From jdm3 at st-and.ac.uk Mon Jan 5 17:11:50 2015
From: jdm3 at st-and.ac.uk (James Mitchell)
Date: Mon, 05 Jan 2015 17:11:50 +0000
Subject: [GAP Forum] [Devel] A new GAP development mailing list
References: <941d49c9979348f9830310e40ff6ece8@UOS-DUN-CAS3.st-andrews.ac.uk>
Message-ID:
Great! Thanks Markus.
On Mon Jan 05 2015 at 1:13:28 PM Markus Pfeiffer <
markus.pfeiffer at morphism.de> wrote:
> Dear all,
>
> I would hereby like to announce a new GAP development mailinglist
>
> gap at gap-system.org
>
> which has a mailman page at
>
> http://mail.gap-system.org/mailman/listinfo/gap
>
> This mailing list has the purpose of discussing the development
> of the GAP system. We welcome everyone who is interested in the
> development to post and contribute.
> The list is archived, and the archive is publically accessible at
>
> https://mail.gap-system.org/pipermail/gap/
>
> Cheers,
> Markus
>
> _______________________________________________
> Devel mailing list
> Devel at gap-system.org
> http://mail.gap-system.org/mailman/listinfo/devel
>
From markus.pfeiffer at morphism.de Mon Jan 5 13:11:27 2015
From: markus.pfeiffer at morphism.de (Markus Pfeiffer)
Date: Mon, 5 Jan 2015 13:11:27 +0000
Subject: [GAP Forum] A new GAP development mailing list
Message-ID: <20150105131127.GH425800@karp.morphism.de>
Dear all,
I would hereby like to announce a new GAP development mailinglist
gap at gap-system.org
which has a mailman page at
http://mail.gap-system.org/mailman/listinfo/gap
This mailing list has the purpose of discussing the development
of the GAP system. We welcome everyone who is interested in the
development to post and contribute.
The list is archived, and the archive is publically accessible at
https://mail.gap-system.org/pipermail/gap/
Cheers,
Markus
From preggyp at dut.ac.za Thu Jan 8 10:20:37 2015
From: preggyp at dut.ac.za (Pragladan Perumal)
Date: Thu, 8 Jan 2015 10:20:37 +0000
Subject: [GAP Forum] FW:
In-Reply-To:
References:
Message-ID:
________________________________________
From: Pragladan Perumal
Sent: Thursday, January 08, 2015 12:19 PM
To: forum at gapsystem.org
Subject:
Hello
Recently loaded Gap on my computer(Windows).
Want to construct the Frobenius group F=11:5
Used the following:
g:=CyclicGroup(11);
FixedpointfreeAutomorphismGroups(g);
However error message comes up:'FixedpointfreeAutomorphismGroups must have value"
Would appreciate advice.
thanks
preggyp
________________________________
"This e-mail is subject to our Disclaimer, to view click http://www.dut.ac.za/disclaimer"
From alexk at mcs.st-andrews.ac.uk Thu Jan 8 10:42:24 2015
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 8 Jan 2015 10:42:24 +0000
Subject: [GAP Forum] FW:
In-Reply-To:
References:
Message-ID:
Hello,
It could be that the spelling of the function is wrong. GAP is case-sensitive,
so e.g. FixedpointfreeAutomorphismGroups and FixedPointFreeAutomorphismGroups
is not the same. It could be that this is a function from a package which has
to be loaded in advance. I can't see such in GAP and packages at all, however,
so could you please let us know where did you learn about the existence of the
function `FixedpointfreeAutomorphismGroups`?
Looks to me like it comes from someone's private code, and might be related to
SONATA package.
HTH
Alexander
On 8 Jan 2015, at 10:20, Pragladan Perumal wrote:
>
> ________________________________________
> From: Pragladan Perumal
> Sent: Thursday, January 08, 2015 12:19 PM
> To: forum at gapsystem.org
> Subject:
>
> Hello
>
> Recently loaded Gap on my computer(Windows).
> Want to construct the Frobenius group F=11:5
> Used the following:
> g:=CyclicGroup(11);
> FixedpointfreeAutomorphismGroups(g);
>
> However error message comes up:'FixedpointfreeAutomorphismGroups must have value"
>
> Would appreciate advice.
>
> thanks
>
> preggyp
>
>
> ________________________________
>
> "This e-mail is subject to our Disclaimer, to view click http://www.dut.ac.za/disclaimer"
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From n.j.loughlin at ncl.ac.uk Fri Jan 9 18:06:13 2015
From: n.j.loughlin at ncl.ac.uk (Nick Loughlin)
Date: Fri, 09 Jan 2015 18:06:13 +0000
Subject: [GAP Forum] Error when Generating FreeMonoid of rank infinity
Message-ID: <54B01895.30803@ncl.ac.uk>
Hi Forum,
I'm working in GAP 4.7.5 in linux, and have tested on a similar set-up
on 4.7.4 with identical results, and 4.5.5, with a different error message.
gap> FreeMonoid( infinity, "m", [ ] );
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 2nd choice method found for `in' on 2 arguments called from
One( M ) in GeneratorsOfMonoid( M ) called from
called from
called from
SetGeneratorsOfMagmaWithOne( M, AsList( gens ) ); called from
MonoidByGenerators( InfiniteListOfGenerators( F ) ) called from
... at line 957 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
I've replicated the result on GAP 4.7.4 on linux on a different
computer. I can get a hold of the monoid (locally named M) in the break
loop, and assign it to a global variable name to use once I exit the
loop, but would appreciate some insight into the nature of this error ?
is it a bug, or have I done something wrong? If it's a bug, is there an
easy workaround I can use for now?
Best,
Nick
From jdm3 at st-and.ac.uk Fri Jan 9 18:28:40 2015
From: jdm3 at st-and.ac.uk (James Mitchell)
Date: Fri, 9 Jan 2015 18:28:40 +0000
Subject: [GAP Forum] Error when Generating FreeMonoid of rank infinity
In-Reply-To: <2537a17693c84bc28e4d729f7bf27551@UOS-DUN-CAS1.st-andrews.ac.uk>
References: <2537a17693c84bc28e4d729f7bf27551@UOS-DUN-CAS1.st-andrews.ac.uk>
Message-ID:
Dear Nick,
Thanks for the report. There is a bug in a method that is called
immediately for any monoid that is created using a set of generators.
The bug only occurs for monoids with infinite generating sets, which
is probably why it never showed up before. If you replace the method
in lines 127 to 135 of the file gap/lib/monoid.gi by the code below,
then your example works ok. You can also just paste the code below
into a GAP session or put it in your .gaprc file, and then after this
your example will work.
InstallImmediateMethod( GeneratorsOfSemigroup,
IsMonoid and HasGeneratorsOfMonoid and IsAttributeStoringRep, 0,
function(M)
if CanEasilyCompareElements(One(M)) and One(M) in GeneratorsOfMonoid(M) then
return GeneratorsOfMonoid(M);
fi;
return Concatenation([One(M)],GeneratorsOfMonoid(M));
end);
Best wishes,
James
On 9 January 2015 at 18:06, Nick Loughlin wrote:
> Hi Forum,
>
> I'm working in GAP 4.7.5 in linux, and have tested on a similar set-up
> on 4.7.4 with identical results, and 4.5.5, with a different error message.
>
>
> gap> FreeMonoid( infinity, "m", [ ] );
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 2nd choice method found for `in' on 2 arguments called from
> One( M ) in GeneratorsOfMonoid( M ) called from
> called from
> called from
> SetGeneratorsOfMagmaWithOne( M, AsList( gens ) ); called from
> MonoidByGenerators( InfiniteListOfGenerators( F ) ) called from
> ... at line 957 of *stdin*
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
>
>
> I've replicated the result on GAP 4.7.4 on linux on a different
> computer. I can get a hold of the monoid (locally named M) in the break
> loop, and assign it to a global variable name to use once I exit the
> loop, but would appreciate some insight into the nature of this error ?
> is it a bug, or have I done something wrong? If it's a bug, is there an
> easy workaround I can use for now?
>
> Best,
> Nick
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
--
James Mitchell
tinyurl.com/jdmitchell
The University of St Andrews is a charity registered in Scotland : No SC013532
From sebastienpalcoux at yahoo.fr Mon Jan 12 09:38:46 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Mon, 12 Jan 2015 09:38:46 +0000 (UTC)
Subject: [GAP Forum] unitary representations
Message-ID: <1066265362.780198.1421055526295.JavaMail.yahoo@jws11161.mail.ir2.yahoo.com>
Hi,
I've the following question (posted?on math.stackexchange with more details):
How getting the unitarized irreducible representations with GAP?http://math.stackexchange.com/q/1101017/84284
Best regards,S?bastien Palcoux
From barakat at mathematik.uni-kl.de Wed Jan 14 11:04:57 2015
From: barakat at mathematik.uni-kl.de (Mohamed Barakat)
Date: Wed, 14 Jan 2015 12:04:57 +0100
Subject: [GAP Forum] GAP Days 2014
Message-ID: <4b1a0a35-213c-440e-8e3e-686ee9ddc10e@HUB2.rwth-ad.de>
Dear all,
we would like to announce the second GAP Days which will take place
in Aachen, 16-20 March, 2015.
For details please visit the webpage of the meeting
http://gapdays.coxeter.de/gapdays2015-spring/
Best wishes,
Mohamed Barakat, Max Horn, and Frank L?beck.
