filtered([1..500000],
 >             y->Length(ContinuedFractionExpansionOfRoot(-pol(-y),10)) < 10);
[ 418488 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418488),10);
[ 0, 1, 1, 5, 4, 2 ]
gap> ContinuedFractionApproximationOfRoot(-pol(-418488),10);
56/103

... and obtain the solution (56/103,-418488).

We can also look what happens slightly below and above -418488:

gap> ContinuedFractionExpansionOfRoot(-pol(-418486),10);
[ 0, 1, 1, 5, 4, 1, 1, 64099453, 1, 1 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418487),10);
[ 0, 1, 1, 5, 4, 1, 1, 128199214, 9, 2 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418488),10);
[ 0, 1, 1, 5, 4, 2 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418489),10);
[ 0, 1, 1, 5, 4, 2, 128199826, 1, 8, 2 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418490),10);
[ 0, 1, 1, 5, 4, 2, 64100066, 2, 1, 1 ]
gap> ContinuedFractionExpansionOfRoot(-pol(-418491),10);
[ 0, 1, 1, 5, 4, 2, 42733479, 1, 1, 3 ]

... and even still

gap> ContinuedFractionExpansionOfRoot(-pol(-420000),10);
[ 0, 1, 1, 5, 4, 2, 85093, 1, 14, 1 ]

If one wishes, one could probably use this pattern to greatly reduce
computation time when looking for further solutions.

Best wishes,

     Stefan Kohl

---------------------------------------------------------------------------
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/
---------------------------------------------------------------------------


From sal at cs.st-and.ac.uk  Thu Feb 14 16:05:40 2008
From: sal at cs.st-and.ac.uk (Steve Linton)
Date: Thu Feb 14 16:04:57 2008
Subject: [GAP Forum] Experimental Patch to Long-standing Itanium Problem
Message-ID: <20080214160540.28f0ee0b@cs.st-and.ac.uk>

Dear GAP Forum,

As some of you will recall, there is a very long standing 
problem running GAP on processors from Intel's Itanium processor family, found
mainly in large multi-processor servers and supercomputers. 

We believe that we have now fixed this problem, and the fix will be included
in the next release of GAP, but, if you wish to try it out in the meantime,
you can download it as a patch to apply to GAP 4r4p10. See
http://www.gap-system.org/Faq/Hardware-OS/hardware-os8.html
for a link to the patch.

Please let us know how you get on.

	Steve Linton


-- 
Steve Linton	School of Computer Science  &
      Centre for Interdisciplinary Research in Computational Algebra
	     University of St Andrews 	 Tel   +44 (1334) 463269
http://www.cs.st-and.ac.uk/~sal 	 Fax   +44 (1334) 463278   

From mlederer at math.uni-bielefeld.de  Thu Feb 14 22:23:44 2008
From: mlederer at math.uni-bielefeld.de (Mathias Lederer)
Date: Thu Feb 14 22:25:11 2008
Subject: [GAP Forum] Wedderburn and representations
Message-ID: <86201AFB-215C-405A-84CB-CE7BA0546E98@math.uni-bielefeld.de>

Dear GAP forum,

I am currently learning to use the Wedderburn package, which I find  
very appealing. I want to apply the Wedderburn also to the following  
situation, which deals with a special class of representations of G.

Take a group G and a field F such that FG is semisimple. Let FG = A_1  
\times \ldots \times A_s be the Weddderburn decomposition of FG.  
Next, let H be a subgroup of G. The vector space

F(G/H) := \oplus_{g \in G} F gH

(that is, a vector space with the coset classes as a basis) has a  
canonical action of G, hence, is an FG-module. Therefore, it is a  
direct sum V_1 \oplus \ldots \oplus V_s, where V_i is a module over  
A_i. The algebra A_i is a matrix algebra over a division algebra,  
say, A_i = M_{n_i}(D_i). Up to isomorphism, there exists a unique  
irreducible A_i-module, to wit, U_i = D_i^{n_i}. Hence the module V_i  
is a direct sum of a number of copies of U_i, say, V_i = U_i^{f_i}.

Here are my questions.

1) The Wedderburn package enables one to compute decomposition FG =  
A_1 \times \ldots \times A_s. If I understand correctly, each A_i is  
not given in the form A_i = M_{n_i}(D_i) as above. Instead, a  
cyclotomic algebra, which is Brauer equivalent to A_i, is given. Can  
one also compute the form A_i = M_{n_i}(D_i)? So do we get the  
division algebra and the size of the matrices?

2) Can one compute the multiplicity f_i with which the irreducible  
A_i-module shows up in F(G/H)?

Many thanks in advance,
Mathias

From adelrio at um.es  Fri Feb 15 22:31:16 2008
From: adelrio at um.es (Angel del Rio)
Date: Fri Feb 15 22:32:14 2008
Subject: [GAP Forum] Wedderburn and representation
Message-ID: <47B612B4.6090402@um.es>

Dear GAP Forum,

This is a reply to a message by Mathias Lederer on Wedderburn 
Decomposition of semisimple group algebras and representations.

