From graham.ellis at nuigalway.ie Fri Jan 4 11:45:22 2019
From: graham.ellis at nuigalway.ie (Ellis, Grahamj)
Date: Fri, 4 Jan 2019 11:45:22 +0000
Subject: [GAP Forum] Second announcement: Cohomology of Arithmetic Groups,
Lattices and Number Theory
In-Reply-To:
References: ,
,
Message-ID:
Dear all,
I'd like to draw your attention to the following conference which will take place at the Centre International de Rencontres Math?matiques, Luminy at the end of March.
TITLE: Cohomology of Arithmetic Groups, Lattices and Number Theory: Geometric and Computational Viewpoint
DATES: 25 - 29 March 2019
PARTICIPANTS: 90 (max)
SPEAKERS: 27
URL: https://conferences.cirm-math.fr/1995.html
This CIRM conference will bring together international experts with diverse skill sets relevant to calculations and applications in the cohomology of arithmetic groups, algebraic K-theory, arithmetic geometry, and lattices. The main goals are to foster new collaborations, to introduce young researchers to these topics, and to broaden our theoretical knowledge with a view to extending the scope of computer aided calculations in this area. (See CIRM URL for more details.)
If you are interested in participating please could you contact one of the organizers and/or submit a pre-registration at http://www.cirm-math.fr/preRegistration/index.php?EX=menu0&id_renc=1995.
Best wishes,
Graham
on behalf of the organizers:
Eva Bayer, Philippe Elbaz-Vincent, Graham Ellis, Paul Gunnells
From alexander.konovalov at st-andrews.ac.uk Mon Jan 7 21:58:58 2019
From: alexander.konovalov at st-andrews.ac.uk (Alexander Konovalov)
Date: Mon, 7 Jan 2019 21:58:58 +0000
Subject: [GAP Forum] lpres package acceptance
Message-ID:
Dear GAP Forum,
It is a pleasure to announce the official acceptance of the GAP
package lpres developed by Ren? Hartung and maintained by
Laurent Bartholdi.
The lpres package defines new GAP objects to work with L-presented
groups, namely groups given by a finite generating set and a
possibly-infinite set of relations given as iterates of finitely
many seed relations by a finite set of endomorphisms. The package
implements nilpotent quotient, Todd-Coxeter and Reidemeister-Schreier
algorithms for L-presented groups.
The lpres package has been already redistributed with GAP since its
version 0.4.1 included in GAP 4.8.7 distribution (March 2017). The
version that has been accepted is lpres 1.0.0, included in GAP 4.10.0
distribution (November 2018). The lpres package is the successor of
the GAP package NQL by Ren? Hartung that has been accepted and
redistributed with GAP 4.4 and has been withdrawn since GAP 4.5. We
are grateful to Ren? Hartung and Laurent Bartholdi for these
contributions, and very pleased to see that the revised functionality
from the NQL package is now available again to the users of the
latest GAP release.
For further information about the package, see its website at
https://gap-packages.github.io/lpres/. The source code is hosted
on GitHub at https://github.com/gap-packages/lpres. For suggestions,
feature requests and bug reports, please use the issue tracker at
https://github.com/gap-packages/lpres/issues.
Best regards
Alexander
From cagmanz at hotmail.com Wed Jan 9 18:27:55 2019
From: cagmanz at hotmail.com (=?iso-8859-9?Q?Abdullah_=C7A=D0MAN?=)
Date: Wed, 9 Jan 2019 18:27:55 +0000
Subject: [GAP Forum] testing equality of infinite ideals
Message-ID:
Dear forum members,
Is there any way to testing equality of ideals with infinite elements in a polynomial ring (For example, the ideals <2*x> and <3*x> in the polynomial ring Z_6[x]).
Regards..
Abdullah ?a?man
From ghorvath at science.unideb.hu Wed Jan 9 21:05:39 2019
From: ghorvath at science.unideb.hu (Horvath Gabor)
Date: Wed, 9 Jan 2019 22:05:39 +0100 (CET)
Subject: [GAP Forum] testing equality of infinite ideals
In-Reply-To:
References:
Message-ID:
Dear Abdullah,
I believe SINGULAR is the program best suited for comparing ideals in
rings:
https://www.singular.uni-kl.de/
Best,
Gabor
On Wed, 9 Jan 2019, Abdullah ?A?MAN wrote:
> Dear forum members,
>
> Is there any way to testing equality of ideals with infinite elements in a polynomial ring (For example, the ideals <2*x> and <3*x> in the polynomial ring Z_6[x]).
>
>
> Regards..
>
>
> Abdullah ?a?man
>
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
>
Horvath Gabor
-------------------------------------------------------------------------------
e-mail: ghorvath at science.unideb.hu
phone: +36 52 512900 / 22798
web: http://www.math.unideb.hu/horvath-gabor
From markus.pfeiffer at st-andrews.ac.uk Fri Jan 11 11:12:22 2019
From: markus.pfeiffer at st-andrews.ac.uk (Markus Pfeiffer)
Date: Fri, 11 Jan 2019 11:12:22 +0000
Subject: [GAP Forum] 2nd Announcement - GAP Days Spring 2019 - Modern
Permutation Group Algorithms - Halle (Saale) Germany
Message-ID: <86lg3rphwv.fsf@st-andrews.ac.uk>
Dear all,
We warmly invite you to the beautiful Halle an der Saale in
Germany for the 9^{th} GAP Days, which will take place
from 18th-22nd March 2019. Registration is open at:
https://www.gapdays.de/gapdays2019-spring/registration
We have set aside a small number of hotel rooms for participants
of the GAP Days, **available until 2nd February**, at the TRYP by
Wyndham Halle. Instructions on how to make use of this offer are
available on the registration page.
The theme of this GAP Days will be ?Modern Permutation Group
Algorithms?. During this GAP Days, we aim to survey, understand,
and develop the algorithmic infrastructure for permutation groups
in GAP. To support these aims, we will begin by spending the first
day reviewing and discussing the current functionality in GAP for
permutations and permutation groups, beginning with the way
permutations are stored and the basic orbit-stabiliser algorithms,
and identifying areas in the code and documentation for
improvement as we proceed.
We will also include a small number of additional talks during the
GAP Days about computing with permutation groups in GAP. If there
is a particular topic in this area that you would like to hear a
talk about, then please include details in the comment box at
registration.
We would like this GAP Days to be an opportunity for all
interested people with little knowledge of the insides of GAP to
join in: this includes undergraduate students, PhD students,
post-docs, and more experienced mathematicians. You will be able
to meet us and each other, and learn about GAP development and
algorithmic group theory in a relaxed and friendly atmosphere.
More information about GAP Days Spring 2019 is available on the
website:
https://www.gapdays.de/gapdays2019-spring
If you have any questions, or doubts about whether this event is
for you, then please feel free to contact us by email at
gapdays2019-spring at gapdays.de
We hope to see you in Halle!
Chris, Markus, Rebecca, and Wilf
From marek at mitros.org Fri Jan 11 12:17:42 2019
From: marek at mitros.org (Marek Mitros)
Date: Fri, 11 Jan 2019 13:17:42 +0100
Subject: [GAP Forum] Group from octonion elements
Message-ID:
Hi,
I have defined octonions over field
o:=OctaveAlgebra(GF(7));
Next create set of some invertible elements belonging to some subalgebra.
And I wanted to see what group is generated by invertible elements in this
subalgebra. Unfortunately I cannot use "Group" function, because I obtain
error "no groups of cyclotomics allowed because of incomatible ^". I am
using GAP version 4.8.8. This subalgebra is associative, because it is
generated by two elements. Therefore invertible elements should form a
group. Do you have any advice or workaround how could I test my group ? I
wanted to use StructureDescription. These are small groups of size
294,336,392 and 686.
gap> g1:=Group([1..5],k->Random(c1i));
#I no groups of cyclotomics allowed because of incompatible ^
Error, usage: Group(,...), Group(), Group(,) called
from
( )
called from read-eval loop at line 74 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
Regards,
Marek
From sl4 at st-andrews.ac.uk Fri Jan 11 13:34:58 2019
From: sl4 at st-andrews.ac.uk (Stephen Linton)
Date: Fri, 11 Jan 2019 13:34:58 +0000
Subject: [GAP Forum] Group from octonion elements
In-Reply-To:
References:
Message-ID: <86153ADE-7852-4364-86AC-29FBE4FFD4E2@st-andrews.ac.uk>
> On 11 Jan 2019, at 12:17, Marek Mitros wrote:
>
> Hi,
>
> I have defined octonions over field
> o:=OctaveAlgebra(GF(7));
>
> Next create set of some invertible elements belonging to some subalgebra.
> And I wanted to see what group is generated by invertible elements in this
> subalgebra. Unfortunately I cannot use "Group" function, because I obtain
> error "no groups of cyclotomics allowed because of incomatible ^". I am
> using GAP version 4.8.8. This subalgebra is associative, because it is
> generated by two elements. Therefore invertible elements should form a
> group. Do you have any advice or workaround how could I test my group ? I
> wanted to use StructureDescription. These are small groups of size
> 294,336,392 and 686.