From felix.goldberg at gmail.com Thu Jan 15 23:55:44 2015
From: felix.goldberg at gmail.com (Felix Goldberg)
Date: Fri, 16 Jan 2015 01:55:44 +0200
Subject: [GAP Forum] How to create partial geometries in GAP?
Message-ID:
Hello,
I would like to work with partial geometries. What is the easiest way to
construct some of them in GAP? Apologies for the extra-noobish question.
Felix
--
----------------------------------
Felix Goldberg, Ph. D.
www.technion.ac.il/~felixg
From jdebeule at cage.ugent.be Fri Jan 16 09:03:40 2015
From: jdebeule at cage.ugent.be (Jan De Beule)
Date: Fri, 16 Jan 2015 10:03:40 +0100
Subject: [GAP Forum] How to create partial geometries in GAP?
In-Reply-To:
References:
Message-ID:
Dear Felix,
This depends very much on how you want to represent the partial geometry you are interested in. There has been work done on partial geometries using the packages GRAPE and DESIGN. You might also be interested in models of partial geometries that are constructed in projective spaces. Therefore the package fining could be useful: http://cage.ugent.be/fining
Best regards,
Jan De Beule
----------------------------------------------------------------------------
Jan De Beule jdebeule at cage.ugent.be
Postdoctoraal onderzoeker FWO
Vakgroep Wiskunde
Krijgslaan 281, S22
B 9000 Gent (Belgium) http://cage.ugent.be/~jdebeule
----------------------------------------------------------------------------
Op 16-jan.-2015, om 00:55 heeft Felix Goldberg het volgende geschreven:
> Hello,
>
> I would like to work with partial geometries. What is the easiest way to
> construct some of them in GAP? Apologies for the extra-noobish question.
>
> Felix
>
> --
> ----------------------------------
> Felix Goldberg, Ph. D.
> www.technion.ac.il/~felixg
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From l.h.soicher at qmul.ac.uk Fri Jan 16 09:31:19 2015
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Fri, 16 Jan 2015 09:31:19 +0000
Subject: [GAP Forum] How to create partial geometries in GAP?
In-Reply-To:
References: ,
Message-ID: <1421400683197.95582@qmul.ac.uk>
Dear Felix, Dear GAP-Forum,
You can use the function PartialLinearSpaces in the GRAPE package to construct and
classify the partial geometries with given (pseudo-geometric) point graph. In particular,
PartialLinearSpaces( ptgraph, s, t )
returns a list of representatives of the distinct isomorphism classes of partial linear spaces
with point graph ptgraph, and parameters (s,t). More information and more options for this
function, as well as examples, can be found in the GRAPE documentation. Please note that
the problem handled by the function PartialLinearSpaces can be extremely difficult,
and a given computation may not finish in any reasonable time!
You may also be interested in my paper:
L.H. Soicher, Is there a McLaughlin geometry?, J. Algebra 300 (2006), 248-255.
Hope this is helpful,
Leonard
________________________________________
From: forum-bounces at gap-system.org on behalf of Jan De Beule
Sent: 16 January 2015 09:03
To: Felix Goldberg
Cc: forum at gap-system.org
Subject: Re: [GAP Forum] How to create partial geometries in GAP?
Dear Felix,
This depends very much on how you want to represent the partial geometry you are interested in. There has been work done on partial geometries using the packages GRAPE and DESIGN. You might also be interested in models of partial geometries that are constructed in projective spaces. Therefore the package fining could be useful: http://cage.ugent.be/fining
Best regards,
Jan De Beule
----------------------------------------------------------------------------
Jan De Beule jdebeule at cage.ugent.be
Postdoctoraal onderzoeker FWO
Vakgroep Wiskunde
Krijgslaan 281, S22
B 9000 Gent (Belgium) http://cage.ugent.be/~jdebeule
----------------------------------------------------------------------------
Op 16-jan.-2015, om 00:55 heeft Felix Goldberg het volgende geschreven:
> Hello,
>
> I would like to work with partial geometries. What is the easiest way to
> construct some of them in GAP? Apologies for the extra-noobish question.
>
> Felix
>
> --
> ----------------------------------
> Felix Goldberg, Ph. D.
> www.technion.ac.il/~felixg
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
From sebastienpalcoux at yahoo.fr Mon Jan 19 21:18:13 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Mon, 19 Jan 2015 21:18:13 +0000 (UTC)
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
Message-ID: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
Hi,
Is it possible to extend the function Sqrt on the cyclotomic numbers?
See below what's happen if we try, for example, with the number E(5) :
gap> Sqrt(E(5));Error, no method found! For debugging hints type ?Recovery from NoMethodFoundError, no 1st choice method found for `Sqrt' on 1 arguments called from( ) called from read-eval-loopEntering break read-eval-print loop ...you can 'quit;' to quit to outer loop, oryou can 'return;' to continuebrk>
Best regards,Sebastien Palcoux
From sebastienpalcoux at yahoo.fr Mon Jan 19 21:24:10 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Mon, 19 Jan 2015 21:24:10 +0000 (UTC)
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
References: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
Message-ID: <1608807403.3885217.1421702650832.JavaMail.yahoo@jws11108.mail.ir2.yahoo.com>
Hi,
In fact, I need Sqrt only for the positive cyclotomic numbers.
Sebastien
Le Mardi 20 janvier 2015 2h48, Palcoux Sebastien a ?crit :
Hi,
Is it possible to extend the function Sqrt on the cyclotomic numbers?
See below what's happen if we try, for example, with the number E(5) :
gap> Sqrt(E(5));Error, no method found! For debugging hints type ?Recovery from NoMethodFoundError, no 1st choice method found for `Sqrt' on 1 arguments called from( ) called from read-eval-loopEntering break read-eval-print loop ...you can 'quit;' to quit to outer loop, oryou can 'return;' to continuebrk>
Best regards,Sebastien Palcoux
From hulpke at fastmail.fm Mon Jan 19 21:43:23 2015
From: hulpke at fastmail.fm (Alexander Hulpke)
Date: Mon, 19 Jan 2015 14:43:23 -0700
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
References: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
Message-ID: <73D5EA8C-EF91-4F8E-BCB4-727E38B6CFF6@fastmail.fm>
Dear Forum,
> On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien wrote:
>
> Hi,
> Is it possible to extend the function Sqrt on the cyclotomic numbers?
How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)
Regards,
Alexander Hulpke
From sebastienpalcoux at yahoo.fr Tue Jan 20 07:31:56 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Tue, 20 Jan 2015 07:31:56 +0000 (UTC)
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <73D5EA8C-EF91-4F8E-BCB4-727E38B6CFF6@fastmail.fm>
References: <73D5EA8C-EF91-4F8E-BCB4-727E38B6CFF6@fastmail.fm>
Message-ID: <783884855.3956199.1421739116713.JavaMail.yahoo@jws11146.mail.ir2.yahoo.com>
Dear Alexander and Forum,
If the cyclotomic number is the square of a cyclotomic number, is there an easy way to find it?
The number I need are the eigenvalues of the matrix of the unitarized inner product of an irreducible representation of a finite group (see the comment of Paul Garett here: http://math.stackexchange.com/q/1107941/84284).?This matrix is positive, I guess its eigenvalues are always cyclotomic (true for the examples I've looked, but I don't know in general), and I hope they are square of cyclotomic. Thanks to these square roots I can compute the unitary matrices for the irreducible representation.
Remark: a function on GAP computing the unitary irreducible representations seems very natural, so if there is not such a function, this should means that there are problems for computing them in general with GAP, isn't it?
Best regards,Sebastien Palcoux?? ?? ?
Le Mardi 20 janvier 2015 3h13, Alexander Hulpke a ?crit :
Dear Forum,
> On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien wrote:
>
> Hi,
> Is it possible to extend the function Sqrt on the cyclotomic numbers?
How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)
Regards,
? Alexander Hulpke
From dmitrii.pasechnik at cs.ox.ac.uk Tue Jan 20 08:59:15 2015
From: dmitrii.pasechnik at cs.ox.ac.uk (Dima Pasechnik)
Date: Tue, 20 Jan 2015 08:59:15 +0000
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <783884855.3956199.1421739116713.JavaMail.yahoo@jws11146.mail.ir2.yahoo.com>
References: <73D5EA8C-EF91-4F8E-BCB4-727E38B6CFF6@fastmail.fm>
<783884855.3956199.1421739116713.JavaMail.yahoo@jws11146.mail.ir2.yahoo.com>
Message-ID: <20150120085915.GB18520@dimpase.cs.ox.ac.uk>
On Tue, Jan 20, 2015 at 07:31:56AM +0000, Palcoux Sebastien wrote:
> Dear Alexander and Forum,
> If the cyclotomic number is the square of a cyclotomic number, is there an easy way to find it?
> The number I need are the eigenvalues of the matrix of the unitarized inner product of an irreducible representation of a finite group (see the comment of Paul Garett here: http://math.stackexchange.com/q/1107941/84284).?This matrix is positive, I guess its eigenvalues are always cyclotomic (true for the examples I've looked, but I don't know in general), and I hope they are square of cyclotomic. Thanks to these square roots I can compute the unitary matrices for the irreducible representation.
You don't need to take square roots. If H is the Hermitian positive definite form
you obtained by the averaging (or in some other way) then H=LDL*, for
L a lower-triangular matrix with 1s on the main diagonal, and D is a diagonal matrix.
L and D can be computed without taking square roots (and so they will stay cyclotomic).
Then conjugating by L gives you the unitary form.