Your first question:
1) The Wedderburn package enables one to compute decomposition FG = A_1 
\times \ldots \times A_s. If I understand correctly, each A_i is not 
given in the form A_i = M_{n_i}(D_i) as above. Instead, a cyclotomic 
algebra, which is Brauer equivalent to A_i, is given. Can one also 
compute the form A_i = M_{n_i}(D_i)? So do we get the division algebra 
and the size of the matrices?

To compute the form M_{n_i}(D_i) is usually a difficult task. In fact 
just to compute the size of the matrices is not obvious.
Notice that the degree of A_i coincides with the degree of each 
irreducible character chi of G which does not vanishes on A_i and it is 
equal to n_im_i, where m_i is the Schur index of A_i, or equivalently 
the Schur degree of chi over F.
In theory, if F is a global field then the calculation of the Schur 
index or even of the Hasse invariant of A_i (or D_i) should be doable by 
using local information (See Reiner, Maximal Orders).
Unfortunately in many cases this is a difficult task and as far as I 
know there is not an "implementable" method to do this.
This is the subject of many research papers.
See for example:

P. Schmid, Representation-groups for the Schur index, J. Algebra 97 
(1985) 101-115.
B. Banieqbal, On bounding the Schur index of induced modules, Bull. LMS 
18 (1986) 17-23.
A. Turull, On the Schur index of quasi primitive characters, Journal  
LMS  35 (1987)  421-432.
A. Herman, Using character correspondence for Schur index computations, 
J. Algebra 159 (2003) 353-360.
A. Herman, Using G-algebras for Schur index computations, J. Algebra 260 
(2003) 463-475.

Your second question:
2) Can one compute the multiplicity f_i with which the irreducible 
A_i-module shows up in F(G/H)?

Unfortunately there is not anything else that can be said because the 
first question is included in the second one for H=1.
Indeed, the multiplicity f_i equals n_i, the size of the matrices and 
computing this is already hard for this case.

Resuming, wedderga, provides a description of the simple components of 
group algebras, but to have a full understanding of these components we 
still need fundamental research on the calculation of Schur indexes and 
local invariants.
Some of the experts in the field are Herman, Turull and Schimd.
They may give more information.

?ngel

-- 
?ngel del R?o Mateos
Departamento de Matem?ticas
Universidad de Murcia
+34 968 363537

From savchuk at math.tamu.edu  Mon Feb 18 05:12:09 2008
From: savchuk at math.tamu.edu (Dmytro Savchuk)
Date: Mon Feb 18 05:13:34 2008
Subject: [GAP Forum] new release of AutomGrp package v 1.1.1
Message-ID: <1001996987185.20080217231209@math.tamu.edu>

Dear Forum,

We  are glad to announce a new release of the package AutomGrp V 1.1.1.

It  provides  methods  for  computations  with  groups  and semigroups
generated  by finite automata or given by wreath recursion, as well as
with their finitely generated subgroups and elements.

Several new features were added and couple of bugs were fixed. For
more details refer to file NEWS in the main folder of the package.

The package and documentation is available at
http://finautom.sourceforge.net/

If  you have any problems with installation, please let us know. Note,
that  it depends on FGA package.

Best Wishes!
Dmytro

From p_niroomand at yahoo.com  Mon Feb 18 15:53:42 2008
From: p_niroomand at yahoo.com (peyman niroomand)
Date: Mon Feb 18 15:59:24 2008
Subject: [GAP Forum] Request
Message-ID: <940948.76528.qm@web50504.mail.re2.yahoo.com>

Dear Gap Forum,

I have a some questions about  GAP.

1) Let G be a finite group and G\wedge G is a Non-abelian Exterior Square of G.   Can we compute the following group with GAP ?
H={g\in G |g\wedge x=1 \for all x\in G}.

2) Can we use GAP to decide when x\wedge y is equal to 1 for any pair (x,y) in G^2 ?


Best Regards.
       
---------------------------------
Be a better friend, newshound, and know-it-all with Yahoo! Mobile.  Try it now.
From savchuk at math.tamu.edu  Mon Feb 18 20:52:22 2008
From: savchuk at math.tamu.edu (Dmytro Savchuk)
Date: Mon Feb 18 20:52:46 2008
Subject: [GAP Forum] new release of AutomGrp package v 1.1.1
Message-ID: <1572053400463.20080218145222@math.tamu.edu>

Dear Forum,

We  are glad to announce a new release of the package AutomGrp V 1.1.1.

It  provides  methods  for  computations  with  groups  and semigroups
generated  by finite automata or given by wreath recursion, as well as
with their finitely generated subgroups and elements.

Several new features were added and couple of bugs were fixed. For
more details refer to file NEWS in the main folder of the package.

The package and documentation is available at
http://finautom.sourceforge.net/

If  you have any problems with installation, please let us know. Note,
that  it depends on FGA package.

Best Wishes!
Dmytro

From hnguyen at math.ufl.edu  Wed Feb 27 21:59:30 2008
From: hnguyen at math.ufl.edu (Hung Ngoc Nguyen)
Date: Wed Feb 27 21:59:52 2008
Subject: [GAP Forum] Character Table of some groups.
Message-ID: <Pine.SOL.4.44.0802271635180.13855-100000@blackbird.math.ufl.edu>

Dear GAP forum,

I want to know the character tables (or atleast character degrees) of the
universal covers of some (simple) orthogonal groups like: O8+(3), O8-(3),
O9(3). It worked when I did with those
orthogonal groups but unfortunately it failed for
their universal covers. I just wonder whether the character tables of
these universal covers are available on GAP ot not? By the way I am using
version 4.4.9.
Thank you very much for your help.