>
> gap> g1:=Group([1..5],k->Random(c1i));
I think your problem is in this line. Group doesn?t work like that. Try
Group(List([1..5]?.))
Steve
> #I no groups of cyclotomics allowed because of incompatible ^
> Error, usage: Group(,...), Group(), Group(,) called
> from
> ( )
> called from read-eval loop at line 74 of *stdin*
> you can 'quit;' to quit to outer loop, or
> you can 'return;' to continue
> brk> quit;
>
> Regards,
> Marek
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
From marek at mitros.org Fri Jan 11 14:20:21 2019
From: marek at mitros.org (Marek Mitros)
Date: Fri, 11 Jan 2019 15:20:21 +0100
Subject: [GAP Forum] Group from octonion elements
In-Reply-To: <86153ADE-7852-4364-86AC-29FBE4FFD4E2@st-andrews.ac.uk>
References:
<86153ADE-7852-4364-86AC-29FBE4FFD4E2@st-andrews.ac.uk>
Message-ID:
Indeed ! Thank you !! Sorry, it was my mistake :(
Regards,
Marek
pt., 11 sty 2019 o 14:35 Stephen Linton napisa?(a):
>
>
> > On 11 Jan 2019, at 12:17, Marek Mitros wrote:
> >
> > Hi,
> >
> > I have defined octonions over field
> > o:=OctaveAlgebra(GF(7));
> >
> > Next create set of some invertible elements belonging to some subalgebra.
> > And I wanted to see what group is generated by invertible elements in
> this
> > subalgebra. Unfortunately I cannot use "Group" function, because I obtain
> > error "no groups of cyclotomics allowed because of incomatible ^". I am
> > using GAP version 4.8.8. This subalgebra is associative, because it is
> > generated by two elements. Therefore invertible elements should form a
> > group. Do you have any advice or workaround how could I test my group ? I
> > wanted to use StructureDescription. These are small groups of size
> > 294,336,392 and 686.
> >
> > gap> g1:=Group([1..5],k->Random(c1i));
>
> I think your problem is in this line. Group doesn?t work like that. Try
> Group(List([1..5]?.))
>
> Steve
>
> > #I no groups of cyclotomics allowed because of incompatible ^
> > Error, usage: Group(,...), Group(), Group(,) called
> > from
> > ( )
> > called from read-eval loop at line 74 of *stdin*
> > you can 'quit;' to quit to outer loop, or
> > you can 'return;' to continue
> > brk> quit;
> >
> > Regards,
> > Marek
> > _______________________________________________
> > Forum mailing list
> > Forum at gap-system.org
> > https://mail.gap-system.org/mailman/listinfo/forum
>
>
From oxeimon at gmail.com Tue Jan 15 22:26:53 2019
From: oxeimon at gmail.com (Will Chen)
Date: Tue, 15 Jan 2019 17:26:53 -0500
Subject: [GAP Forum] Is there a way to teach GAP that a particular map is
injective or surjective?
Message-ID:
Dear Forum,
Suppose I have two groups G, H, and a homomorphism f : G --> H, defined
using "GroupHomomorphismByImages".
Suppose I know that f is surjective, and that moreover there is a
generating set X of H for which I can provide explicit preimages in G.
Is there a way of giving GAP this information?
Ie, in my situation, trying to call the PreImage operation on f sometimes
takes over 5 minutes (at which point I opted to break), but presumably if I
can give GAP explicit preimages for generators, it can then decompose every
element of H as a word in those generators, and use the explicit preimages
to find a preimage for that word.
If necessary, I'm happy to assume that G,H are finitely presented.
- Will
--
William Chen
NSF Postdoctoral Fellow, Department of Mathematics
McGill University,
Montreal, Quebec, H3A 0B9
oxeimon at gmail.com
From Alexander.Hulpke at colostate.edu Tue Jan 15 22:32:52 2019
From: Alexander.Hulpke at colostate.edu (Hulpke,Alexander)
Date: Tue, 15 Jan 2019 22:32:52 +0000
Subject: [GAP Forum] Is there a way to teach GAP that a particular map
is injective or surjective?
In-Reply-To:
References:
Message-ID:
Dear Forum,
> On Jan 15, 2019, at 3:26 PM, Will Chen wrote:
>
> Dear Forum,
>
> Suppose I have two groups G, H, and a homomorphism f : G --> H, defined
> using "GroupHomomorphismByImages".
>
> Suppose I know that f is surjective, and that moreover there is a
> generating set X of H for which I can provide explicit preimages in G.
>
> Is there a way of giving GAP this information?
You can use
SetIsInjective(map,true) and SetIsSurjective(map,true).
You also might want to use PreImagesRepresentative instead of PreImage.
Then is f is given on pre-images of X with image set X, and H is finitely presented, GAP should be able to calculate such pre-images for arbitrary elements.
All the best,
Alexander Hulpke
From kurt.ewald at balbec.de Thu Jan 17 16:25:01 2019
From: kurt.ewald at balbec.de (kurt.ewald at balbec.de)
Date: Thu, 17 Jan 2019 17:25:01 +0100
Subject: [GAP Forum] Question
Message-ID: <064701d4ae81$32b5daa0$98218fe0$@balbec.de>
Hallo,
I want to get the definition of the
FrobeniusGroup and the Kernel and Component
of the SymetricGroup(3)
Thanks
Kurt Ewald
From pbrooksb at bucknell.edu Thu Feb 7 03:16:46 2019
From: pbrooksb at bucknell.edu (Peter Brooksbank)
Date: Thu, 7 Feb 2019 03:16:46 +0000
Subject: [GAP Forum] Workshop on Tensors (2nd Announcement)
Message-ID:
Dear colleagues,
The Department of Mathematics at Colorado State University and the
Department of Computer Science at the University of Colorado, Boulder
invite interested participants to attend a workshop and conference on *Tensors:
Algebra, Computation, and Applications (TACA)*. The central theme of
tensors is meant to bring together several complementary research
areas??pure & applied mathematics, quantum physics, big data, scientific
computing, & theoretical computer science??whose interactions could lead to
breakthroughs.
The workshop will consist of:
- Mini-courses + group problem sessions (June 4?8, U. Colorado Boulder
Campus)
- Presentations of contemporary research and software demonstrations
(June 9-14, Colorado State University ?Pingree Park? Mountain Campus).
Further details about the mini-courses??drawn from the following
topics??will be included in our third announcement in early March:
- Foundations of algebraic computation
- Statistical analysis of tensor data
- Quantum computation
- Complexity of tensor computations and applications to Computational
Complexity
- Tensor equivalence and isomorphism testing in groups and algebras
We especially encourage graduate students and younger researchers to apply
to attend these workshops and subsequent joint problem sessions.
Researchers interested in attending mini courses and the conference should
fill out the following Google form if you have not already done so. (This
is still an informal expression of interest, not yet official
registration.)
https://docs.google.com/forms/d/e/1FAIpQLSfx4bngQZWUfX74Nb_pAv0GZUcVJ0JOYp9ImngbMz38P5ToWg/viewform?usp=sf_link
*Limited funds are available on a need basis to offset travel costs for
participants, and we are now accepting applications for such funding.*
We hope you can join us!
Best regards,
The Organizers
(Peter Brooksbank, Joshua Grochow, Alexander Hulpke, Youming Qiao, James
Wilson)
--
*Peter A. Brooksbank*
*Professor of Mathematics*
*Bucknell University*
From surinder.kaur at iitrpr.ac.in Sat Feb 9 07:43:26 2019
From: surinder.kaur at iitrpr.ac.in (Surinder Kaur)
Date: Sat, 9 Feb 2019 13:13:26 +0530
Subject: [GAP Forum] Normal subgroups of unit group of group algebra FD_8,
for the field F with 4 elements
Message-ID:
Dear all
Is there any way to get all the normal subgroups of the normalized unit
group V(FD_8), where FD_8 is the group ring of the dihedral group D_8 and F
is the field with 4 elements. I tried the following straight forward way
but it's not working.
g:=DihedralGroup(8);;
f:=GF(4);;
fg:=GroupRing(f,g);;
e:=Identity(fg);;
u:=Units(fg);;
h:=NormalSubgroups(u);;
Print(h, "\n");
--
*Regards*
*Surinder Kaur*
*Research scholar *
*Department of Mathematics *
*IIT Ropar*
From sk239 at st-andrews.ac.uk Sat Feb 9 11:15:30 2019
From: sk239 at st-andrews.ac.uk (Stefan Kohl)
Date: Sat, 9 Feb 2019 11:15:30 +0000
Subject: [GAP Forum] Normal subgroups of unit group of group algebra
FD_8, for the field F with 4 elements
In-Reply-To:
References:
Message-ID:
As far as I see, your group u is a 2-step nilpotent group of order 2^14 * 3, which suggests that it has quite a lot of normal subgroups. So you may need at least some patience, even if you convert the group into a pc group first in order to speed up the computation.