HTH,
Dmitrii
> Remark: a function on GAP computing the unitary irreducible representations seems very natural, so if there is not such a function, this should means that there are problems for computing them in general with GAP, isn't it?
> Best regards,Sebastien Palcoux?? ?? ?
>
> Le Mardi 20 janvier 2015 3h13, Alexander Hulpke a ?crit :
>
>
> Dear Forum,
>
> > On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien wrote:
> >
> > Hi,
> > Is it possible to extend the function Sqrt on the cyclotomic numbers?
>
> How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)
>
> Regards,
>
> ? Alexander Hulpke
From sebastienpalcoux at yahoo.fr Tue Jan 20 10:07:18 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Tue, 20 Jan 2015 10:07:18 +0000 (UTC)
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <20150120085915.GB18520@dimpase.cs.ox.ac.uk>
References: <20150120085915.GB18520@dimpase.cs.ox.ac.uk>
Message-ID: <823721166.4100790.1421748438894.JavaMail.yahoo@jws11117.mail.ir2.yahoo.com>
Dear Dima and Forum.
I don't understand how your answer solves my problem, perhaps there is a misunderstanding:
What I want are the unitary matrices representing the elements of the group G for an irreducible representation V.For so, we should conjugate the non-unitary matrices (given by GAP) by the matrix R=S.P with S^{-2} the diagonalization D of the matrix X of the Hermitian positive definite formobtained by the averaging (or in some other way) and P the matrix of the change of basis (into the eigenvectors basis of X). ?In this process, we need the find the square root of D, i.e. ?the square root of positive cyclotomic numbers.
Is there an other process for doing that without having to compute square root?of positive cyclotomic numbers?
Best regards,S?bastien
Le Mardi 20 janvier 2015 14h29, Dima Pasechnik a ?crit :
On Tue, Jan 20, 2015 at 07:31:56AM +0000, Palcoux Sebastien wrote:
> Dear Alexander and Forum,
> If the cyclotomic number is the square of a cyclotomic number, is there an easy way to find it?
> The number I need are the eigenvalues of the matrix of the unitarized inner product of an irreducible representation of a finite group (see the comment of Paul Garett here: http://math.stackexchange.com/q/1107941/84284).?This matrix is positive, I guess its eigenvalues are always cyclotomic (true for the examples I've looked, but I don't know in general), and I hope they are square of cyclotomic. Thanks to these square roots I can compute the unitary matrices for the irreducible representation.
You don't need to take square roots. If H is the Hermitian positive definite form
you obtained by the averaging (or in some other way) then H=LDL*, for
L a lower-triangular matrix with 1s on the main diagonal, and D is a diagonal matrix.
L and D can be computed without taking square roots (and so they will stay cyclotomic).
Then conjugating by L gives you the unitary form.
HTH,
Dmitrii
> Remark: a function on GAP computing the unitary irreducible representations seems very natural, so if there is not such a function, this should means that there are problems for computing them in general with GAP, isn't it?
> Best regards,Sebastien Palcoux?? ?? ?
>
>? ? ? Le Mardi 20 janvier 2015 3h13, Alexander Hulpke a ?crit :
>? ?
>
>? Dear Forum,
>
> > On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien wrote:
> >
> > Hi,
> > Is it possible to extend the function Sqrt on the cyclotomic numbers?
>
> How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)
>
> Regards,
>
> ? Alexander Hulpke
From simon.king at uni-jena.de Fri Jan 16 10:23:43 2015
From: simon.king at uni-jena.de (Simon King)
Date: Fri, 16 Jan 2015 11:23:43 +0100
Subject: [GAP Forum] Second announcement CoGrAl2015
Message-ID: <348ddbfab30d1418c3c0b7f1556d4c4b89436894170544119@webmail.uni-jena.de>
Dear colleagues,
This is the second announcement of a workshop entitled
Computations in Groups and Algebras (CoGrAl2015)
===================================
organised by Simon King, J?rgen M?ller, and Benjamin Sambale,
and taking place soon at
* Friedrich Schiller University Jena (Germany),
* from Monday, February 16th, to Thursday, February 19th, 2015.
The aim of the workshop is to shed some light on various recent
aspects of finite group theory, with a particular view towards
algorithms and computations. More specifically, we will focus
on the following topics:
* Cohomology of finite-dimensional algebras
* Structure of p-groups and fusion systems
* Block theory of finite groups
Invited speakers are:
Jon Carlson (Athens, GA)
David Craven (Birmingham)
Heiko Dietrich (Melbourne)
Bettina Eick (Braunschweig)
Graham Ellis (Galway)
David Green (Jena)
Ellen Henke (Aberdeen)
Frank Himstedt (M?nchen)
Max Horn (Gie?en)
Gregor Kemper (M?nchen)
Viktor Levandovskyy (Aachen)
Nadia Mazza (Lancaster)
Eamonn O'Brien (Auckland)
G?tz Pfeiffer (Galway)
Peter Symonds (Manchester)
For more details please visit the web page
* http://cogral2015.uni-jena.de/.
We would be very glad if this convinced you to visit Jena and
to attend the workshop. We are looking forward to seeing you!
With kind regards
S.K., J.M., B.S.
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From Bill.Allombert at math.u-bordeaux.fr Mon Jan 19 21:55:36 2015
From: Bill.Allombert at math.u-bordeaux.fr (Bill Allombert)
Date: Mon, 19 Jan 2015 22:55:36 +0100
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To: <1608807403.3885217.1421702650832.JavaMail.yahoo@jws11108.mail.ir2.yahoo.com>
References: <1252258313.3879212.1421702293308.JavaMail.yahoo@jws11111.mail.ir2.yahoo.com>
<1608807403.3885217.1421702650832.JavaMail.yahoo@jws11108.mail.ir2.yahoo.com>
Message-ID: <20150119215536.GJ17455@yellowpig>
> Le Mardi 20 janvier 2015 2h48, Palcoux Sebastien a ?crit :
>
>
> Hi,
> Is it possible to extend the function Sqrt on the cyclotomic numbers?
> See below what's happen if we try, for example, with the number E(5) :
> gap> Sqrt(E(5));Error, no method found! For debugging hints type ?Recovery from NoMethodFoundError, no 1st choice method found for `Sqrt' on 1 arguments called from( ) called from read-eval-loopEntering break read-eval-print loop ...you can 'quit;' to quit to outer loop, oryou can 'return;' to continuebrk>
Sqrt(E(5)) is +/- E(5)^3, and more generally Sqrt(E(p)) is +/- E(p)^((p+1)/2)
for odd p.
gap> (E(5)^3)^2;
E(5)
However, in the general the square root of a cyclotomic number is not a
cyclotomic number, for example Sqrt(2) is a cyclotomic number, but not
Sqrt(Sqrt(2)).
Cheers,
Bill.
From phjelmstad at msn.com Tue Jan 20 01:07:58 2015
From: phjelmstad at msn.com (PAUL)
Date: Mon, 19 Jan 2015 19:07:58 -0600
Subject: [GAP Forum] M24, M12
Message-ID:
Is there an easy way to generate a Steiner system S(5,8,24) for the Mathieu Group M24, if a Steiner system S(5,6,12) for the Mathieu Group is known? PGH
From l.h.soicher at qmul.ac.uk Tue Jan 20 11:08:10 2015
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Tue, 20 Jan 2015 11:08:10 +0000
Subject: [GAP Forum] M24, M12
In-Reply-To:
References:
Message-ID: <1421752089957.30201@qmul.ac.uk>
Dear PGH, Dear GAP Forum,
The Steiner systems S(5,6,12), S(5,8,24) and related block designs can be produced
by the DESIGN package for GAP, using its function WittDesign, which is described in
the DESIGN package documentation. In particular,
WittDesign(24) returns the unique (up to isomorphism) Steiner system S(5,8,24)
(also called a 5-(24,8,1) design). The function does not, however, construct this
design from a Steiner system S(5,6,12).
Hope this is helpful,
Leonard
________________________________________
From: forum-bounces at gap-system.org on behalf of PAUL
Sent: 20 January 2015 01:07
To: forum at gap-system.org
Subject: [GAP Forum] M24, M12
Is there an easy way to generate a Steiner system S(5,8,24) for the Mathieu Group M24, if a Steiner system S(5,6,12) for the Mathieu Group is known? PGH
_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
From dmitrii.pasechnik at cs.ox.ac.uk Tue Jan 20 14:05:30 2015
From: dmitrii.pasechnik at cs.ox.ac.uk (Dima Pasechnik)
Date: Tue, 20 Jan 2015 14:05:30 +0000
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
Message-ID:
Dear Sebastien,
Once again, your X can be written as X=L*DL, with D diagonal and real. The group L^-1 G L preserves the Hermitian form x*Dx. In particular any g in this group satisfies g*Dg=D. As it acts irreducibly, D is a scalar matrix, thus g is unitary.
Indeed, for computing D cyclotomics might not suffice, but we do not need D explicitly.
Dima
On 20 Jan 2015 10:07, Palcoux Sebastien wrote:
>
> Dear Dima and Forum.
>
> I don't understand how your answer solves my problem, perhaps there is a misunderstanding:
>
> What I want are the unitary matrices representing the elements of the group G for an irreducible representation V.
> For so, we should conjugate the non-unitary matrices (given by GAP) by the matrix R=S.P with S^{-2} the diagonalization D of the matrix X of the Hermitian positive definite form
> obtained by the averaging (or in some other way) and P the matrix of the change of basis (into the eigenvectors basis of X). ?
> In this process, we need the find the square root of D, i.e. ?the square root of positive cyclotomic numbers.