Hung Ngoc Nguyen
Mathematics Department
University of Florida

From frank.luebeck at math.rwth-aachen.de  Wed Feb 27 23:48:11 2008
From: frank.luebeck at math.rwth-aachen.de (Frank =?iso-8859-1?Q?L=FCbeck?=)
Date: Wed Feb 27 23:48:32 2008
Subject: [GAP Forum] Character Table of some groups.
In-Reply-To: <Pine.SOL.4.44.0802271635180.13855-100000@blackbird.math.ufl.edu>
References: <Pine.SOL.4.44.0802271635180.13855-100000@blackbird.math.ufl.edu>
Message-ID: <20080227234811.GA31235@beteigeuze>

On Wed, Feb 27, 2008 at 04:59:30PM -0500, Hung Ngoc Nguyen wrote:
> Dear GAP forum,
> 
> I want to know the character tables (or atleast character degrees) of the
> universal covers of some (simple) orthogonal groups like: O8+(3), O8-(3),
> O9(3). It worked when I did with those
> orthogonal groups but unfortunately it failed for
> their universal covers. I just wonder whether the character tables of
> these universal covers are available on GAP ot not? By the way I am using
> version 4.4.9.
> Thank you very much for your help.
> 
> Hung Ngoc Nguyen
> Mathematics Department
> University of Florida

Dear Hung Ngoc Nguyen, dear Forum,

I think the complete character tables of the universal covers of the
mentioned simple groups are not known (and so not in the GAP character table
library).

But you can find the lists of character degrees (and multiplicities) for these
groups, and even covers of O8+(q), O8-(q), O9(q) for all prime powers q,
on the web page:

  http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/DegMult/

See under "D_4(q)_sc", "^2D_4(q)_sc", "B_4(q)_sc", respectively.

With best regards,

  Frank

-- 
///  Dr. Frank L?beck, Lehrstuhl D f?r Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\

From kksa at math.ku.dk  Thu Feb 28 09:34:17 2008
From: kksa at math.ku.dk (Kasper Andersen)
Date: Thu Feb 28 09:34:46 2008
Subject: [GAP Forum] cubic equations
In-Reply-To: <47B198FD.3060707@mathematik.uni-stuttgart.de>
References: <409319.59515.qm@web53306.mail.re2.yahoo.com>
	<47B198FD.3060707@mathematik.uni-stuttgart.de>
Message-ID: <alpine.LSU.1.00.0802271207350.21899@galois.math.ku.dk>

Dear Forum,

Some time ago Muniru Asiru asked the following question:

> Dear Forum,
>
> Muniru Asiru asked:
>
>> Please assist me in programming Gap to find x(rational
>> number) and y(integer number) so that
>> (y-1)x^3+yx^2+(y+1)x-y=0,  y<>1.
>> 
>> The only solutions I got is (x,y)=(1/2,3).  Could
>> anyone help find others?

Nikos Apostolakis noted two more solutions, namely (1,0) and 
(56/103,-418488). There are two other trivial solutions namely (0,0) and 
(-1,0). I claim that these 5 are the only solutions:

As already noted by Nikos Apostolakis, the equation can be rewritten as

y = (x^3-x)/(x^3+x^2+x-1)

(note that 1 and -1 are not roots of x^3+x^2+x-1, so this polynomial does 
not have any rational roots). Following Nikos, we write x=m/n for coprime 
integers m and n and get

y = m*(m^2-n^2)/(m^3+m^2 n+m n^2-n^3)

Since y is an integer we must have

\pm m^3+m^2 n+m n^2-n^3 = GCD(m^3+m^2 n+m n^2-n^3, m*(m^2-n^2)),

where \pm denotes plus/minus. However m^3+m^2 n+m n^2-n^3 and m are 
coprime since GCD(m,n)=1, so

GCD(m^3+m^2 n+m n^2-n^3, m*(m^2-n^2)) = GCD(m^3+m^2 n+m n^2-n^3, m^2-n^2)

Since (m^3+m^2 n+m n^2-n^3) - (n-m)*(m^2-n^2) = 2 m^3 we get

GCD(m^3+m^2 n+m n^2-n^3, m^2-n^2) = GCD(2 m^3, m^2-n^2)

Now m^3 and m^2-n^2 are coprime so

GCD(2 m^3, m^2-n^2) = GCD(2, m^2-n^2) = 1 or 2.

Combining the equations we finally get

(*) m^3+m^2 n+m n^2-n^3 = d

where d= \pm 1 or \pm 2. This is a socalled Thue equation. These have a 
finite number of integer solutions which can be computed efficiently using 
Bakers theory of linear forms in logarithms. For details, see the recent 
book "Number Theory. Volume II: Analytic and Modern Tools" by Henri Cohen 
(GTM 240), section 12.10 and the references there. The procedure has been 
implemented in Magma, one finds that the solutions to (*) are

d=1: (m,n) = (-1,-2), (0,-1), (1,0) or (56,103)

d=2: (m,n) = (1,-1) or (1,1)

The solutions for d=-1 and d=-2 are (-m,-n) so we do not get any new 
values of x in these cases. Hence

x = 1/2, 0, 56/103, -1 or 1.