Best regards,
Stefan Kohl
________________________________
From: Surinder Kaur
Sent: Saturday, February 9, 2019 8:43:26 AM
To: forum at gap-system.org
Subject: [GAP Forum] Normal subgroups of unit group of group algebra FD_8, for the field F with 4 elements
Dear all
Is there any way to get all the normal subgroups of the normalized unit
group V(FD_8), where FD_8 is the group ring of the dihedral group D_8 and F
is the field with 4 elements. I tried the following straight forward way
but it's not working.
g:=DihedralGroup(8);;
f:=GF(4);;
fg:=GroupRing(f,g);;
e:=Identity(fg);;
u:=Units(fg);;
h:=NormalSubgroups(u);;
Print(h, "\n");
--
*Regards*
*Surinder Kaur*
*Research scholar *
*Department of Mathematics *
*IIT Ropar*
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
From heiko.dietrich at monash.edu Mon Feb 18 08:37:35 2019
From: heiko.dietrich at monash.edu (Heiko Dietrich)
Date: Mon, 18 Feb 2019 19:37:35 +1100
Subject: [GAP Forum] postdoc position at Monash University (Melbourne)
Message-ID:
Dear all,
I am currently advertising for a postdoc position at Monash University,
Melbourne, to work on an Australian Research Council project "Computing
with Lie groups and algebras: nilpotent orbits and applications" that is
led together by Willem de Graaf (University of Trento) and myself. The
position is for two years and we are looking for someone with a
research background in Lie theory (Lie algebras, Lie groups, algebraic
groups) and computational algebra (GAP or Magma).
More information, including details of how to apply can be found at
http://careers.pageuppeople.com/513/cw/en/job/588214/research-fellow-computational-lie-theory
Best wishes,
Heiko (and Willem)
--
Dr Heiko Dietrich
Senior Lecturer
School of Mathematical Sciences
Monash University VIC 3800
Australia
T: +61-3-9905-4771
E: heiko.dietrich at monash.edu
W: users.monash.edu/~heikod
From caj21 at st-andrews.ac.uk Tue Feb 19 14:40:38 2019
From: caj21 at st-andrews.ac.uk (Christopher Jefferson)
Date: Tue, 19 Feb 2019 14:40:38 +0000
Subject: [GAP Forum] 2 Year Postdoc Position - University of St Andrews,
Permutation Groups
Message-ID:
We are advertising a 2 year post at the University of St Andrews, looking at improving and overhauling many of the fundamental algorithms used for permutation groups, in particular stabilizer chains and base and strong generating sets.
If you have any questions about this post, please ask. This job will be part of a larger research group, and we are happy to work with people with different specialities. In particular, there is no need to be an expert GAP programmer.
Under Dr Christopher Jefferson, the role will involve the development of new algorithms for fundamental problems in computation group theory, in particular improved methods for finding, storing and modifying stabilizer chains and base and strong generating sets of permutation groups, This will also involve practical implementation and automated tuning of these algorithms. Therefore it is advantageous to have a background in the theory of permutation groups, computational group theory and algorithm design and implementation - Closes 13th March 2019.
https://www.jobs.ac.uk/job/BQE428/research-fellow-ar1696sb
From dk2572 at nyu.edu Mon Jan 28 15:10:05 2019
From: dk2572 at nyu.edu (Delaram Kahrobaei)
Date: Mon, 28 Jan 2019 15:10:05 -0000
Subject: [GAP Forum] PhD studentships at University of York (UK) on
Post-quantum Cryptography
Message-ID:
Dear all,
We are advertising for PhD studentships for non-EU/UK citizens at the
University of York (UK) on topics related to Post-quantum algebraic
cryptography.
The deadline is January 31, 2019. Please write Professor Kahrobaei as the
name of supervisor.
Interested students could apply here
For non-EU/UK citizens:
https://www.york.ac.uk/study/postgraduate-research/funding/international/ygrs/
For Chinese Nationals:
https://www.york.ac.uk/study/postgraduate-research/funding/china-scholarships/
Many thanks for helping spread the word,
With kind regards,
Delaram
--
Professor Delaram Kahrobaei
Chair of Cyber Security
Department of Computer Science (CSE 039)
University of York, U.K.
Professor of Computer Science (Adjunct)
New York University, U.S.A.
https://sites.google.com/a/nyu.edu/delaram-kahrobaei/
From alexander.konovalov at st-andrews.ac.uk Wed Feb 20 13:13:23 2019
From: alexander.konovalov at st-andrews.ac.uk (Alexander Konovalov)
Date: Wed, 20 Feb 2019 13:13:23 +0000
Subject: [GAP Forum] PhD studentships at University of York (UK)
on Post-quantum Cryptography
In-Reply-To:
References:
Message-ID:
The correct link seems to be
https://www.findaphd.com/phds/project/post-quantum-cryptography/?p104181
Alexander
> On 28 Jan 2019, at 15:09, Delaram Kahrobaei wrote:
>
> Dear all,
>
> We are advertising for PhD studentships for non-EU/UK citizens at the
> University of York (UK) on topics related to Post-quantum algebraic
> cryptography.
>
> The deadline is January 31, 2019. Please write Professor Kahrobaei as the
> name of supervisor.
>
> Interested students could apply here
>
> For non-EU/UK citizens:
> https://www.york.ac.uk/study/postgraduate-research/funding/international/ygrs/
>
> For Chinese Nationals:
> https://www.york.ac.uk/study/postgraduate-research/funding/china-scholarships/
>
>
> Many thanks for helping spread the word,
>
> With kind regards,
> Delaram
> --
> Professor Delaram Kahrobaei
> Chair of Cyber Security
> Department of Computer Science (CSE 039)
> University of York, U.K.
> Professor of Computer Science (Adjunct)
> New York University, U.S.A.
> https://sites.google.com/a/nyu.edu/delaram-kahrobaei/
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
--
Dr. Alexander Konovalov, Senior Research Fellow
Centre for Interdisciplinary Research in Computational Algebra (CIRCA)
School of Computer Science, University of St Andrews
Software Sustainability Institute Fellow
https://alexk.host.cs.st-andrews.ac.uk
--
The University of St Andrews is a charity registered in Scotland:No.SC013532
From shahmaths_problem at hotmail.com Thu Feb 21 10:22:38 2019
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Thu, 21 Feb 2019 10:22:38 +0000
Subject: [GAP Forum] How to define in GAP another binary operation on a
multiplication table
Message-ID:
Dear all,
Suppose I have a multiplication table of a group or a quasigroup say of C_5. I want to define a new binary operation on it say x O y= (x*c)*y where c is a fixed element. I would be thankful if someone writes a function for doing it. I have written the following one but it does not give me the desired result.
h:= CyclicGroup(IsPermGroup,5);
slist:=AsSortedList(h);
c:= slist[2];
l:=List(slist,a -> List(slist, b -> ((a * c) * b)));
q:=List(l,t -> List(t,p -> Position(slist,p)));
return QuasigroupByCayleyTable(TransposedMat(AsSortedList(q)));
Muhammad Shah
From shahmaths_problem at hotmail.com Thu Feb 21 10:29:09 2019
From: shahmaths_problem at hotmail.com (muhammad shah)
Date: Thu, 21 Feb 2019 10:29:09 +0000
Subject: [GAP Forum] How can I find all anti-automorphisms?
Message-ID:
Dear All,
How can I find all anti-automorphisms of a group and specially of a quasigroup in GAP. Is there any command for it?
I will be thankful.
Muhammad Shah
From oxeimon at gmail.com Fri Feb 22 20:58:29 2019
From: oxeimon at gmail.com (Will Chen)
Date: Fri, 22 Feb 2019 15:58:29 -0500
Subject: [GAP Forum] best way to work with modules under group rings
Message-ID:
Hi all,
Given a finite metabelian group G, let A be its abelianization, and G' be
its derived subgroup. I would like to get a handle on G' as an A-module.
I'm happy to work with either Z[A]-modules or (Z/n)[A]-modules.
For example, I would like to be able to:
1. Compute A-module generators for G'
2. Construct A-module homomorphisms between A-modules by specifying where
they send generators.
3. Compute kernels and images of A-module homomorphisms, as well as
constructing submodules and quotient modules...
4. Compute the groups of units of finite quotients of Z[A]...
What is the best way to do such things in GAP?
- Will
--
William Chen
NSF Postdoctoral Fellow, Department of Mathematics
McGill University,
Montreal, Quebec, H3A 0B9
oxeimon at gmail.com
From Alexander.Hulpke at colostate.edu Fri Feb 22 23:50:03 2019
From: Alexander.Hulpke at colostate.edu (Hulpke,Alexander)
Date: Fri, 22 Feb 2019 23:50:03 +0000
Subject: [GAP Forum] best way to work with modules under group rings
In-Reply-To:
References:
Message-ID: <0693E42A-A661-475F-BCF5-33030A76F5F1@colostate.edu>
Dear Forum, Dear Will,
For most cases, I would linearize the module and use matrix method to work with it.