>
> Is there an other process for doing that without having to compute square root?of positive cyclotomic numbers?
>
> Best regards,
> S?bastien
>
>
>
> Le Mardi 20 janvier 2015 14h29, Dima Pasechnik a ?crit :
>
>
> On Tue, Jan 20, 2015 at 07:31:56AM +0000, Palcoux Sebastien wrote:
> > Dear Alexander and Forum,
> > If the cyclotomic number is the square of a cyclotomic number, is there an easy way to find it?
> > The number I need are the eigenvalues of the matrix of the unitarized inner product of an irreducible representation of a finite group (see the comment of Paul Garett here: http://math.stackexchange.com/q/1107941/84284).?This matrix is positive, I guess its eigenvalues are always cyclotomic (true for the examples I've looked, but I don't know in general), and I hope they are square of cyclotomic. Thanks to these square roots I can compute the unitary matrices for the irreducible representation.
>
> You don't need to take square roots. If H is the Hermitian positive definite form
> you obtained by the averaging (or in some other way) then H=LDL*, for
> L a lower-triangular matrix with 1s on the main diagonal, and D is a diagonal matrix.
> L and D can be computed without taking square roots (and so they will stay cyclotomic).
> Then conjugating by L gives you the unitary form.
>
> HTH,
> Dmitrii
>
>
>
> > Remark: a function on GAP computing the unitary irreducible representations seems very natural, so if there is not such a function, this should means that there are problems for computing them in general with GAP, isn't it?
> > Best regards,Sebastien Palcoux?? ?? ?
> >
> >? ? ? Le Mardi 20 janvier 2015 3h13, Alexander Hulpke a ?crit :
> >? ?
> >
> >? Dear Forum,
> >
> > > On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien wrote:
> > >
> > > Hi,
> > > Is it possible to extend the function Sqrt on the cyclotomic numbers?
> >
> > How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)
> >
> > Regards,
> >
> > ? Alexander Hulpke
>
>
From dmitrii.pasechnik at cs.ox.ac.uk Wed Jan 21 10:46:56 2015
From: dmitrii.pasechnik at cs.ox.ac.uk (Dima Pasechnik)
Date: Wed, 21 Jan 2015 10:46:56 +0000
Subject: [GAP Forum] Sqrt for the cyclotomic numbers
In-Reply-To:
References:
Message-ID: <20150121104656.GB29515@dimpase.cs.ox.ac.uk>
On Tue, Jan 20, 2015 at 02:05:30PM +0000, Dima Pasechnik wrote:
> Dear Sebastien,
>
> Once again, your X can be written as X=L*DL, with D diagonal and real. The
> group L^-1 G L preserves the Hermitian form x*Dx. In particular any g in this
> group satisfies g*Dg=D.
> As it acts irreducibly, D is a scalar matrix, thus g is unitary.
Sorry, this last claim is wrong: to get a unitary g, you will need
to take D^(1/2) g D^(-1/2). I suppose this is still easier
to compute than taking square roots during the diagonalisation of X.
>
> Indeed, for computing D cyclotomics might not suffice, but we do not need D
> explicitly.
here I meant "computing D^(1/2)", certainly, not just D.
I shall never again write to Form from a mobile phone. :-)
Dima
>
> Dima
>
>
> On 20 Jan 2015 10:07, Palcoux Sebastien wrote:
> >
> > Dear Dima and Forum.
> >
> > I don't understand how your answer solves my problem, perhaps there is a
> > misunderstanding:
> >
> > What I want are the unitary matrices representing the elements of the group
> > G for an irreducible representation V. For so, we should conjugate the
> > non-unitary matrices (given by GAP) by the matrix R=S.P with S^{-2} the
> > diagonalization D of the matrix X of the Hermitian positive definite form
> > obtained by the averaging (or in some other way) and P the matrix of the
> > change of basis (into the eigenvectors basis of X). ? In this process, we
> > need the find the square root of D, i.e. ?the square root of positive
> > cyclotomic numbers.
> >
> > Is there an other process for doing that without having to compute square
> > root?of positive cyclotomic numbers?
> >
> > Best regards, S?bastien
> >
> >
> >
> > Le Mardi 20 janvier 2015 14h29, Dima Pasechnik
> > a ?crit :
> >
> >
> > On Tue, Jan 20, 2015 at 07:31:56AM +0000, Palcoux Sebastien wrote:
> > > Dear Alexander and Forum, If the cyclotomic number is the square of a
> > > cyclotomic number, is there an easy way to find it? The number I need
> > > are the eigenvalues of the matrix of the unitarized inner product of an
> > > irreducible representation of a finite group (see the comment of Paul
> > > Garett here: http://math.stackexchange.com/q/1107941/84284).?This matrix
> > > is positive, I guess its eigenvalues are always cyclotomic (true for the
> > > examples I've looked, but I don't know in general), and I hope they are
> > > square of cyclotomic. Thanks to these square roots I can compute the
> > > unitary matrices for the irreducible representation.
> >
> > You don't need to take square roots. If H is the Hermitian positive
> > definite form you obtained by the averaging (or in some other way) then
> > H=LDL*, for L a lower-triangular matrix with 1s on the main diagonal, and D
> > is a diagonal matrix. L and D can be computed without taking square roots
> > (and so they will stay cyclotomic). Then conjugating by L gives you the
> > unitary form.
> >
> > HTH, Dmitrii
> >
> >
> >
> > > Remark: a function on GAP computing the unitary irreducible
> > > representations seems very natural, so if there is not such a function,
> > > this should means that there are problems for computing them in general
> > > with GAP, isn't it? Best regards,Sebastien Palcoux?? ?? ?
> > >
> > >? ? ? Le Mardi 20 janvier 2015 3h13, Alexander Hulpke
> > >a ?crit : ? ?
> > >
> > >? Dear Forum,
> > >
> > > > On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien
> > > > wrote:
> > > >
> > > > Hi, Is it possible to extend the function Sqrt on the cyclotomic
> > > > numbers?
> > >
> > > How would you represent this root? In general the square root of a
> > > cylotomic is not cyclotomic again. (You could form a formal
> > > AlgebraicExtension, but then you lose the irrational cyclotomics for
> > > operations.)
> > >
> > > Regards,
> > >
> > > ? Alexander Hulpke
> >
> >
> _______________________________________________ Forum mailing list
> Forum at mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
From felix.goldberg at gmail.com Wed Jan 21 12:33:07 2015
From: felix.goldberg at gmail.com (Felix Goldberg)
Date: Wed, 21 Jan 2015 14:33:07 +0200
Subject: [GAP Forum] How to obtain the incidence matrix of a partial
geometry?
Message-ID:
Hello all,
I am running the code in the example in Section 9.2 of the GRAPE manual (
http://www.maths.qmul.ac.uk/~leonard/grape/manual/CHAP009.htm) , which
generates the Haemers partial geometry pg(4,17,2).
All works well but I cannot understand where exactly the incidence matrix
is stored and how to access it. The manual (referred to above) says that
there is a *delta* associated to the geometry output by the function
PartialLinearSpaces
but I can't find it.
I tried to run RecNames on the output (the variable called *haemers*) and
got this:
[ "names", "group", "order", "representatives", "isSimple", "isGraph",
"schreierVector", "adjacencies" ]
No sign of *delta* and apparently no incidence matrix.
Any help will be greatly appreciated.
Thanks,
Felix
--
----------------------------------
Felix Goldberg, Ph. D.
www.technion.ac.il/~felixg
From sven.reichard at tu-dresden.de Wed Jan 21 12:51:03 2015
From: sven.reichard at tu-dresden.de (Sven Reichard)
Date: Wed, 21 Jan 2015 13:51:03 +0100
Subject: [GAP Forum] How to obtain the incidence matrix of a partial
geometry?
In-Reply-To:
References:
Message-ID: <54BFA0B7.9060405@tu-dresden.de>
Hello Felix,
the geometry is returned as an incidence graph in GRAPE format. For each
vertex x of that graph, Adjacency(haemers, x) will give you its
neighbours. From that you can reconstruct the adjacency matrix if you want.
For example with the following function:
AdjacencyMatrix := function ( gamma )
local result, x, y;
result := NullMat( gamma.order, gamma.order );
for x in [ 1 .. gamma.order ] do
for y in Adjacency( gamma, x ) do
result[x][y] := 1;
od;
od;
return result;
end
However it could be worth your while working with the graph format as it is.
"delta" just refers to the incidence graph. PartialLinearSpaces returns
a list of those.
Hope this helps,
Sven Reichard
Institut f?r Algebra
TU Dresden
On 01/21/2015 01:33 PM, Felix Goldberg wrote:
> Hello all,
>
> I am running the code in the example in Section 9.2 of the GRAPE manual (
> http://www.maths.qmul.ac.uk/~leonard/grape/manual/CHAP009.htm) , which
> generates the Haemers partial geometry pg(4,17,2).
>
> All works well but I cannot understand where exactly the incidence matrix
> is stored and how to access it. The manual (referred to above) says that
> there is a *delta* associated to the geometry output by the function
> PartialLinearSpaces
> but I can't find it.
>
> I tried to run RecNames on the output (the variable called *haemers*) and
> got this:
>
> [ "names", "group", "order", "representatives", "isSimple", "isGraph",
> "schreierVector", "adjacencies" ]
>
> No sign of *delta* and apparently no incidence matrix.
>
> Any help will be greatly appreciated.