Plugging these into the equation y=(x^3-x)/(x^3+x^2+x-1) now gives the 5 
solutions above.

best wishes,

Kasper

From hnguyen at math.ufl.edu  Thu Feb 28 20:57:49 2008
From: hnguyen at math.ufl.edu (Hung Ngoc Nguyen)
Date: Thu Feb 28 20:58:15 2008
Subject: [GAP Forum] Character Table of some groups.
In-Reply-To: <20080227234811.GA31235@beteigeuze>
Message-ID: <Pine.SOL.4.44.0802281548510.22075-100000@blackbird.math.ufl.edu>

Dear Joe, Frank and all,

Thank you very much for your replies. The website Frank gave to me is more
than what I need.

I have one more question for Frank: In the lists of character degrees
and their multiplicities, did you put the character degrees (as
polinomials of q) in increasing order of the degrees of these polinomials.
I believe so but I just want to make sure.

Sincerely,
Hung Nguyen.


On Thu, 28 Feb 2008, Frank [iso-8859-1] Lübeck wrote:

> On Wed, Feb 27, 2008 at 04:59:30PM -0500, Hung Ngoc Nguyen wrote:
> > Dear GAP forum,
> >
> > I want to know the character tables (or atleast character degrees) of the
> > universal covers of some (simple) orthogonal groups like: O8+(3), O8-(3),
> > O9(3). It worked when I did with those
> > orthogonal groups but unfortunately it failed for
> > their universal covers. I just wonder whether the character tables of
> > these universal covers are available on GAP ot not? By the way I am using
> > version 4.4.9.
> > Thank you very much for your help.
> >
> > Hung Ngoc Nguyen
> > Mathematics Department
> > University of Florida
>
> Dear Hung Ngoc Nguyen, dear Forum,
>
> I think the complete character tables of the universal covers of the
> mentioned simple groups are not known (and so not in the GAP character table
> library).
>
> But you can find the lists of character degrees (and multiplicities) for these
> groups, and even covers of O8+(q), O8-(q), O9(q) for all prime powers q,
> on the web page:
>
>   http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/DegMult/
>
> See under "D_4(q)_sc", "^2D_4(q)_sc", "B_4(q)_sc", respectively.
>
> With best regards,
>
>   Frank
>
> --
> ///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
> \\\                    52062 Aachen, Germany                          \\\
> ///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
> \\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\
>


From frank.luebeck at math.rwth-aachen.de  Fri Feb 29 08:45:44 2008
From: frank.luebeck at math.rwth-aachen.de (Frank =?iso-8859-1?Q?L=FCbeck?=)
Date: Fri Feb 29 08:46:12 2008
Subject: [GAP Forum] Character Table of some groups.
In-Reply-To: <Pine.SOL.4.44.0802281548510.22075-100000@blackbird.math.ufl.edu>
References: <20080227234811.GA31235@beteigeuze>
	<Pine.SOL.4.44.0802281548510.22075-100000@blackbird.math.ufl.edu>
Message-ID: <20080229084544.GA18180@beteigeuze>

On Thu, Feb 28, 2008 at 03:57:49PM -0500, Hung Ngoc Nguyen wrote:
> Dear Joe, Frank and all,
> 
> Thank you very much for your replies. The website Frank gave to me is more
> than what I need.
> 
> I have one more question for Frank: In the lists of character degrees
> and their multiplicities, did you put the character degrees (as
> polinomials of q) in increasing order of the degrees of these polinomials.
> I believe so but I just want to make sure.

Dear Hung Nguyen,

The ordering is described on the mentioned webpage:

----
Further remarks

The degrees  are ordered by  increasing size  for sufficiently large  q. But
note  that for  small  special values  of  q the  ordering  can be  slightly
different. Also for some small q some of the degrees may not occur (when the
polynomial describing the multiplicity specializes to zero).
----

In particular, the answer to your question is yes (higher polynomial degree
will give larger numbers when evaluated at sufficiently large q).

Best regards,

  Frank

-- 
///  Dr. Frank L?beck, Lehrstuhl D f?r Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\

From kksa at math.ku.dk  Fri Feb 29 10:51:12 2008
From: kksa at math.ku.dk (Kasper Andersen)
Date: Fri Feb 29 10:51:34 2008
Subject: [GAP Forum] Memory problem
Message-ID: <Pine.LNX.4.64.0802291010410.7980@pc000ffea6285d.math.ku.dk>

Hi!

As part of a joint project with Bob Oliver and Joana Ventura, I'm using 
GAP to do a number of computations. I'm running a loop over several 
2-groups for which I want to perform a certain test. For the first group 
(SmallGroup(128,313)) the program returns false fairly quickly. Then after 
a longer wait, it runs out of memory for the next group 
(SmallGroup(128,314)), see the log file attached below. When I try to do 
the computation in the reverse order (SmallGroup(128,314) first and then 
SmallGroup(128,313)) the same thing happens: The first answer appears 
quickly and then after a waiting for some time, GAP runs out of memory 
during the computation for the next group.

So here are my questions:

1) How do I increase the permitted memory (the log file suggest the -o 
flag, but there also seems to be others -m, -K, -c and -a). Which one(s) 
should I use? Should I recompile GAP with some parameters changed?