In this world a module is given by matrices, describing the algebra generator's (or group generator's) action on the vector space, homomorphisms are simply matrices. There is a set of tools that goes under the name of `MeatAxe` that allows for irreducibility tests, module decompositions, homomorphism tests. Many of the operations have a prefix `MTX.`, this was intended to allow easy swap of multiple meataxe libraries (though this is not really used).
For example (I know its not metabelian, but just to illustrate), taking V4 as a module for S4:
gap> s4:=Group((1,2,3,4),(1,2));;
gap> v4:=Group((1,2)(3,4),(1,3)(2,4));
Group([ (1,2)(3,4), (1,3)(2,4) ])
gap> IsNormal(s4,v4);
true
gap> pcgs:=Pcgs(v4); # like a basis, allows decomposition
Pcgs([ (1,3)(2,4), (1,2)(3,4) ])
gap> ExponentsOfPcElement(pcgs,(1,4)(2,3));
[ 1, 1 ]
gap> mats:=LinearActionLayer(s4,pcgs); # matrix action of s4 generators
[ , ]
gap> mo:=GModuleByMats(mats,GF(2));
rec( IsOverFiniteField := true, dimension := 2, field := GF(2),
generators := [ ,
], isMTXModule := true )
gap> MTX.IsIrreducible(mo);
true
gap> MTX.Isomorphism(mo,MTX.DualModule(mo)); # isomorphism, given as matrix
[ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2) ] ]
# note: MTX.Isomorphism assumes the module is simple. There also is `MTX.IsomorphismModules` that allows for arbitrary modules.
Best,
Alexander
-- Alexander Hulpke, Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
On Feb 23, 2019, at 7:58 AM, Will Chen > wrote:
Hi all,
Given a finite metabelian group G, let A be its abelianization, and G' be
its derived subgroup. I would like to get a handle on G' as an A-module.
I'm happy to work with either Z[A]-modules or (Z/n)[A]-modules.
For example, I would like to be able to:
1. Compute A-module generators for G'
2. Construct A-module homomorphisms between A-modules by specifying where
they send generators.
3. Compute kernels and images of A-module homomorphisms, as well as
constructing submodules and quotient modules...
4. Compute the groups of units of finite quotients of Z[A]...
What is the best way to do such things in GAP?
- Will
--
William Chen
NSF Postdoctoral Fellow, Department of Mathematics
McGill University,
Montreal, Quebec, H3A 0B9
oxeimon at gmail.com
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
From johannes.hahn at uni-jena.de Mon Feb 25 23:01:15 2019
From: johannes.hahn at uni-jena.de (Johannes Hahn)
Date: Tue, 26 Feb 2019 00:01:15 +0100
Subject: [GAP Forum] Atoms of a boolean algebra of sets
Message-ID: <008e01d4cd5e$039c93c0$0ad5bb40$@uni-jena.de>
Dear forum,
Let?s say a have a list of subsets of a fixed finite set $\Omega$. Is there a nice and easy way to find the atoms of the Boolean algebra generated by these sets? Of course, I could implement this by hand, but it seems to me that something like this probably already exists and I simply had bad luck finding it.
A related question: Let?s say I have a list of partitions of $\Omega$ (i.e. a set of pairwise disjoint subsets that cover all of $\Omega$). Is there a nice and easy way to find the common refinement of all these partitions?
Best wishes
Johannes Hahn.
From sk239 at st-andrews.ac.uk Tue Feb 26 00:07:12 2019
From: sk239 at st-andrews.ac.uk (Stefan Kohl)
Date: Tue, 26 Feb 2019 00:07:12 +0000
Subject: [GAP Forum] Atoms of a boolean algebra of sets
In-Reply-To: <008e01d4cd5e$039c93c0$0ad5bb40$@uni-jena.de>
References: <008e01d4cd5e$039c93c0$0ad5bb40$@uni-jena.de>
Message-ID:
Dear Johannes,
As to your second question: I think it should be straightforward to adapt RCWA's internal function
'CommonRefinementOfPartitionsOfZ_NC' for this purpose. That function computes the common refinement of a set of partitions of the integers into finitely many residue classes:
#############################################################################
##
#F CommonRefinementOfPartitionsOfZ_NC( ) . . special case R = Z
##
InstallGlobalFunction( CommonRefinementOfPartitionsOfZ_NC,
function ( partitions )
local table, partition, mods, res, m,
pow, mj, r, i, j, k;
mods := List(partitions,P->List(P,Mod));
res := List(partitions,P->List(P,Residues));
m := Lcm(Concatenation(mods));
table := List([1..m],i->0);
pow := 1;
for i in [1..Length(partitions)] do
for j in [1..Length(partitions[i])] do
mj := mods[i][j];
for r in res[i][j] do
for k in [r,r+mj..r+(Int(m/mj)-1)*mj] do
table[k+1] := table[k+1] + pow;
od;
od;
pow := pow + pow;
od;
od;
partition := EquivalenceClasses([1..m],r->table[r]);
return Set(List(partition,r->ResidueClassUnion(Integers,m,r-1)));
end );
Hope this helps,
Stefan
________________________________
From: Johannes Hahn
Sent: Tuesday, February 26, 2019 12:01:15 AM
To: forum at gap-system.org
Subject: [GAP Forum] Atoms of a boolean algebra of sets
Dear forum,
Let?s say a have a list of subsets of a fixed finite set $\Omega$. Is there a nice and easy way to find the atoms of the Boolean algebra generated by these sets? Of course, I could implement this by hand, but it seems to me that something like this probably already exists and I simply had bad luck finding it.
A related question: Let?s say I have a list of partitions of $\Omega$ (i.e. a set of pairwise disjoint subsets that cover all of $\Omega$). Is there a nice and easy way to find the common refinement of all these partitions?
Best wishes
Johannes Hahn.
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
From johannes.hahn at uni-jena.de Tue Feb 26 11:49:50 2019
From: johannes.hahn at uni-jena.de (Johannes Hahn)
Date: Tue, 26 Feb 2019 12:49:50 +0100
Subject: [GAP Forum] Atoms of a boolean algebra of sets
In-Reply-To:
References: <008e01d4cd5e$039c93c0$0ad5bb40$@uni-jena.de>
Message-ID: <000001d4cdc9$61eba220$25c2e660$@uni-jena.de>
Thank you very much, Stefan and Jean. That solves my problem.
Best wishes
Johannes.
Von: Stefan Kohl
Gesendet: Dienstag, 26. Februar 2019 01:07
An: Johannes Hahn ; forum at gap-system.org
Betreff: Re: [GAP Forum] Atoms of a boolean algebra of sets
Dear Johannes,
As to your second question: I think it should be straightforward to adapt RCWA's internal function
'CommonRefinementOfPartitionsOfZ_NC' for this purpose. That function computes the common refinement of a set of partitions of the integers into finitely many residue classes:
#############################################################################
##
#F CommonRefinementOfPartitionsOfZ_NC( ) . . special case R = Z
##
InstallGlobalFunction( CommonRefinementOfPartitionsOfZ_NC,
function ( partitions )
local table, partition, mods, res, m,
pow, mj, r, i, j, k;
mods := List(partitions,P->List(P,Mod));
res := List(partitions,P->List(P,Residues));
m := Lcm(Concatenation(mods));
table := List([1..m],i->0);
pow := 1;
for i in [1..Length(partitions)] do
for j in [1..Length(partitions[i])] do
mj := mods[i][j];
for r in res[i][j] do
for k in [r,r+mj..r+(Int(m/mj)-1)*mj] do
table[k+1] := table[k+1] + pow;
od;
od;
pow := pow + pow;
od;
od;
partition := EquivalenceClasses([1..m],r->table[r]);
return Set(List(partition,r->ResidueClassUnion(Integers,m,r-1)));
end );
Hope this helps,
Stefan
_____
From: Johannes Hahn < johannes.hahn at uni-jena.de>
Sent: Tuesday, February 26, 2019 12:01:15 AM
To: forum at gap-system.org
Subject: [GAP Forum] Atoms of a boolean algebra of sets
Dear forum,
Let?s say a have a list of subsets of a fixed finite set $\Omega$. Is there a nice and easy way to find the atoms of the Boolean algebra generated by these sets? Of course, I could implement this by hand, but it seems to me that something like this probably already exists and I simply had bad luck finding it.
A related question: Let?s say I have a list of partitions of $\Omega$ (i.e. a set of pairwise disjoint subsets that cover all of $\Omega$). Is there a nice and easy way to find the common refinement of all these partitions?
Best wishes
Johannes Hahn.
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
From bernhard.boehmler at googlemail.com Fri Mar 1 16:44:20 2019
From: bernhard.boehmler at googlemail.com (Bernhard Boehmler)
Date: Fri, 1 Mar 2019 17:44:20 +0100
Subject: [GAP Forum] Question concerning the gap function
NameOfEquivalentLibraryCharacterTable
Message-ID:
Dear GAP Forum,
I am running gap 4.10.0 inside sage 8.6 and get an error message after
gap> G:=SymmetricGroup(7);
Sym( [ 1 .. 7 ] )
gap> ct:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 7 ] ) )
gap> NameOfEquivalentLibraryCharacterTable(ct);
(the error message is printed below).