>
> Thanks,
> Felix
>
>
>
>
From alireza_abdollahi at yahoo.com Wed Jan 21 13:32:32 2015
From: alireza_abdollahi at yahoo.com (Ali)
Date: Wed, 21 Jan 2015 17:02:32 +0330
Subject: [GAP Forum] a third output for IsAbelian
In-Reply-To: <54BFA0B7.9060405@tu-dresden.de>
References:
<54BFA0B7.9060405@tu-dresden.de>
Message-ID:
Dears,
I have a long list L of groups with finite presentations. I would like to apply IsAbelian on L and Filtered all groups which are not Abelian. Through the computations, IsAbelian could not treat an special group and so the Filtered will not be terminated. I would like to know if there is a way to define a third output for IsAbelian such as FAIL which means that it is tried to test abelianness by a certain limit ( e.g. Time or number of cosets or ...) but not succeeded. If such thing exists I can apply this new IsAbelian to the list L to obtain all groups which are not abelian or the old IsAbelian fails to give a true or false. Then I can handle the filtered list by hand since I guess the latter list should be short.
The same question for IsSolvable and ....
Best Wishes
Alireza Abdollahi
From hulpke at math.colostate.edu Wed Jan 21 17:25:29 2015
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Wed, 21 Jan 2015 10:25:29 -0700
Subject: [GAP Forum] a third output for IsAbelian
In-Reply-To:
References:
<54BFA0B7.9060405@tu-dresden.de>
Message-ID: <1FB44AC4-DD9E-482F-B4DF-BEAAB9A4A32B@math.colostate.edu>
Dear Forum,
> On Jan 21, 2015, at 1/21/15 6:32, Ali wrote:
>
> Dears,
>
> I have a long list L of groups with finite presentations. I would like to apply IsAbelian on L and Filtered all groups which are not Abelian. Through the computations, IsAbelian could not treat an special group and so the Filtered will not be terminated. I would like to know if there is a way to define a third output for IsAbelian such as FAIL which means that it is tried to test abelianness by a certain limit ( e.g. Time or number of cosets or ...) but not succeeded. If such thing exists I can apply this new IsAbelian to the list L to obtain all groups which are not abelian or the old IsAbelian fails to give a true or false. Then I can handle the filtered list by hand since I guess the latter list should be short.
>
> The same question for IsSolvable and ....
This depends a bit on the groups in question, but `IsAbelian' etc. will by default calculate a faithful representation. If your groups are huge this will most likely fail every time.
What I would do as a first step is to look at quotient groups: Solvable Quotient, Action on cosets of Low Index subgroups and see whether rthese quotient groups already exclude the properties. This has (quotient size/subgroup index) easy parameters that will limit the initial calculations.
This should give you a good initial filtering of non-candidates.
Best,
Alexander Hulpke
>
> Best Wishes
> Alireza Abdollahi
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From sebastienpalcoux at yahoo.fr Mon Jan 26 18:12:33 2015
From: sebastienpalcoux at yahoo.fr (Palcoux Sebastien)
Date: Mon, 26 Jan 2015 18:12:33 +0000 (UTC)
Subject: [GAP Forum] subgroups lattices of simple groups
Message-ID: <1152961621.836980.1422295953749.JavaMail.yahoo@mail.yahoo.com>
Hi Forum,
Is it possible to access at the?Atlas of subgroup lattices of finite almost simple groups?(of Thomas Connor and Dimitri Leemans) with GAP?Is there a package?
Best regards,S?bastien
From hulpke at fastmail.fm Mon Jan 26 22:17:19 2015
From: hulpke at fastmail.fm (Alexander Hulpke)
Date: Mon, 26 Jan 2015 15:17:19 -0700
Subject: [GAP Forum] subgroups lattices of simple groups
In-Reply-To: <1152961621.836980.1422295953749.JavaMail.yahoo@mail.yahoo.com>
References: <1152961621.836980.1422295953749.JavaMail.yahoo@mail.yahoo.com>
Message-ID:
Dear Forum,
Sebastien Palcoux asked:
> Is it possible to access at the Atlas of subgroup lattices of finite almost simple groups (of Thomas Connor and Dimitri Leemans) with GAP?Is there a package?
To my knowledge there is no ready implementation. However if there are data files available (I did not find any online), they probably could be read in with little effort.
Regards,
Alexander Hulpke
From l.h.soicher at qmul.ac.uk Wed Jan 28 13:38:05 2015
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Wed, 28 Jan 2015 13:38:05 +0000
Subject: [GAP Forum] The stability of group libraries
Message-ID: <1422452294146.69150@qmul.ac.uk>
Dear GAP Developers, Dear GAP-Forum,
I would like to know what the policy is concerning the groups
in the the very useful GAP libraries of transitive permutation groups and
of primitive permutation groups (and any other group library you wish to comment on)
as regards to any possible changes wihen changes are made in GAP. In particular,
were the actual groups in the library, their GeneratorsOfGroup, and their indexing
within the library fixed in perpetuity when the library was initially made available in GAP4,
and if not, what is the mechanism to alert users to any changes? This is important
for being able to repeat, check, report on, and extend results made using specific
groups in a given library.
Thank you for your help,
Leonard
From alexk at mcs.st-andrews.ac.uk Wed Jan 28 13:52:42 2015
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Wed, 28 Jan 2015 13:52:42 +0000
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <1422452294146.69150@qmul.ac.uk>
References: <1422452294146.69150@qmul.ac.uk>
Message-ID: <19FEA9EA-912E-4B04-9EE5-6B880B401CBD@mcs.st-andrews.ac.uk>
Dear Leonard,
Thank you - that's really an important issue. My understanding is that the indexing
should stay the same for all the time, i.e. outputs of TransitiveGroup(m,n) should
be isomorphic in any version of the library.
IMHO, other information may change - it looks fine to me if e.g. in a new version a
group will be given by more optimal presentation. The mechanism to alert users stays
with their authors, and they should be encouraged to list all potentially disruptive
changes in release announcements and documentation.
Best wishes
Alexander
On 28 Jan 2015, at 13:38, Leonard Soicher wrote:
> Dear GAP Developers, Dear GAP-Forum,
>
> I would like to know what the policy is concerning the groups
> in the the very useful GAP libraries of transitive permutation groups and
> of primitive permutation groups (and any other group library you wish to comment on)
> as regards to any possible changes wihen changes are made in GAP. In particular,
> were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> within the library fixed in perpetuity when the library was initially made available in GAP4,
> and if not, what is the mechanism to alert users to any changes? This is important
> for being able to repeat, check, report on, and extend results made using specific
> groups in a given library.
>
> Thank you for your help,
> Leonard
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From stefan at mcs.st-and.ac.uk Wed Jan 28 14:24:11 2015
From: stefan at mcs.st-and.ac.uk (Stefan Kohl)
Date: Wed, 28 Jan 2015 14:24:11 -0000 (UTC)
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <1422452294146.69150@qmul.ac.uk>
References: <1422452294146.69150@qmul.ac.uk>
Message-ID:
Dear Leonard,
obviously a definitive answer to your question needs to be left to the
authors of the group libraries in question, but I have seen so many references
to e.g. SmallGroup(n,k) for particular values n and k in the literature that
it would likely cause major disruption if this would suddenly be a different group.
I would assume the same to hold for other group libraries, like the ones of
transitive groups and of primitive groups. However I am less sure about whether
details like which generators are stored are guaranteed to remain unchanged
in future versions.
Best wishes,
Stefan
On Wed, January 28, 2015 1:38 pm, Leonard Soicher wrote:
> Dear GAP Developers, Dear GAP-Forum,
>
> I would like to know what the policy is concerning the groups
> in the the very useful GAP libraries of transitive permutation groups and
> of primitive permutation groups (and any other group library you wish to comment on)
> as regards to any possible changes wihen changes are made in GAP. In particular,
> were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> within the library fixed in perpetuity when the library was initially made available in
> GAP4,
> and if not, what is the mechanism to alert users to any changes? This is important
> for being able to repeat, check, report on, and extend results made using specific
> groups in a given library.
>
> Thank you for your help,
> Leonard
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
From dmitrii.pasechnik at cs.ox.ac.uk Wed Jan 28 14:50:54 2015
From: dmitrii.pasechnik at cs.ox.ac.uk (Dmitrii Pasechnik)
Date: Wed, 28 Jan 2015 14:50:54 +0000
Subject: [GAP Forum] The stability of group libraries
In-Reply-To:
References: <1422452294146.69150@qmul.ac.uk>
Message-ID: <20150128145054.GA21680@cs.ox.ac.uk>
On Wed, Jan 28, 2015 at 02:24:11PM -0000, Stefan Kohl wrote:
> obviously a definitive answer to your question needs to be left to the
> authors of the group libraries in question, but I have seen so many references
> to e.g. SmallGroup(n,k) for particular values n and k in the literature that
> it would likely cause major disruption if this would suddenly be a different group.
If I recall right, there are (otherwise independent from GAP) software packages that identify
groups by their "GAP numbers", e.g. PARI/GP does this.
Just in case,
Dima
From hulpke at math.colostate.edu Wed Jan 28 16:02:12 2015
From: hulpke at math.colostate.edu (Alexander Hulpke)
Date: Wed, 28 Jan 2015 09:02:12 -0700
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <1422452294146.69150@qmul.ac.uk>
References: <1422452294146.69150@qmul.ac.uk>
Message-ID: <206937A8-2C76-4C2E-B205-00FA1862CEE1@math.colostate.edu>
Dear Leonard, Dear Forum,
> I would like to know what the policy is concerning the groups
> in the the very useful GAP libraries of transitive permutation groups and
> of primitive permutation groups (and any other group library you wish to comment on)
> as regards to any possible changes wihen changes are made in GAP. In particular,
> were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> within the library fixed in perpetuity when the library was initially made available in GAP4,
> and if not, what is the mechanism to alert users to any changes? This is important
> for being able to repeat, check, report on, and extend results made using specific
> groups in a given library.