2) As stated, starting with either of the two groups first produces an 
answer quickly. So neither of the two computations in themselves crash 
GAP. So in both cases, the computation for group number 2 should also be 
doable if a proper garbage collection is done or if there is sufficient 
memory, right? Is there a way to force GAP to do a garbage collection? 
Naively one should think that doubling the permitted memory should work. I 
also tried running the program with the flag -m 1g, but unfortunately the 
result is the same: The first answer appears fairly quickly and then after 
a long wait GAP crashes. Is there anything else I could do?

best wishes and thanks in advance,

Kasper Andersen

PS If it helps I can send the GAP program used for the computation.

gap> Read("cor33-gap");
86
313 1 false
exceeded the permitted memory (`-o' command line option) at
img := One( Range( hom ) );
  called from
ImagesRepresentative( map, gen ) called from
func( elm ) called from
List( GeneratorsOfMagmaWithInverses( elms ), function ( gen )
       return ImagesRepresentative( map, gen );
   end ) called from
ImagesSet( map, elm ) called from
Image( f, Kold ) called from
...
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

From iano at compsoc.nuigalway.ie  Fri Feb 29 11:56:22 2008
From: iano at compsoc.nuigalway.ie (Ian McLoughlin)
Date: Fri Feb 29 11:56:39 2008
Subject: [GAP Forum] Small Group 8 of Order 24
Message-ID: <9d5eef600802290356n7f86d198oe277d8e97c73aba5@mail.gmail.com>

Hi,

would anyone know what small group 8 of order 24 is usually labelled?
I think it is the following group...

< a , b , c | a^3 , b^4 , c^2 , bcb=c , aba=b , ac=ca >.

Thanks,
Ian

-- 
Ian McLoughlin
emailme@ianmcloughlin.com

From savchuk at math.tamu.edu  Fri Feb 29 17:18:08 2008
From: savchuk at math.tamu.edu (Dmytro Savchuk)
Date: Fri Feb 29 17:19:02 2008
Subject: [GAP Forum] Small Group 8 of Order 24
In-Reply-To: <9d5eef600802290356n7f86d198oe277d8e97c73aba5@mail.gmail.com>
References: <9d5eef600802290356n7f86d198oe277d8e97c73aba5@mail.gmail.com>
Message-ID: <59643473686.20080229111808@math.tamu.edu>

Dear Ian,

It looks that you are correct

gap> F:=FreeGroup(["a","b","c"]);
<free group on the generators [ a, b, c ]>
gap> a:=F.1;; b:=F.2;; c:=F.3;;
gap> FF:=F/[a^3,b^4,c^2,b*c*b*c,a*b*a*b^-1,a*c*a^-1*c];
<fp group on the generators [ a, b, c ]>
gap> IdSmallGroup(FF);
[ 24, 8 ]


Best Regards,
Dmytro



Friday, February 29, 2008, 5:56:22 AM, you wrote:

IM> Hi,

IM> would anyone know what small group 8 of order 24 is usually labelled?
IM> I think it is the following group...

IM> < a , b , c | a^3 , b^4 , c^2 , bcb=c , aba=b , ac=ca >.

IM> Thanks,
IM> Ian




-- 
Best regards,
 Dmytro                            mailto:savchuk@math.tamu.edu

From dongjc at njau.edu.cn  Mon Mar  3 08:38:34 2008
From: dongjc at njau.edu.cn (=?gb2312?B?tq2+rrPJ?=)
Date: Mon Mar  3 08:53:28 2008
Subject: [GAP Forum] Can GAP handle with infinite field with positive
	characteristic?
Message-ID: <QHLQMPEUQFVCOVJMQSNRNMDNHNQS.dongjc@njau.edu.cn>

Dear forum,Dear everyone:
I want to know how to build infinite field with positive characteristic in GAP,such as algebraically closed field with characteristic 3. Thank you!
Jing-cheng Dong
From vdabbagh at sfu.ca  Thu Mar 13 06:18:12 2008
From: vdabbagh at sfu.ca (Vahid Dabbaghian)
Date: Thu Mar 13 06:20:29 2008
Subject: [GAP Forum] similar matrices
Message-ID: <200803130618.m2D6IChH016446@rm-rstar.sfu.ca>


Dear GAP forum,

Suppose A and B are similar and invertible matrices on C. Does anybody know
a function or a program in GAP to compute an invertible matrix P such that
P^{-1}AP=B ?

Thanks in advance
Vahid
__________________________
The IRMACS Centre (ASB 10905)
Simon Fraser University
8888 University Drive
Burnaby, BC V5A 1S6 
Canada
E-mail: vdabbagh@sfu.ca
http://www.sfu.ca/~vdabbagh

From burkhard at hoefling.name  Thu Mar 13 11:26:56 2008
From: burkhard at hoefling.name (=?ISO-8859-1?Q?Burkhard_H=F6fling?=)
Date: Thu Mar 13 11:27:29 2008
Subject: [GAP Forum] similar matrices
In-Reply-To: <200803130618.m2D6IChH016446@rm-rstar.sfu.ca>
References: <200803130618.m2D6IChH016446@rm-rstar.sfu.ca>
Message-ID: <B8E17BBE-118C-415B-B176-64E3C5406BBE@hoefling.name>


On 13.03.2008, at 07:18, Vahid Dabbaghian wrote:

>
> Dear GAP forum,
>
> Suppose A and B are similar and invertible matrices on C. Does  
> anybody know
> a function or a program in GAP to compute an invertible matrix P  
> such that
> P^{-1}AP=B ?