But, when I use my old stand-alone version of gap (GAP 4.9.2 of
04-Jul-2018) it works (and "A7.2" is returned).
I have not installed the Browse package in gap inside sage (I'm not sure,
if NameOfEquivalentLibraryCharacterTable requires this).
I would be grateful for any help.
Thanks in advance.
Sincerely yours,
Bernhard Boehmler
boehmler at mahlzahn:~$ sage
??????????????????????????????????????????????????????????????????????
? SageMath version 8.6, Release Date: 2019-01-15 ?
? Using Python 2.7.15. Type "help()" for help. ?
??????????????????????????????????????????????????????????????????????
sage: gap.console()
????????? GAP 4.10.0 of 01-Nov-2018
? GAP ? https://www.gap-system.org
????????? Architecture: x86_64-pc-linux-gnu-default64
Configuration: gmp 6.0.0, readline
Loading the library and packages ...
Packages: AClib 1.3.1, Alnuth 3.1.0, AtlasRep 1.5.1, AutoDoc 2018.09.20,
AutPGrp 1.10, CRISP 1.4.4, Cryst 4.1.18, CrystCat 1.1.8,
CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, GAPDoc 1.6.2,
IRREDSOL 1.4, LAGUNA 3.9.0, Polenta 1.3.8, Polycyclic 2.14,
PrimGrp 3.3.2, RadiRoot 2.8, ResClasses 4.7.1, SmallGrp 1.3,
Sophus 1.24, TomLib 1.2.7, TransGrp 2.0.4, utils 0.59
Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> G:=SymmetricGroup(7);
Sym( [ 1 .. 7 ] )
gap> ct:=CharacterTable(G);
CharacterTable( Sym( [ 1 .. 7 ] ) )
gap> NameOfEquivalentLibraryCharacterTable(ct);
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 1st choice method found for `Length' on 1 arguments at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:
250 called from
Length( gens
) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
grp.gi:437\
2 called from
MakeGroupyType( FamilyObj( gens ),
IsGroup and IsAttributeStoringRep and HasIsEmpty
and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id, true
) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
grp.gi:442\
4 called from
GroupByGenerators( libtbl.AutomorphismsOfTable, ()
) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
p4/ctadmin.tbi:815 called from
CharacterTableFromLibrary( str
) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
ctbl.gi:40\
99 called from
CharacterTable( val
) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
p4/ctadmin.tbi:2137 called from
... at *stdin*:3
type 'quit;' to quit to outer loop
brk>
gap> NamesOfEquivalentLibraryCharacterTables(ct);
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 1st choice method found for `Length' on 1 arguments at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:250
called from
Length( gens ) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/grp.gi:4372
called from
MakeGroupyType( FamilyObj( gens ), IsGroup and IsAttributeStoringRep and
HasIsEmpty and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id, true
) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
grp.gi:4424 called from
GroupByGenerators( libtbl.AutomorphismsOfTable, () ) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:815
called from
CharacterTableFromLibrary( str ) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/ctbl.gi:4099
called from
CharacterTable( val ) at
/home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:2137
called from
... at *stdin*:3
type 'quit;' to quit to outer loop
brk>
gap> CT:=CharacterTable("S7");
CharacterTable( "A7.2" )
gap> TransformingPermutationsCharacterTables(CT,ct);
rec( columns := (2,3,5,10,4,8,15,11,9)(6,12)(13,14), group := Group(()),
rows := (1,15,6,13,7,3,14,10,12,8,11,5,9,4,2) )
gap>
From sam at Math.RWTH-Aachen.De Fri Mar 1 17:10:39 2019
From: sam at Math.RWTH-Aachen.De (Thomas Breuer)
Date: Fri, 1 Mar 2019 18:10:39 +0100
Subject: [GAP Forum] Question concerning the gap function
NameOfEquivalentLibraryCharacterTable
In-Reply-To:
References:
Message-ID: <20190301171039.5q3qgj3oppdhp77b@hamal.math.rwth-aachen.de>
Dear Bernhard, dear Forum,
this problem is new in GAP 4.10.0,
I hope it will disappear in the next GAP version.
As a temporary remedy, I propose either not to use GAP 4.10.0
or to read the following piece of code into the GAP session
after startup.
InstallMethod( GroupByGenerators,
[ IsGroup, IsMultiplicativeElementWithInverse ],
function( G, id )
return GroupWithGenerators( GeneratorsOfGroup( G ), id );
end );
I am sorry for the inconveniences.
All the best,
Thomas
On Fri, Mar 01, 2019 at 05:44:20PM +0100, Bernhard Boehmler wrote:
> Dear GAP Forum,
>
> I am running gap 4.10.0 inside sage 8.6 and get an error message after
>
> gap> G:=SymmetricGroup(7);
> Sym( [ 1 .. 7 ] )
> gap> ct:=CharacterTable(G);
> CharacterTable( Sym( [ 1 .. 7 ] ) )
> gap> NameOfEquivalentLibraryCharacterTable(ct);
>
> (the error message is printed below).
>
> But, when I use my old stand-alone version of gap (GAP 4.9.2 of
> 04-Jul-2018) it works (and "A7.2" is returned).
>
> I have not installed the Browse package in gap inside sage (I'm not sure,
> if NameOfEquivalentLibraryCharacterTable requires this).
>
> I would be grateful for any help.
>
> Thanks in advance.
>
> Sincerely yours,
> Bernhard Boehmler
>
>
>
>
>
> boehmler at mahlzahn:~$ sage
> ??????????????????????????????????????????????????????????????????????
> ? SageMath version 8.6, Release Date: 2019-01-15 ?
> ? Using Python 2.7.15. Type "help()" for help. ?
> ??????????????????????????????????????????????????????????????????????
> sage: gap.console()
> ????????? GAP 4.10.0 of 01-Nov-2018
> ? GAP ? https://www.gap-system.org
> ????????? Architecture: x86_64-pc-linux-gnu-default64
> Configuration: gmp 6.0.0, readline
> Loading the library and packages ...
> Packages: AClib 1.3.1, Alnuth 3.1.0, AtlasRep 1.5.1, AutoDoc 2018.09.20,
> AutPGrp 1.10, CRISP 1.4.4, Cryst 4.1.18, CrystCat 1.1.8,
> CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, GAPDoc 1.6.2,
> IRREDSOL 1.4, LAGUNA 3.9.0, Polenta 1.3.8, Polycyclic 2.14,
> PrimGrp 3.3.2, RadiRoot 2.8, ResClasses 4.7.1, SmallGrp 1.3,
> Sophus 1.24, TomLib 1.2.7, TransGrp 2.0.4, utils 0.59
> Try '??help' for help. See also '?copyright', '?cite' and '?authors'
> gap> G:=SymmetricGroup(7);
> Sym( [ 1 .. 7 ] )
> gap> ct:=CharacterTable(G);
> CharacterTable( Sym( [ 1 .. 7 ] ) )
> gap> NameOfEquivalentLibraryCharacterTable(ct);
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 1st choice method found for `Length' on 1 arguments at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:
> 250 called from
> Length( gens
> ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> grp.gi:437\
> 2 called from
> MakeGroupyType( FamilyObj( gens ),
> IsGroup and IsAttributeStoringRep and HasIsEmpty
> and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id, true
> ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> grp.gi:442\
> 4 called from
> GroupByGenerators( libtbl.AutomorphismsOfTable, ()
> ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
> p4/ctadmin.tbi:815 called from
> CharacterTableFromLibrary( str
> ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> ctbl.gi:40\
> 99 called from
> CharacterTable( val
> ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
> p4/ctadmin.tbi:2137 called from
> ... at *stdin*:3
> type 'quit;' to quit to outer loop
> brk>
> gap> NamesOfEquivalentLibraryCharacterTables(ct);
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 1st choice method found for `Length' on 1 arguments at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:250
> called from
> Length( gens ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/grp.gi:4372
> called from
> MakeGroupyType( FamilyObj( gens ), IsGroup and IsAttributeStoringRep and
> HasIsEmpty and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id, true
> ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> grp.gi:4424 called from
> GroupByGenerators( libtbl.AutomorphismsOfTable, () ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:815
> called from
> CharacterTableFromLibrary( str ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/ctbl.gi:4099
> called from
> CharacterTable( val ) at
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:2137
> called from
> ... at *stdin*:3
> type 'quit;' to quit to outer loop
> brk>
> gap> CT:=CharacterTable("S7");
> CharacterTable( "A7.2" )
> gap> TransformingPermutationsCharacterTables(CT,ct);
> rec( columns := (2,3,5,10,4,8,15,11,9)(6,12)(13,14), group := Group(()),
> rows := (1,15,6,13,7,3,14,10,12,8,11,5,9,4,2) )
> gap>
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
From bernhard.boehmler at googlemail.com Fri Mar 1 17:45:53 2019
From: bernhard.boehmler at googlemail.com (Bernhard Boehmler)
Date: Fri, 1 Mar 2019 18:45:53 +0100
Subject: [GAP Forum] Question concerning the gap function
NameOfEquivalentLibraryCharacterTable
In-Reply-To: <20190301171039.5q3qgj3oppdhp77b@hamal.math.rwth-aachen.de>
References:
<20190301171039.5q3qgj3oppdhp77b@hamal.math.rwth-aachen.de>
Message-ID:
Dear Thomas Breuer, dear GAP Forum,
thank you very much for the very fast reply.