We guarantee the following for the most prominent group libraries. (Guarantees are not exactly the same, as the construction processes differ).
- In the library of small groups, the numbering of isomorphism types is guaranteed to be stable. Actual group generators, or the PC presentations used could theoretically change (though there is no intention to do so, unless it would reflect a deeper mathematical understanding, and if this happened I'd expect an explicit announcement in the release notes.)
- In the library of transitive groups, the actual permutation groups (but not the generators used) are guaranteed to be stable. So you could refer to a particular point set and a particular group in a combinatorial construction.
- The *old* library of primitive groups had in fact an unstable numbering, dependent on the implementation of the subgroup lattice algorithm. This library was therefore retired with the release of GAP 4.2.
- The *new* library of primitive groups, release with GAP 4.2, guarantees a stable numbering (which for degree up to 50 is compatible with lists published in the literature), but does not guarantee a fixed S_n representative or particular generators.
(To the best of my knowledge the numbering of groups is compatible with other systems that provide such libraries.)
There is no mechanism for explicitly alerting users of changes in the non-guaranteed properties. A change in the guaranteed properties would presumably mean that the library was retired and replaced with a new library.
Needless to say, any such promises are only worth as much as the promiser, as anyone who endowed a chantry before 1545 can tell you.
Best,
Alexander
From D.F.Holt at warwick.ac.uk Wed Jan 28 16:54:48 2015
From: D.F.Holt at warwick.ac.uk (Derek Holt)
Date: Wed, 28 Jan 2015 16:54:48 +0000
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <206937A8-2C76-4C2E-B205-00FA1862CEE1@math.colostate.edu>
References: <1422452294146.69150@qmul.ac.uk>
<206937A8-2C76-4C2E-B205-00FA1862CEE1@math.colostate.edu>
Message-ID: <20150128165448.GA1067@warwick.ac.uk>
Dear Alexander, dear Forum,
On Wed, Jan 28, 2015 at 09:02:12AM -0700, Alexander Hulpke wrote:
> Dear Leonard, Dear Forum,
>
> > I would like to know what the policy is concerning the groups
> > in the the very useful GAP libraries of transitive permutation groups and
> > of primitive permutation groups (and any other group library you wish to comment on)
> > as regards to any possible changes wihen changes are made in GAP. In particular,
> > were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> > within the library fixed in perpetuity when the library was initially made available in GAP4,
> > and if not, what is the mechanism to alert users to any changes? This is important
> > for being able to repeat, check, report on, and extend results made using specific
> > groups in a given library.
>
> We guarantee the following for the most prominent group libraries. (Guarantees are not exactly the same, as the construction processes differ).
>
> - In the library of small groups, the numbering of isomorphism types is guaranteed to be stable. Actual group generators, or the PC presentations used could theoretically change (though there is no intention to do so, unless it would reflect a deeper mathematical understanding, and if this happened I'd expect an explicit announcement in the release notes.)
>
> - In the library of transitive groups, the actual permutation groups (but not the generators used) are guaranteed to be stable. So you could refer to a particular point set and a particular group in a combinatorial construction.
>
> - The *old* library of primitive groups had in fact an unstable numbering, dependent on the implementation of the subgroup lattice algorithm. This library was therefore retired with the release of GAP 4.2.
>
> - The *new* library of primitive groups, release with GAP 4.2, guarantees a stable numbering (which for degree up to 50 is compatible with lists published in the literature), but does not guarantee a fixed S_n representative or particular generators.
>
> (To the best of my knowledge the numbering of groups is compatible with other systems that provide such libraries.)
Magma has the same numbering for the small groups and transitive groups
databases, but a completely different numbering for the primitive groups.
I believe that the divergence resulted originally as a result of errors
(missing groups) in the old list, which were rectified in different ways.
It seems very unlikely indeed that there are errors in either the small groups
or the transitive groups databases, because they have been independently
checked, but I guess that if a mistake were to be found then that might
force a chage in numbering.
Derek.
> There is no mechanism for explicitly alerting users of changes in the non-guaranteed properties. A change in the guaranteed properties would presumably mean that the library was retired and replaced with a new library.
>
> Needless to say, any such promises are only worth as much as the promiser, as anyone who endowed a chantry before 1545 can tell you.
>
> Best,
>
> Alexander
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From l.h.soicher at qmul.ac.uk Thu Jan 29 07:53:01 2015
From: l.h.soicher at qmul.ac.uk (Leonard Soicher)
Date: Thu, 29 Jan 2015 07:53:01 +0000
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <20150128165448.GA1067@warwick.ac.uk>
References: <1422452294146.69150@qmul.ac.uk>
<206937A8-2C76-4C2E-B205-00FA1862CEE1@math.colostate.edu>,
<20150128165448.GA1067@warwick.ac.uk>
Message-ID: <1422517990612.11642@qmul.ac.uk>
Dear Alexander K., Stefan, Dima, Alexander H., Derek, and GAP-Forum,
Thank you for the useful replies.
> - In the library of transitive groups, the actual permutation groups
> (but not the generators used) are guaranteed to be stable. So you could refer
> to a particular point set and a particular group in a combinatorial construction.
>
Good.
>
> - The *new* library of primitive groups, release with GAP 4.2, guarantees a stable
> numbering [...] but does not guarantee a fixed S_n representative or particular generators.
>
It would be better if the actual permutation groups in the library of
primitive groups could be guaranteed to be stable.
Why would this not be possible?
Finally, the guarantees (or their lack, or any cautions) for specific libraries should be
documented in the GAP reference manual.
Thanks,
Leonard
________________________________________
From: Derek Holt
Sent: 28 January 2015 16:54
To: Alexander Hulpke
Cc: Leonard Soicher; forum at gap-system.org
Subject: Re: [GAP Forum] The stability of group libraries
Dear Alexander, dear Forum,
On Wed, Jan 28, 2015 at 09:02:12AM -0700, Alexander Hulpke wrote:
> Dear Leonard, Dear Forum,
>
> > I would like to know what the policy is concerning the groups
> > in the the very useful GAP libraries of transitive permutation groups and
> > of primitive permutation groups (and any other group library you wish to comment on)
> > as regards to any possible changes wihen changes are made in GAP. In particular,
> > were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> > within the library fixed in perpetuity when the library was initially made available in GAP4,
> > and if not, what is the mechanism to alert users to any changes? This is important
> > for being able to repeat, check, report on, and extend results made using specific
> > groups in a given library.
>
> We guarantee the following for the most prominent group libraries. (Guarantees are not exactly the same, as the construction processes differ).
>
> - In the library of small groups, the numbering of isomorphism types is guaranteed to be stable. Actual group generators, or the PC presentations used could theoretically change (though there is no intention to do so, unless it would reflect a deeper mathematical understanding, and if this happened I'd expect an explicit announcement in the release notes.)
>
> - In the library of transitive groups, the actual permutation groups (but not the generators used) are guaranteed to be stable. So you could refer to a particular point set and a particular group in a combinatorial construction.
>
> - The *old* library of primitive groups had in fact an unstable numbering, dependent on the implementation of the subgroup lattice algorithm. This library was therefore retired with the release of GAP 4.2.
>
> - The *new* library of primitive groups, release with GAP 4.2, guarantees a stable numbering (which for degree up to 50 is compatible with lists published in the literature), but does not guarantee a fixed S_n representative or particular generators.
>
> (To the best of my knowledge the numbering of groups is compatible with other systems that provide such libraries.)
Magma has the same numbering for the small groups and transitive groups
databases, but a completely different numbering for the primitive groups.
I believe that the divergence resulted originally as a result of errors
(missing groups) in the old list, which were rectified in different ways.
It seems very unlikely indeed that there are errors in either the small groups
or the transitive groups databases, because they have been independently
checked, but I guess that if a mistake were to be found then that might
force a chage in numbering.
Derek.
> There is no mechanism for explicitly alerting users of changes in the non-guaranteed properties. A change in the guaranteed properties would presumably mean that the library was retired and replaced with a new library.
>
> Needless to say, any such promises are only worth as much as the promiser, as anyone who endowed a chantry before 1545 can tell you.
>
> Best,
>
> Alexander
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From pjc at mcs.st-andrews.ac.uk Thu Jan 29 10:47:46 2015
From: pjc at mcs.st-andrews.ac.uk (Peter Cameron)
Date: Thu, 29 Jan 2015 10:47:46 -0000 (UTC)
Subject: [GAP Forum] The stability of group libraries
In-Reply-To: <1422452294146.69150@qmul.ac.uk>
References: <1422452294146.69150@qmul.ac.uk>
Message-ID:
Just a brief addendum to Alexander's comment.
?kos Seress, Primitive groups with no regular orbits on the set of
subsets, Bull. London Math. Soc. 29 (1997), 697-704, identifies primitive
groups by their (old) GAP numbers. It is now a bit of work to match them
with the new numbers.
In cases like this where the numbering changes, for whatever reason, I
think it is important to have a mechanism to match old numbers to new.
Peter.