A straightforward way is to write AP = PB and to solve the system of  
linear equations in the entries of P. For reasonalby samll matrices,  
this works well.

If your matrices are over the complex numbers, then you can also  
conjugate both into Jordan normal form and find a suitable  
permutation matrix to conjugate one Jordan normal form into the other.

A similar approach might work for matrices over finite fields. In my  
package IRREDSOL, I have used such an approach for computing  
conjugating matrices of irreducible matrix groups.

Cheers,

Burkhard.

From graham.ellis at nuigalway.ie  Thu Mar 13 17:21:11 2008
From: graham.ellis at nuigalway.ie (Ellis, Grahamj)
Date: Thu Mar 13 17:22:42 2008
Subject: [GAP Forum] applied computational algebra course
References: <Pine.LNX.4.64.0803131142170.19796@croever.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA3511@EVS1.ac.nuigalway.ie>
	<Pine.LNX.4.64.0803131414350.19796@croever.nuigalway.ie>
	<7BC4FCB2B695D64CBF525CEC6437532701BA3514@EVS1.ac.nuigalway.ie>
Message-ID: <7BC4FCB2B695D64CBF525CEC6437532701BA3516@EVS1.ac.nuigalway.ie>

 
The Maths Department at NUI Galway are offering a new one-year 
master's programme in "Applied Computational Algebra", starting 
September 2008. If you happen to know of any students who might be 
interested, it would be much appreciated if you could direct them 
to the web link

http://hamilton.nuigalway.ie/DeBrunCentre/masters.pdf 

which gives details of the programme.

Thanks,
Graham


From mim_ at op.pl  Fri Mar 14 09:02:04 2008
From: mim_ at op.pl (mim_@op.pl)
Date: Fri Mar 14 09:07:35 2008
Subject: [GAP Forum] Another memory problem
Message-ID: <Q86638938-3d3c6593e0f1adcfc4efbb1d028a6c11@pmq2.test.onet.pl>

Hi,

I am using Deriviations function to calculate Lie Algebra of derivations of some algebra created from octonions. I have noticed that Derivations works up to 36-dimension algebra. If the original algebra is bigger dimension there is memory problem and GAP quits.
I have looked into the Derivations function in lib/alglie.gi file. The matrix 
A:= NullMat( n^2, n^3, R ); is created and this is the reason of the memory problem.

I start GAP with option -m 300m. If I try bigger value I see following error:

  D:\gap4r4\bin>D:\GAP4R4\bin\gapw95.exe -m 400m -o 3000m -g -l D:\GAP4R4\
  gap: cannot extend the workspace any more
  gap: Press <Enter> to end program

So it looks I can only use 300MB of memory for GAP. But I have 1.5GB memory in my laptop. I can also define paging file which should be used as memory. I am using Windows XP Professional, processor Intel 1.7Ghz, IBM laptop R52.

Example of error in Derivations:
A:=MatrixAlgebra(Rationals, 6);     ba:=Basis(A);     DA:=Derivations(ba);
Error is shown:
gap: cannot extend the workspace any more
gap: Press <Enter> to end program

I have following questions
1. Why I can only start GAP with -m 300m option ?
2. How to test how much memory given matrix A is using in GAP ?
3. Has anybody tried to overwrite Derivations function to use smaller matrices ? E.g. we could declare smaller matrices NullMat( n^2, n^2, R ) in loop and solve partially equation via NullspaceMatDestructive(). Finally build intersection space for the result.

Regards,
Marek Mitros

From mim_ at op.pl  Mon Mar 17 11:32:17 2008
From: mim_ at op.pl (mim_@op.pl)
Date: Mon Mar 17 11:32:37 2008
Subject: [GAP Forum] Re: Another memory problem
In-Reply-To: Q86638938-3d3c6593e0f1adcfc4efbb1d028a6c11@pmq2.test.onet.pl
Message-ID: <Q87635449-e782993136954f16cf1d0dc539048e51@pmq1.test.onet.pl>

Thank you for the answers I have received ! It helped. I can use GAP with more memory now.

I believe there is a way to create function for Derivations, which consumes less memory. In the matrix A:= NullMat( n^2, n^3, R ); most of the entries are zeros.

I have tested it for algebra M6:=MatrixAlgebra(Rationals, 6);
There are 22476 non zero entries among 36^5=60466176.

I will try to create such function when I have more time.