Your workaround works very well (it seems to be a bit more memory consuming
when compared to NameOfEquivalentLibraryCharacterTable in the gap 4.9.2
version, but, anyway),
thank you very much for the help! :-)
Sincerely yours,
Bernhard Boehmler
On Fri, Mar 1, 2019 at 6:10 PM Thomas Breuer
wrote:
> Dear Bernhard, dear Forum,
>
> this problem is new in GAP 4.10.0,
> I hope it will disappear in the next GAP version.
>
> As a temporary remedy, I propose either not to use GAP 4.10.0
> or to read the following piece of code into the GAP session
> after startup.
>
> InstallMethod( GroupByGenerators,
> [ IsGroup, IsMultiplicativeElementWithInverse ],
> function( G, id )
> return GroupWithGenerators( GeneratorsOfGroup( G ), id );
> end );
>
> I am sorry for the inconveniences.
>
> All the best,
> Thomas
>
>
> On Fri, Mar 01, 2019 at 05:44:20PM +0100, Bernhard Boehmler wrote:
> > Dear GAP Forum,
> >
> > I am running gap 4.10.0 inside sage 8.6 and get an error message after
> >
> > gap> G:=SymmetricGroup(7);
> > Sym( [ 1 .. 7 ] )
> > gap> ct:=CharacterTable(G);
> > CharacterTable( Sym( [ 1 .. 7 ] ) )
> > gap> NameOfEquivalentLibraryCharacterTable(ct);
> >
> > (the error message is printed below).
> >
> > But, when I use my old stand-alone version of gap (GAP 4.9.2 of
> > 04-Jul-2018) it works (and "A7.2" is returned).
> >
> > I have not installed the Browse package in gap inside sage (I'm not sure,
> > if NameOfEquivalentLibraryCharacterTable requires this).
> >
> > I would be grateful for any help.
> >
> > Thanks in advance.
> >
> > Sincerely yours,
> > Bernhard Boehmler
> >
> >
> >
> >
> >
> > boehmler at mahlzahn:~$ sage
> > ??????????????????????????????????????????????????????????????????????
> > ? SageMath version 8.6, Release Date: 2019-01-15 ?
> > ? Using Python 2.7.15. Type "help()" for help. ?
> > ??????????????????????????????????????????????????????????????????????
> > sage: gap.console()
> > ????????? GAP 4.10.0 of 01-Nov-2018
> > ? GAP ? https://www.gap-system.org
> > ????????? Architecture: x86_64-pc-linux-gnu-default64
> > Configuration: gmp 6.0.0, readline
> > Loading the library and packages ...
> > Packages: AClib 1.3.1, Alnuth 3.1.0, AtlasRep 1.5.1, AutoDoc
> 2018.09.20,
> > AutPGrp 1.10, CRISP 1.4.4, Cryst 4.1.18, CrystCat 1.1.8,
> > CTblLib 1.2.2, FactInt 1.6.2, FGA 1.4.0, GAPDoc 1.6.2,
> > IRREDSOL 1.4, LAGUNA 3.9.0, Polenta 1.3.8, Polycyclic 2.14,
> > PrimGrp 3.3.2, RadiRoot 2.8, ResClasses 4.7.1, SmallGrp 1.3,
> > Sophus 1.24, TomLib 1.2.7, TransGrp 2.0.4, utils 0.59
> > Try '??help' for help. See also '?copyright', '?cite' and '?authors'
> > gap> G:=SymmetricGroup(7);
> > Sym( [ 1 .. 7 ] )
> > gap> ct:=CharacterTable(G);
> > CharacterTable( Sym( [ 1 .. 7 ] ) )
> > gap> NameOfEquivalentLibraryCharacterTable(ct);
> > Error, no method found! For debugging hints type ?Recovery from
> > NoMethodFound
> > Error, no 1st choice method found for `Length' on 1 arguments at
> > /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:
> > 250 called from
> > Length( gens
> > ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> > grp.gi:437\
> > 2 called from
> > MakeGroupyType( FamilyObj( gens ),
> > IsGroup and IsAttributeStoringRep and HasIsEmpty
> > and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id, true
> > ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> > grp.gi:442\
> > 4 called from
> > GroupByGenerators( libtbl.AutomorphismsOfTable, ()
> > ) at
> > /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
> > p4/ctadmin.tbi:815 called from
> > CharacterTableFromLibrary( str
> > ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> > ctbl.gi:40\
> > 99 called from
> > CharacterTable( val
> > ) at
> > /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/ga\
> > p4/ctadmin.tbi:2137 called from
> > ... at *stdin*:3
> > type 'quit;' to quit to outer loop
> > brk>
> > gap> NamesOfEquivalentLibraryCharacterTables(ct);
> > Error, no method found! For debugging hints type ?Recovery from
> > NoMethodFound
> > Error, no 1st choice method found for `Length' on 1 arguments at
> >
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/methsel2.g:250
> > called from
> > Length( gens ) at
> > /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> grp.gi:4372
> > called from
> > MakeGroupyType( FamilyObj( gens ), IsGroup and IsAttributeStoringRep and
> > HasIsEmpty and HasGeneratorsOfMagmaWithInverses and HasOne, gens, id,
> true
> > ) at /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> > grp.gi:4424 called from
> > GroupByGenerators( libtbl.AutomorphismsOfTable, () ) at
> >
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:815
> > called from
> > CharacterTableFromLibrary( str ) at
> > /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/lib/
> ctbl.gi:4099
> > called from
> > CharacterTable( val ) at
> >
> /home/boehmler/Schreibtisch/Drarbeit/SAGE/local/share/gap/pkg/ctbllib/gap4/ctadmin.tbi:2137
> > called from
> > ... at *stdin*:3
> > type 'quit;' to quit to outer loop
> > brk>
> > gap> CT:=CharacterTable("S7");
> > CharacterTable( "A7.2" )
> > gap> TransformingPermutationsCharacterTables(CT,ct);
> > rec( columns := (2,3,5,10,4,8,15,11,9)(6,12)(13,14), group := Group(()),
> > rows := (1,15,6,13,7,3,14,10,12,8,11,5,9,4,2) )
> > gap>
> > _______________________________________________
> > Forum mailing list
> > Forum at gap-system.org
> > https://mail.gap-system.org/mailman/listinfo/forum
>
From JPS675 at student.bham.ac.uk Tue Mar 5 14:58:15 2019
From: JPS675 at student.bham.ac.uk (Jack Saunders)
Date: Tue, 5 Mar 2019 14:58:15 +0000
Subject: [GAP Forum] PGTC 2019 registration open
Message-ID:
Dear all,
Registration for the Postgraduate Group Theory Conference (PGTC) 2019 at the University of Birmingham is now open!
For more information on how to register, check our website at http://web.mat.bham.ac.uk/pgtc19/registration.html.
The 21st incarnation of the Postgraduate Group Theory Conference (PGTC) will take place from the 23rd to the 25th of July 2019 in the University of Birmingham. We will also hold a GAP satellite event on Monday 22nd and Friday 26th of July, more information about which may be found at https://www.codima.ac.uk/pgtc2019/
The PGTC is a conference aimed at postgraduate students in group theory and related areas where students at all stages of postgraduate study can attend and give talks in a friendly environment. The opening and closing talks will be given by Professors Martin Liebeck and Colva Roney-Dougal, respectively, and the bulk of the conference will be made up of contributed talks from postgraduate students.
Thanks,
Jack Saunders
On behalf of the PGTC organising committee.
Website: http://web.mat.bham.ac.uk/pgtc19/
Facebook: https://www.facebook.com/PGTC2019
Email: PGTC at contacts.bham.ac.uk
From rsw9 at cornell.edu Tue Mar 5 15:27:53 2019
From: rsw9 at cornell.edu (Russ Woodroofe)
Date: Tue, 5 Mar 2019 16:27:53 +0100
Subject: [GAP Forum] FPSAC software demonstrations
Message-ID: <17DB8977-7A6B-450F-96B3-61330E5A1E6E@cornell.edu>
Dear all,
Formal Power Series and Algebraic Combinatorics (FPSAC) in 2019 will take place in Ljubljana, Slovenia. This is one of the main conferences in algebraic combinatorics. From the webpage, "topics include all aspects of combinatorics and their relations with other parts of mathematics, physics, computer science, and biology."
There is a Software Demonstration portion of FPSAC. The deadline is March 15th. I understand that so far there are few software submissions. FPSAC could be a great way for information about your software to reach a large audience of people in algebraic combinatorics and related areas.
More information is at
http://fpsac2019.fmf.uni-lj.si/
Submissions are by email to fpsac19 at fmf.uni-lj.si with subject line "computer demonstration". More information can be found under the "Submissions" tab of the above website.