> Dear GAP Developers, Dear GAP-Forum,
>
> I would like to know what the policy is concerning the groups
> in the the very useful GAP libraries of transitive permutation groups and
> of primitive permutation groups (and any other group library you wish to
> comment on)
> as regards to any possible changes wihen changes are made in GAP. In
> particular,
> were the actual groups in the library, their GeneratorsOfGroup, and their
> indexing
> within the library fixed in perpetuity when the library was initially made
> available in GAP4,
> and if not, what is the mechanism to alert users to any changes? This is
> important
> for being able to repeat, check, report on, and extend results made using
> specific
> groups in a given library.
>
> Thank you for your help,
> Leonard
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
--
This email address will stop working sometime soon. Please use the address
pjc20 at st-andrews.ac.uk instead.
From hulpke at fastmail.fm Fri Jan 30 16:41:40 2015
From: hulpke at fastmail.fm (Alexander Hulpke)
Date: Fri, 30 Jan 2015 09:41:40 -0700
Subject: [GAP Forum] The stability of group libraries
In-Reply-To:
References: <1422452294146.69150@qmul.ac.uk>
Message-ID: <948B2B69-C338-4EC2-BCA8-CEFCD18C0559@fastmail.fm>
Dear Peter, Dear Forum,
> Just a brief addendum to Alexander's comment.
>
> ?kos Seress, Primitive groups with no regular orbits on the set of
> subsets, Bull. London Math. Soc. 29 (1997), 697-704, identifies primitive
> groups by their (old) GAP numbers. It is now a bit of work to match them
> with the new numbers.
>
> In cases like this where the numbering changes, for whatever reason, I
> think it is important to have a mechanism to match old numbers to new.
I could not sympathize more with this. The problem with the primitive groups library before 4.2 was that in some cases (basically if the socle is not simple), the arrangement of the primitive groups depended on a subgroup lattice computation (the intention had been to save storage), which in turn might have depended on the setting of the random number generator. That is, in two different sessions of the same release, `PrimitiveGroup' might have given different (nonisomorphic) groups for the same number.
This problem was the reason for changing the library. While in many cases the group numbering never changed (the intention was to make the numbering stable, not to relabel for the sake of it), it is hard to specify what did not change or to give a translation list.
The only range of degrees, for which I dare to make a promise about what changed or give a translation list, is the groups of degree up to 50. These always agreed with the lists by Sims, as well as the published version by Buekenhout/Leemans. (This incidentally includes all groups that occur in ?kos' paper you refer to.)
All the best,
Alexander
From goetz.pfeiffer at nuigalway.ie Thu Feb 5 15:23:15 2015
From: goetz.pfeiffer at nuigalway.ie (Goetz Pfeiffer)
Date: Thu, 5 Feb 2015 15:23:15 +0000
Subject: [GAP Forum] subgroups lattices of simple groups
In-Reply-To: <1152961621.836980.1422295953749.JavaMail.yahoo@mail.yahoo.com>
References: <1152961621.836980.1422295953749.JavaMail.yahoo@mail.yahoo.com>
Message-ID: <54D38AE3.5000705@nuigalway.ie>
Dear S?bastien, dear Forum,
An alternative source of information on subgroup
lattices, or more precisely the poset of conjugacy
classes of subgroups, of certain finite groups of
modest size is GAP's library of tables of marks
(http://schmidt.nuigalway.ie/tomlib), currently
maintained by Liam Naughton.
Goetz Pfeiffer
On 26/01/15 18:12, Palcoux Sebastien wrote:
> Hi Forum,
> Is it possible to access at the Atlas of subgroup lattices of finite almost simple groups (of Thomas Connor and Dimitri Leemans) with GAP?Is there a package?
> Best regards,S?bastien
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>
--
------------------------------------------------------------------------
goetz.pfeiffer at nuigalway.ie http://schmidt.nuigalway.ie/~goetz
Mathematics, NUI Galway, Ireland. phone +353-91-49-3591
From s.murthy at mykolab.com Wed Feb 11 14:05:31 2015
From: s.murthy at mykolab.com (Sandeep Murthy)
Date: Wed, 11 Feb 2015 14:05:31 +0000
Subject: [GAP Forum] Serialisation
Message-ID: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Hi
I am trying to use the IO_PickleToString() method from the SCSCP package
to test out how GAP serialises group objects. This does not appear to be
working as expected on the isomorphic groups Sym(3) and D_6 (dihedral group).
gap> IO_PickleToString( SymmetricGroup( 3 ) );
"PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
This looks OK but for D_6 it fails:
gap> IO_PickleToString( DihedralGroup( 6 ) );
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `IO_Pickle' on 2 arguments called from
IO_Pickle( s, obj ); called from
( )
called from read-eval loop at line 20 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>
Why is this? Both should return OpenMath strings.
Sandeep
From steve.linton at st-andrews.ac.uk Wed Feb 11 14:15:09 2015
From: steve.linton at st-andrews.ac.uk (Stephen Linton)
Date: Wed, 11 Feb 2015 14:15:09 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID:
Dear GAP Forum,
> On 11 Feb 2015, at 14:05, Sandeep Murthy wrote:
>
> Hi
>
> I am trying to use the IO_PickleToString() method from the SCSCP package
> to test out how GAP serialises group objects. This does not appear to be
> working as expected on the isomorphic groups Sym(3) and D_6 (dihedral group).
>
> gap> IO_PickleToString( SymmetricGroup( 3 ) );
> "PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>
> This looks OK but for D_6 it fails:
>
> gap> IO_PickleToString( DihedralGroup( 6 ) );
> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
> Error, no 1st choice method found for `IO_Pickle' on 2 arguments called from
> IO_Pickle( s, obj ); called from
> ( )
> called from read-eval loop at line 20 of *stdin*
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
> brk>
>
> Why is this? Both should return OpenMath strings.
>
> Sandeep
The difference is that DihedralGroup(6) does NOT, by default, return a permutation group.
gap> DihedralGroup(6);
There is currently no pickling method for pc groups.
You can ask GAP for D_6 as a permutation group:
gap> DihedralGroup(IsPermGroup, 6);
Group([ (1,2,3), (2,3) ])
IO_PickleToString should work for this group.
As an aside the outputs of IO_PickleToString are NOT OpenMath. The IO_Pickle functions use their own format which only they can reliably read.
Steve
From caj21 at st-andrews.ac.uk Wed Feb 11 14:17:51 2015
From: caj21 at st-andrews.ac.uk (Christopher Jefferson)
Date: Wed, 11 Feb 2015 14:17:51 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID:
IO_PickleToString comes from the IO package, rather than the SCSCP package.
IO's Pickle provides a different set of methods to serialise GAP objects,
which tend to be smaller and faster to parse/unparse than openmath, but as
you saw do not implement all types.
If you want to use open math, then use the 'OM' methods:
gap> OMPrint(SymmetricGroup(3));
23121
gap> OMPrint(DihedralGroup(6));
256
On 11/02/2015 14:05, "Sandeep Murthy" wrote:
>Hi
>
>I am trying to use the IO_PickleToString() method from the SCSCP package
>to test out how GAP serialises group objects. This does not appear to be
>working as expected on the isomorphic groups Sym(3) and D_6 (dihedral
>group).
>
>gap> IO_PickleToString( SymmetricGroup( 3 ) );
>"PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>
>This looks OK but for D_6 it fails:
>
>gap> IO_PickleToString( DihedralGroup( 6 ) );
>Error, no method found! For debugging hints type ?Recovery from
>NoMethodFound
>Error, no 1st choice method found for `IO_Pickle' on 2 arguments called
>from
>IO_Pickle( s, obj ); called from
>( )
> called from read-eval loop at line 20 of *stdin*
>you can 'quit;' to quit to outer loop, or
>you can 'return;' to continue
>brk>
>
>Why is this? Both should return OpenMath strings.
>
>Sandeep
From s.murthy at mykolab.com Wed Feb 11 14:28:20 2015
From: s.murthy at mykolab.com (Sandeep Murthy)
Date: Wed, 11 Feb 2015 14:28:20 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To:
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID:
Thanks for the information.
But it seems SCSCP.IO_PickleToString calls IO.IO_Pickle() according to this page
http://www.gap-system.org/Manuals/pkg/scscp/doc/chap9.html#X84F055ED860120D5
and the description of the string output is that it is in ""pickled" format as OpenMath strings?.
I don?t need OM output, it?s just important that it is a compact string output that
can be used to reconstruct the object if necessary.
This serial ID is part of a JSON record I am writing to a data file for a given group in the
small groups library. Which method do I use to get the permutation group form of any
given group in this library?
Sandeep Murthy
s.murthy at mykolab.com
> On 11 Feb 2015, at 14:17, Christopher Jefferson wrote:
>
> IO_PickleToString comes from the IO package, rather than the SCSCP package.
>
> IO's Pickle provides a different set of methods to serialise GAP objects,
> which tend to be smaller and faster to parse/unparse than openmath, but as
> you saw do not implement all types.
>
> If you want to use open math, then use the 'OM' methods:
>
> gap> OMPrint(SymmetricGroup(3));
>
>
>
>
>
>
> 2
> 3
> 1
>
>
>
> 2
> 1
>
>
>
> gap> OMPrint(DihedralGroup(6));
>
>
>
> 25
> 6
>
>
>
>
>
>
> On 11/02/2015 14:05, "Sandeep Murthy" wrote:
>
>> Hi
>>
>> I am trying to use the IO_PickleToString() method from the SCSCP package
>> to test out how GAP serialises group objects. This does not appear to be
>> working as expected on the isomorphic groups Sym(3) and D_6 (dihedral
>> group).