Regards,
Marek Mitros
 
mim_@op.pl napisa?(a): 
(...)
 > 
 > Example of error in Derivations:
 > A:=MatrixAlgebra(Rationals, 6);     ba:=Basis(A);     DA:=Derivations(ba);
 > Error is shown:
 > gap: cannot extend the workspace any more
 > gap: Press <Enter> to end program
 > 
 > I have following questions
 > 1. Why I can only start GAP with -m 300m option ?
 > 2. How to test how much memory given matrix A is using in GAP ?
 > 3. Has anybody tried to overwrite Derivations function to use smaller matrices ? E.g. we could declare smaller matrices NullMat( n^2, n^2, R ) in loop and solve partially equation via NullspaceMatDestructive(). Finally build intersection space for the result.
 > 
 > Regards,
 > Marek Mitros
 > 
 > 
 > 

From matmackaizer at yahoo.ca  Wed Mar 19 04:46:47 2008
From: matmackaizer at yahoo.ca (Minh Vaughn)
Date: Wed Mar 19 04:47:18 2008
Subject: [GAP Forum] Proof of Existence of Unique Monic Polynomial of
	Minimal Degree
Message-ID: <226494.21163.qm@web45115.mail.sp1.yahoo.com>

I would be grateful for a proof of the following problem:

Suppose R is a unique factorization domain, and suppose S is an integral domain which is integral over R.  Then for every element s in S there is a UNIQUE monic polynomial P in R[x] of MINIMAL degree, such that P(s) = 0.

Thanks.
-Tim
       
---------------------------------
Looking for the perfect gift? Give the gift of Flickr!
From oova1980 at yahoo.de  Tue Mar 25 09:49:49 2008
From: oova1980 at yahoo.de (Knut Kasimir)
Date: Tue Mar 25 09:50:19 2008
Subject: [GAP Forum] Complex numbers (again) and Lie closure
Message-ID: <781000.38164.qm@web25915.mail.ukl.yahoo.com>

Hi,

so I've read (hopefully) all forum threads concerning the absence of complex numbers in GAP. I know that there are alternatives, eg. cyclotomic fields and algebraic extensions of the Rationals. But since I am rather unexperienced in using GAP, I would like to know to what extent these "workarounds" can replace complex numbers, especially when I want to work with Lie algebras over a complex field.

What I want to do with GAP is the following: Given a set of complex square matrices, find out if they form a vectorspace under repeated commutation, i.e. a Lie algebra. In other words, do these given matrices generate a Lie algebra under repeated commutation?

Since these matrices can be large, I am looking for an efficient way to deal with this problem and I was hoping that GAP would be well suited. But then I discovered that there were no complex numbers in GAP, and "the workarounds" might prevent an efficient computation (or a computation at all)...

Comments welcome! :-)




      Lesen Sie Ihre E-Mails jetzt einfach von unterwegs.
www.yahoo.de/go
From jbohanon2 at gmail.com  Tue Mar 25 19:56:55 2008
From: jbohanon2 at gmail.com (Joe Bohanon)
Date: Tue Mar 25 19:57:29 2008
Subject: [GAP Forum] GAP @ Home?
Message-ID: <47E95907.8070405@gmail.com>

At the CGT conference last week the concept of "GAP @ Home" was thrown 
out there sort of as a joke, but I'm wondering if that might actually be 
possible. 
I'm curious to know if anyone here has heard of BOINC.  I forget what 
the acronym stands for, but it's a meta-client through Berkeley for SETI 
and other programs like it, including one that searches for big primes.

I know at least for the prime programs, you don't even need GUI to set 
it up.  It would be cool if people could make their processor available 
for some of these enormous group theoretic calculations that would be 
impossible on a single machine.

Joe

From mjcforsenate at yahoo.com  Tue Mar 25 20:37:56 2008
From: mjcforsenate at yahoo.com (Michael McDonald)
Date: Tue Mar 25 20:38:21 2008
Subject: [GAP Forum] GAP @ Home?
In-Reply-To: <47E95907.8070405@gmail.com>
Message-ID: <647771.73192.qm@web39509.mail.mud.yahoo.com>

I've had dim, unformulated thoughts along these lines
and am happy that someone has brought them out in the
open.  Might ParGAP be extensible along these lines?
>From my quick trials after installing GAP and
compiling
the packages, I think I'm recalling correctly that
you can specify a list of processors/computers via a
url-like format on which parGAP can launch a thread.
This might be managed by hand with small groups of
trusted participants.

To get an application of much complexity going,
compiling GAP code to native machine language would be
preferable than the normal GAP interpreter as codes
can execute for months or years.  An interpreted
application is probably something like a factor of ten
slower.

I'm willing to contribute cycles and coding to such a
boinced-up GAP project, although I still need to learn
the GAP system a liitle more.

Mike

--- Joe Bohanon <jbohanon2@gmail.com> wrote:

> At the CGT conference last week the concept of "GAP
> @ Home" was thrown 
> out there sort of as a joke, but I'm wondering if
> that might actually be 
> possible. 
> I'm curious to know if anyone here has heard of
> BOINC.  I forget what 
> the acronym stands for, but it's a meta-client
> through Berkeley for SETI 
> and other programs like it, including one that
> searches for big primes.
> 
> I know at least for the prime programs, you don't
> even need GUI to set 
> it up.  It would be cool if people could make their
> processor available 
> for some of these enormous group theoretic
> calculations that would be 
> impossible on a single machine.
> 
> Joe
> 
> _______________________________________________
> Forum mailing list
> Forum@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
> 

From degraaf at science.unitn.it  Wed Mar 26 08:47:45 2008
From: degraaf at science.unitn.it (degraaf@science.unitn.it)
Date: Wed Mar 26 09:17:20 2008
Subject: [GAP Forum] Re: Complex numbers (again) and Lie closure
Message-ID: <20080326094745.0uyi026u8g0swo8w@www.unitn.it>

Dear Knut,


You asked the following:

> What I want to do with GAP is the following: Given a set of complex  
> square matrices, find out if they form a vectorspace under repeated  
> commutation, i.e. a > Lie algebra. In other words, do these given  
> matrices generate a Lie algebra under repeated commutation?