I'll further remark that immediately following FPSAC is a workshop "Free and Practical Software for Algebraic Combinatorics", which may also be of interest.
https://wiki.sagemath.org/fpsac19
Best,
--Russ
From jorisvergeest at hotmail.com Fri Mar 8 21:28:10 2019
From: jorisvergeest at hotmail.com (Joris Vergeest)
Date: Fri, 8 Mar 2019 21:28:10 +0000
Subject: [GAP Forum] Repsn matrices appear to be not homomorphic to group
(for A5)
Message-ID:
Dear Forum,
I tried to verify, for the A5 group, whether the group of 60 matrices produced by Repsn is homomorphic to A5.
They appear to be not
One example:
The 60 group elements g1, g2, ..., g60 are sort-listed using List(G).
3D representation matrices Mi are obtained using Repsn: Mi = gi^IrreducibleAffordingRepresentation(selChar), for some fixed character selChar.
It is expected that Mi * Mj = Mk, where k is chosen such that gi * gj = gk; then we are dealing with a homomorphism.
For group A5 take i = 2, j = 3. Then:
g2 = (1,5,4),
g3 = (1,4,5),
g2 * g3 = g1 = () , the identity element. That is g2 and g3 are inverses of each other.
Now from Repsn we obtain:
M2 =
[ [ -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4, 2/5*E(5)-2/5*E(5)^2-2/5*E(5)^3+2/5*E(5)^4,
2/5*E(5)+3/5*E(5)^2+3/5*E(5)^3+2/5*E(5)^4 ],
[ 0, 0, -1 ],
[ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -2/5*E(5)-3/5*E(5)^2-3/5*E(5)^3-2/5*E(5)^4,
3/5*E(5)+2/5*E(5)^2+2/5*E(5)^3+3/5*E(5)^4 ] ]
M3 = [ [ -E(5)-E(5)^4, E(5)^2+E(5)^3, -2 ], [ E(5)^2+E(5)^3, -1, E(5)^2+E(5)^3 ],
[ 1, -E(5)^2-E(5)^3, -E(5)^2-E(5)^3 ] ]
M1 = [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
So M2 * M3 should be equal to M1.
In Gap we find:
M2 * M3 =
[ [ 2/5*E(5)+8/5*E(5)^2+8/5*E(5)^3+2/5*E(5)^4, -2/5*E(5)+7/5*E(5)^2+7/5*E(5)^3-2/5*E(5)^4,
11/5*E(5)+14/5*E(5)^2+14/5*E(5)^3+11/5*E(5)^4 ],
[ -1, E(5)^2+E(5)^3, E(5)^2+E(5)^3 ],
[ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4,
4/5*E(5)+1/5*E(5)^2+1/5*E(5)^3+4/5*E(5)^4 ] ]
which is not equal to M1.
All products Mi * Mj for which neither Mi nor Mj are the identity appear inconsistent with a homomorphism.
BTW: I know that for A5 "correct" representations have been found. However, I need a reliable method to generate representations for automatic processing of many groups.
Any advise is welcome,
Joris
From dmitrii.pasechnik at cs.ox.ac.uk Sat Mar 9 07:55:15 2019
From: dmitrii.pasechnik at cs.ox.ac.uk (Dmitrii Pasechnik)
Date: Sat, 9 Mar 2019 07:55:15 +0000
Subject: [GAP Forum] Repsn matrices appear to be not homomorphic to
group (for A5)
In-Reply-To:
References:
Message-ID: <20190309075514.GA23662@cs.ox.ac.uk>
Dear Joris,
On Fri, Mar 08, 2019 at 09:28:10PM +0000, Joris Vergeest wrote:
>
> I tried to verify, for the A5 group, whether the group of 60 matrices produced by Repsn is homomorphic to A5.
> They appear to be not
>
> One example:
>
> The 60 group elements g1, g2, ..., g60 are sort-listed using List(G).
>
> 3D representation matrices Mi are obtained using Repsn: Mi = gi^IrreducibleAffordingRepresentation(selChar), for some fixed character selChar.
Different calls to IrreducibleAffordingRepresentation(selChar) might
produce different representations, I suppose this is exactly the
problem you see here.
Store it in a variable, e.g.
rep:=IrreducibleAffordingRepresentation(selChar);
then compute Mi's as follows:
Mi:=gi^rep;
After this change everything should be working right.
Hope this helps,
Dmitrii
>
> It is expected that Mi * Mj = Mk, where k is chosen such that gi * gj = gk; then we are dealing with a homomorphism.
>
> For group A5 take i = 2, j = 3. Then:
>
> g2 = (1,5,4),
> g3 = (1,4,5),
> g2 * g3 = g1 = () , the identity element. That is g2 and g3 are inverses of each other.
>
> Now from Repsn we obtain:
>
> M2 =
> [ [ -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4, 2/5*E(5)-2/5*E(5)^2-2/5*E(5)^3+2/5*E(5)^4,
> 2/5*E(5)+3/5*E(5)^2+3/5*E(5)^3+2/5*E(5)^4 ],
> [ 0, 0, -1 ],
> [ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -2/5*E(5)-3/5*E(5)^2-3/5*E(5)^3-2/5*E(5)^4,
> 3/5*E(5)+2/5*E(5)^2+2/5*E(5)^3+3/5*E(5)^4 ] ]
>
> M3 = [ [ -E(5)-E(5)^4, E(5)^2+E(5)^3, -2 ], [ E(5)^2+E(5)^3, -1, E(5)^2+E(5)^3 ],
> [ 1, -E(5)^2-E(5)^3, -E(5)^2-E(5)^3 ] ]
>
> M1 = [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
>
> So M2 * M3 should be equal to M1.
>
> In Gap we find:
>
> M2 * M3 =
> [ [ 2/5*E(5)+8/5*E(5)^2+8/5*E(5)^3+2/5*E(5)^4, -2/5*E(5)+7/5*E(5)^2+7/5*E(5)^3-2/5*E(5)^4,
> 11/5*E(5)+14/5*E(5)^2+14/5*E(5)^3+11/5*E(5)^4 ],
> [ -1, E(5)^2+E(5)^3, E(5)^2+E(5)^3 ],
> [ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4,
> 4/5*E(5)+1/5*E(5)^2+1/5*E(5)^3+4/5*E(5)^4 ] ]
>
> which is not equal to M1.
>
> All products Mi * Mj for which neither Mi nor Mj are the identity appear inconsistent with a homomorphism.
>
> BTW: I know that for A5 "correct" representations have been found. However, I need a reliable method to generate representations for automatic processing of many groups.
>
> Any advise is welcome,
>
> Joris
>
>
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
From jorisvergeest at hotmail.com Sat Mar 9 12:26:40 2019
From: jorisvergeest at hotmail.com (Joris Vergeest)
Date: Sat, 9 Mar 2019 12:26:40 +0000
Subject: [GAP Forum] Repsn matrices appear to be not homomorphic to
group (for A5)
In-Reply-To: <20190309075514.GA23662@cs.ox.ac.uk>
References: ,
<20190309075514.GA23662@cs.ox.ac.uk>
Message-ID:
Dear Dmitrii, thank you! Problem solved. Joris
________________________________________
From: Dmitrii Pasechnik
Sent: Saturday, March 9, 2019 08:55
To: Joris Vergeest
Cc: forum at gap-system.org
Subject: Re: [GAP Forum] Repsn matrices appear to be not homomorphic to group (for A5)
Dear Joris,
On Fri, Mar 08, 2019 at 09:28:10PM +0000, Joris Vergeest wrote:
>
> I tried to verify, for the A5 group, whether the group of 60 matrices produced by Repsn is homomorphic to A5.
> They appear to be not
>
> One example:
>
> The 60 group elements g1, g2, ..., g60 are sort-listed using List(G).
>
> 3D representation matrices Mi are obtained using Repsn: Mi = gi^IrreducibleAffordingRepresentation(selChar), for some fixed character selChar.
Different calls to IrreducibleAffordingRepresentation(selChar) might
produce different representations, I suppose this is exactly the
problem you see here.
Store it in a variable, e.g.
rep:=IrreducibleAffordingRepresentation(selChar);
then compute Mi's as follows:
Mi:=gi^rep;
After this change everything should be working right.
Hope this helps,
Dmitrii
>
> It is expected that Mi * Mj = Mk, where k is chosen such that gi * gj = gk; then we are dealing with a homomorphism.
>
> For group A5 take i = 2, j = 3. Then:
>
> g2 = (1,5,4),
> g3 = (1,4,5),
> g2 * g3 = g1 = () , the identity element. That is g2 and g3 are inverses of each other.
>
> Now from Repsn we obtain:
>
> M2 =
> [ [ -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4, 2/5*E(5)-2/5*E(5)^2-2/5*E(5)^3+2/5*E(5)^4,
> 2/5*E(5)+3/5*E(5)^2+3/5*E(5)^3+2/5*E(5)^4 ],
> [ 0, 0, -1 ],
> [ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -2/5*E(5)-3/5*E(5)^2-3/5*E(5)^3-2/5*E(5)^4,
> 3/5*E(5)+2/5*E(5)^2+2/5*E(5)^3+3/5*E(5)^4 ] ]
>
> M3 = [ [ -E(5)-E(5)^4, E(5)^2+E(5)^3, -2 ], [ E(5)^2+E(5)^3, -1, E(5)^2+E(5)^3 ],
> [ 1, -E(5)^2-E(5)^3, -E(5)^2-E(5)^3 ] ]
>
> M1 = [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]
>
> So M2 * M3 should be equal to M1.