>>
>> gap> IO_PickleToString( SymmetricGroup( 3 ) );
>> "PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>>
>> This looks OK but for D_6 it fails:
>>
>> gap> IO_PickleToString( DihedralGroup( 6 ) );
>> Error, no method found! For debugging hints type ?Recovery from
>> NoMethodFound
>> Error, no 1st choice method found for `IO_Pickle' on 2 arguments called
>> from
>> IO_Pickle( s, obj ); called from
>> ( )
>> called from read-eval loop at line 20 of *stdin*
>> you can 'quit;' to quit to outer loop, or
>> you can 'return;' to continue
>> brk>
>>
>> Why is this? Both should return OpenMath strings.
>>
>> Sandeep
>
From s.murthy at mykolab.com Wed Feb 11 14:29:24 2015
From: s.murthy at mykolab.com (Sandeep Murthy)
Date: Wed, 11 Feb 2015 14:29:24 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To:
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID: <9017E73B-C698-4ACC-995B-9200184DE4C2@mykolab.com>
Thanks for the information.
But it seems SCSCP.IO_PickleToString calls IO.IO_Pickle() according to this page
http://www.gap-system.org/Manuals/pkg/scscp/doc/chap9.html#X84F055ED860120D5
and the description of the string output is that it is in ""pickled" format as OpenMath strings?.
I don?t need OM output, it?s just important that it is a compact string output that
can be used to reconstruct the object if necessary.
This serial ID is part of a JSON record I am writing to a data file for a given group in the
small groups library. Which method do I use to get the permutation group form of any
given group in this library?
Sandeep Murthy
s.murthy at mykolab.com
> On 11 Feb 2015, at 14:17, Christopher Jefferson wrote:
>
> IO_PickleToString comes from the IO package, rather than the SCSCP package.
>
> IO's Pickle provides a different set of methods to serialise GAP objects,
> which tend to be smaller and faster to parse/unparse than openmath, but as
> you saw do not implement all types.
>
> If you want to use open math, then use the 'OM' methods:
>
> gap> OMPrint(SymmetricGroup(3));
>
>
>
>
>
>
> 2
> 3
> 1
>
>
>
> 2
> 1
>
>
>
> gap> OMPrint(DihedralGroup(6));
>
>
>
> 25
> 6
>
>
>
>
>
>
> On 11/02/2015 14:05, "Sandeep Murthy" wrote:
>
>> Hi
>>
>> I am trying to use the IO_PickleToString() method from the SCSCP package
>> to test out how GAP serialises group objects. This does not appear to be
>> working as expected on the isomorphic groups Sym(3) and D_6 (dihedral
>> group).
>>
>> gap> IO_PickleToString( SymmetricGroup( 3 ) );
>> "PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>>
>> This looks OK but for D_6 it fails:
>>
>> gap> IO_PickleToString( DihedralGroup( 6 ) );
>> Error, no method found! For debugging hints type ?Recovery from
>> NoMethodFound
>> Error, no 1st choice method found for `IO_Pickle' on 2 arguments called
>> from
>> IO_Pickle( s, obj ); called from
>> ( )
>> called from read-eval loop at line 20 of *stdin*
>> you can 'quit;' to quit to outer loop, or
>> you can 'return;' to continue
>> brk>
>>
>> Why is this? Both should return OpenMath strings.
>>
>> Sandeep
>
From alexk at mcs.st-andrews.ac.uk Thu Feb 12 23:42:36 2015
From: alexk at mcs.st-andrews.ac.uk (Alexander Konovalov)
Date: Thu, 12 Feb 2015 23:42:36 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID:
Hi Sandeep,
As it was already noted here, the cause of the problem is that one of
these two groups is a permutation group and the other - pc group. The
GAP manual has a section "Saving a Pc Group" which may help you:
http://www.gap-system.org/Manuals/doc/ref/chap46.html#X85696AB9791DF047
- see GapInputPcGroup there.
Also, for pc groups you may use the pair of functions CodePcGroup and
PcGroupCode, see them here:
http://www.gap-system.org/Manuals/doc/ref/chap46.html#X8041C2D88721EEA9
These were invented to store large libraries of small groups, and for
really huge groups, they will may work slow. However, GapInputPcGroup
performs quite well - I've found the log file for a group of order 3^728
which I was saving several years ago. The group was saved in 9 seconds
and restored in 12 seconds, and the file size was "only" 6.5 MB (gzipped
- 1.5 MB):
gap> PrintTo( "save", GapInputPcGroup( V, "V729_13" ) );
gap> time;
9217
gap> Read("save");
#I A group of order
2209395351413957253683909547381599161963288912918954731542644224734870827044293093746906\
7135836134418530028589701635375804525993982486739360716170312948236428294558462634156750\
2928525358477130679078983517688062896651637532904132693253013488158239242149787728540685\
561563573806847600207803782218928387605966850445847423444996735145737566710612948961
has been defined.
#I It is called V729_13
gap> time;
12154
gap>
Hope this helps,
Alexander
On 11 Feb 2015, at 14:05, Sandeep Murthy wrote:
> Hi
>
> I am trying to use the IO_PickleToString() method from the SCSCP package
> to test out how GAP serialises group objects. This does not appear to be
> working as expected on the isomorphic groups Sym(3) and D_6 (dihedral group).
>
> gap> IO_PickleToString( SymmetricGroup( 3 ) );
> "PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>
> This looks OK but for D_6 it fails:
>
> gap> IO_PickleToString( DihedralGroup( 6 ) );
> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
> Error, no 1st choice method found for `IO_Pickle' on 2 arguments called from
> IO_Pickle( s, obj ); called from
> ( )
> called from read-eval loop at line 20 of *stdin*
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
> brk>
>
> Why is this? Both should return OpenMath strings.
>
> Sandeep
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
From s.murthy at mykolab.com Fri Feb 13 00:38:16 2015
From: s.murthy at mykolab.com (Sandeep Murthy)
Date: Fri, 13 Feb 2015 00:38:16 +0000
Subject: [GAP Forum] Serialisation
In-Reply-To:
References: <824C2FBD-BCFF-4A28-B483-123CF30705D8@mykolab.com>
Message-ID:
Thanks.
Sandeep Murthy
s.murthy at mykolab.com
> On 12 Feb 2015, at 23:42, Alexander Konovalov wrote:
>
> Hi Sandeep,
>
> As it was already noted here, the cause of the problem is that one of
> these two groups is a permutation group and the other - pc group. The
> GAP manual has a section "Saving a Pc Group" which may help you:
>
> http://www.gap-system.org/Manuals/doc/ref/chap46.html#X85696AB9791DF047
>
> - see GapInputPcGroup there.
>
> Also, for pc groups you may use the pair of functions CodePcGroup and
> PcGroupCode, see them here:
>
> http://www.gap-system.org/Manuals/doc/ref/chap46.html#X8041C2D88721EEA9
>
> These were invented to store large libraries of small groups, and for
> really huge groups, they will may work slow. However, GapInputPcGroup
> performs quite well - I've found the log file for a group of order 3^728
> which I was saving several years ago. The group was saved in 9 seconds
> and restored in 12 seconds, and the file size was "only" 6.5 MB (gzipped
> - 1.5 MB):
>
> gap> PrintTo( "save", GapInputPcGroup( V, "V729_13" ) );
> gap> time;
> 9217
> gap> Read("save");
> #I A group of order
> 2209395351413957253683909547381599161963288912918954731542644224734870827044293093746906\
> 7135836134418530028589701635375804525993982486739360716170312948236428294558462634156750\
> 2928525358477130679078983517688062896651637532904132693253013488158239242149787728540685\
> 561563573806847600207803782218928387605966850445847423444996735145737566710612948961
> has been defined.
> #I It is called V729_13
> gap> time;
> 12154
> gap>
>
> Hope this helps,
> Alexander
>
>
>
> On 11 Feb 2015, at 14:05, Sandeep Murthy wrote:
>
>> Hi
>>
>> I am trying to use the IO_PickleToString() method from the SCSCP package
>> to test out how GAP serialises group objects. This does not appear to be
>> working as expected on the isomorphic groups Sym(3) and D_6 (dihedral group).
>>
>> gap> IO_PickleToString( SymmetricGroup( 3 ) );
>> "PRMGILIS\>2PERM\>7(1,2,3)PERM\>5(1,2)INTG\>16FAIL?
>>
>> This looks OK but for D_6 it fails:
>>
>> gap> IO_PickleToString( DihedralGroup( 6 ) );
>> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
>> Error, no 1st choice method found for `IO_Pickle' on 2 arguments called from
>> IO_Pickle( s, obj ); called from
>> ( )
>> called from read-eval loop at line 20 of *stdin*
>> you can 'quit;' to quit to outer loop, or
>> you can 'return;' to continue
>> brk>
>>
>> Why is this? Both should return OpenMath strings.
>>
>> Sandeep
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>
From matan at svgalib.org Fri Feb 13 22:25:34 2015
From: matan at svgalib.org (Matan Ziv-Av)
Date: Sat, 14 Feb 2015 00:25:34 +0200 (IST)
Subject: [GAP Forum] Performance degradation of LookupDictionary() for
partitions between 4.7.2 and 4.7.6
Message-ID:
Hello,
there seems to be a decrease in the performance of LookupDictionary(),
at least for partitions. A simple example is below:
In 4.7.6:
gap> d:=NewDictionary([[1],[2..10]],true);