The problem here is that you need some exact representation of the complex
numbers that you use. (Just a floating point representation does not work.)
If the entries of your matrices are algebraic over Q, then you can represent
them as entries in a number field. Otherwise I don't see how your problem
could be solved.

Best wishes,

Willem de Graaf



From max at quendi.de  Fri Mar 28 16:30:11 2008
From: max at quendi.de (Max Horn)
Date: Fri Mar 28 16:30:43 2008
Subject: [GAP Forum] Transitive subgrops of Sym(n) of order n
Message-ID: <37043.XVdYXF9DRFA=.1206721811.squirrel@webmailer.hosteurope.de>

Dear GAP forum,

is there an "efficient" way to compute (the conjugacy classes of) all
transitive subgroups of SymmetricGroup(n) or order n?

I.e. something more efficient than

Filtered(ConjugacyClassesSubgroups(SymmetricGroup(n)),
  x -> n=Size(Representative(x)) and IsTransitive(Representative(x)))

which has to compute all conjugacy classes.


Thanks!
Max

From nmd at uiuc.edu  Sat Mar 29 03:40:28 2008
From: nmd at uiuc.edu (Nathan Dunfield)
Date: Sat Mar 29 03:41:01 2008
Subject: [GAP Forum] Finding only one GQuotient
Message-ID: <6FE04480-9B05-45FF-86F7-AC6D4B5B85FD@uiuc.edu>

Dear GAP folks,

The manual indicates [1] that GQuotients should return only the first  
quotient it finds if the "findall" option is set to false.  However,  
when I try

gap> GQuotients(FreeGroup(2), AlternatingGroup(5) : findall := false);

I get all 19 epimorphisms.   What am I doing wrong?

	Thanks,

	Nathan

GAP info: 4.4.10 on OS X/Intel version 10.4.

[1] http://www.gap-system.org/Manuals/doc/htm/ref/CHAP038.htm#SSEC009.2

From thomas.breuer at math.rwth-aachen.de  Mon Mar 31 08:46:04 2008
From: thomas.breuer at math.rwth-aachen.de (Thomas Breuer)
Date: Mon Mar 31 08:46:31 2008
Subject: [GAP Forum] Transitive subgrops of Sym(n) of order n
In-Reply-To: <37043.XVdYXF9DRFA=.1206721811.squirrel@webmailer.hosteurope.de>
References: <37043.XVdYXF9DRFA=.1206721811.squirrel@webmailer.hosteurope.de>
Message-ID: <20080331074604.GA26239@gemma.math.rwth-aachen.de>

proposed answer to the GAP Forum
------------------------------------------------------------------------
Dear GAP Forum,

Max Horn asked:

> is there an "efficient" way to compute (the conjugacy classes of) all
> transitive subgroups of SymmetricGroup(n) or order n?
> 
> I.e. something more efficient than
> 
> Filtered(ConjugacyClassesSubgroups(SymmetricGroup(n)),
>   x -> n=Size(Representative(x)) and IsTransitive(Representative(x)))
> 
> which has to compute all conjugacy classes.

Any group of order n has only one transitive permutation representation
on n points, up to equivalence: its regular permutation representation.
That is, the classes of transitive groups of degree and order n
are given by the classes of regular permutation representations of
the groups of order n.
So if one knows the groups of order n, up to isomorphism,
then one can write down the required subgroups of the symmetric group
of degree n.
(This condition is satisfied for not too large n,
via the GAP library of small groups;
see "Small Groups" in the GAP Reference Manual.)

Here is one possibility to do this explicitly in GAP.

    List( AllSmallGroups( n ), G -> Action( G, Elements( G ), OnRight ) );

All the best,
Thomas

From jbohanon2 at gmail.com  Mon Mar 31 16:56:28 2008
From: jbohanon2 at gmail.com (Joe Bohanon)
Date: Mon Mar 31 16:56:52 2008
Subject: [GAP Forum] Transitive subgrops of Sym(n) of order n
In-Reply-To: <20080331074604.GA26239@gemma.math.rwth-aachen.de>
References: <37043.XVdYXF9DRFA=.1206721811.squirrel@webmailer.hosteurope.de>
	<20080331074604.GA26239@gemma.math.rwth-aachen.de>
Message-ID: <47F109AC.3020907@gmail.com>

I know this isn't exactly what was asked, but a few weeks ago at CGT, 
Derek Holt spoke about finding certain kinds of subgroups of S_n up to 
conjugacy.  Up to 4095, the primitive ones are known.  Up to 32 the 
transitive ones are known.  And up to 18 ALL of the (conjugacy classes 
of) subgroups of S_n are known.

There's a paper about finding the transitive ones on his website (which 
references a paper of Alexander Hulpke's on the same subject).
Joe

Thomas Breuer wrote:
> proposed answer to the GAP Forum
> -------