>
> In Gap we find:
>
> M2 * M3 =
> [ [ 2/5*E(5)+8/5*E(5)^2+8/5*E(5)^3+2/5*E(5)^4, -2/5*E(5)+7/5*E(5)^2+7/5*E(5)^3-2/5*E(5)^4,
> 11/5*E(5)+14/5*E(5)^2+14/5*E(5)^3+11/5*E(5)^4 ],
> [ -1, E(5)^2+E(5)^3, E(5)^2+E(5)^3 ],
> [ -2/5*E(5)+2/5*E(5)^2+2/5*E(5)^3-2/5*E(5)^4, -3/5*E(5)-2/5*E(5)^2-2/5*E(5)^3-3/5*E(5)^4,
> 4/5*E(5)+1/5*E(5)^2+1/5*E(5)^3+4/5*E(5)^4 ] ]
>
> which is not equal to M1.
>
> All products Mi * Mj for which neither Mi nor Mj are the identity appear inconsistent with a homomorphism.
>
> BTW: I know that for A5 "correct" representations have been found. However, I need a reliable method to generate representations for automatic processing of many groups.
>
> Any advise is welcome,
>
> Joris
>
>
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
From alexander.konovalov at st-andrews.ac.uk Tue Mar 12 09:59:47 2019
From: alexander.konovalov at st-andrews.ac.uk (Alexander Konovalov)
Date: Tue, 12 Mar 2019 09:59:47 +0000
Subject: [GAP Forum] GAP 4.10.1 release announcement
Message-ID:
Dear GAP Forum,
The next minor release of GAP, version 4.10.1, is now available at
http://www.gap-system.org/Releases/
An overview of changes introduced in GAP 4.10.1 is given below,
with numbers of issues and pull requests in the GAP repository
at https://github.com/gap-system/gap.
1. Changes in the core GAP system introduced in GAP 4.10.1
* Fixes in the experimental way to allow 3rd party code to link GAP
as a library:
- Do not start a session when loading workspace if --nointeract
command line option is used (#2840).
- Add prototype for GAP_Enter and GAP_Leave macros (#3096).
- Prevent infinite recursions in echoandcheck and
SyWriteandcheck (#3102).
- Remove environ arguments and sysenviron (#3111).
* Fixes in the experimental support for using the Julia garbage
collector:
- Fix task scanning for the Julia GC (#2969).
- Fix stack marking for the Julia GC (#3199).
- Specify the Julia binary instead of the Julia prefix (#3243).
- Export Julia CFLAGS, LDFLAGS, and LIBS to sysinfo.gap (#3248).
* Improved and extended functionality:
- Always generate sysinfo.gap (previously, it was only generated if
the "compatibility mode" of the build system was enabled) (#3042).
- Add support for writing to ERROR_OUTPUT from kernel code (#3043).
- Add make check (#3285).
* Changed documentation:
- Fix documentation of NumberFFVector (Reference: NumberFFVector)
and add an example (#3079).
* Fixed bugs that could lead to crashes:
- Fix readline crash when using autocomplete with
colored-completion-prefix turned on in Bash (#2991).
- Fix overlapping memcpy in APPEND_LIST (#3216).
* Fixed bugs that could lead to incorrect results:
- Fix bugs in the code for partial permutations (#3220).
- Fix a bug in Gcd for polynomials not returning standard associates,
introduced in GAP 4.10.0 (#3227).
* Fixed bugs that could lead to break loops:
- Change GroupWithGenerators (Reference: GroupWithGenerators) to
accept collections again (to avoid regressions in code that
relied on this undocumented behavior) (#3095).
- Fix ShallowCopy (Reference: ShallowCopy) for for a Knuth-Bendix
rewriting system (#3128). [Reported by Ignat Soroko]
- Fix IsMonomialMatrix (Reference: IsMonomialMatrix) to work with
compressed matrices (#3149). [Reported by Dominik Bernhardt]
* Removed or obsolete functionality:
- Disable make install (previously it displayed a warning which
often got ignored) (#3005).
* Other fixed bugs:
- Fix some errors which stopped triggering a break loop (#3013).
- Fix compiler error with GCC 4.4.7 (#3026).
- Fix string copying logic (#3071).
2. New and updated packages since GAP 4.10.0
GAP 4.10.1 distribution contains 145 packages, including updated
versions of 35 packages from GAP 4.10.0 distribution, and also the
following five new packages:
- MajoranaAlgebras by Markus Pfeiffer and Madeleine Whybrow, which
constructs Majorana representations of finite groups.
- PackageManager by Michael Torpey, providing a collection of
functions for installing and removing GAP packages, with the
eventual aim of becoming a full pip-style package manager for
the GAP system.
- Thelma by Victor Bovdi and Vasyl Laver, implementing algorithms
to deal with threshold elements.
- walrus by Markus Pfeiffer, providing methods for proving
hyperbolicity of finitely presented groups in polynomial time.
- YangBaxter by Leandro Vendramin and Alexander Konovalov, which
provides functionality to construct classical and skew braces,
and also includes a database of classical and skew braces of
small orders.
The full list of new and updated packages in GAP 4.10.1 distribution
is given below.
Package name | Version | Date
------------------------------------------
AutoDoc | 2019.02.22 | 22/02/2019
Carat | 2.2.3 | 04/11/2018
cvec | 2.7.1 | 23/02/2019
datastructures | 0.2.3 | 18/12/2018
Digraphs | 0.15.0 | 15/02/2019
FR | 2.4.6 | 03/11/2018
Guarana | 0.96.2 | 15/11/2018
HAP | 1.19 | 05/02/2019
hecke | 1.5.2 | 06/02/2019
HeLP | 3.4 | 20/11/2018
JupyterKernel | 1.3 | 23/02/2019
JupyterViz | 1.4.0 | 21/02/2019
kbmag | 1.5.8 | 19/02/2019
LAGUNA | 3.9.2 | 19/02/2019
LieRing | 2.4 | 22/02/2019
loops | 3.4.1 | 06/11/2018
lpres | 1.0.1 | 14/11/2018
MajoranaAlgebras | 1.4 | 06/12/2018
MapClass | 1.4.4 | 02/12/2018
matgrp | 0.60 | 15/11/2018
ModIsom | 2.5.0 | 19/02/2019
nq | 2.5.4 | 15/02/2019
NumericalSgps | 1.1.10 | 06/11/2018
orb | 4.8.2 | 23/02/2019
PackageManager | 0.2.3 | 22/02/2019
polymaking | 0.8.2 | 23/02/2019
RCWA | 4.6.3 | 27/11/2018
RDS | 1.7 | 23/02/2019
Repsn | 3.1.0 | 22/02/2019
Semigroups | 3.1.1 | 15/02/2019
singular | 2019.02.22 | 22/02/2019
SLA | 1.5.1 | 22/02/2019
Thelma | 1.02 | 06/02/2019
ToricVarieties | 2018.10.12 | 12/10/2018
utils | 0.61 | 28/11/2018
walrus | 0.99 | 19/02/2019
Wedderga | 4.9.5 | 30/11/2018
XGAP | 4.29 | 10/11/2018
YangBaxter | 0.7.0 | 23/02/2019
ZeroMQInterface | 0.11 | 01/11/2018
------------------------------------------
We encourage all users to upgrade to GAP 4.10.1. You can download
source archives for Linux and macOS, as well as the GAP installer
for Windows from http://www.gap-system.org/Releases/. If you need
any help or would like to report any problems, please do not
hesitate to contact us at support at gap-system.org, or submit
new issues on GitHub:
https://github.com/gap-system/gap/issues
There is also a 'gap' tag for questions about GAP at the
Mathematics Q&A site:
http://math.stackexchange.com/tags/gap/info
In addition, you may find some GAP related news on Twitter:
http://twitter.com/gap_system
Wishing you fun and success using GAP,
Alexander Konovalov
on behalf of the GAP Group
From zohrehsayanjali at gmail.com Fri Mar 15 14:22:09 2019
From: zohrehsayanjali at gmail.com (zohreh sayanjali)
Date: Fri, 15 Mar 2019 17:52:09 +0330
Subject: [GAP Forum] A request for finding a group
Message-ID:
Dear GAP Forum,
I am trying to figure out if there is any perfect group G whose normal
minimal subgroup, say N, is an elementary abelian 2-group of order 2^6,
G/N is isomorphic to L2(8) and cd(G) = {1, 18, 9, 8, 7}, where the number
of irreducible characters whose degrees are 18 is 98.
Unfortunately, I do not know how to construct such a group and figure out
about its character degrees. I would really appreciate it if you help me to
find them, if there exists any.
Regards,
zohreh sayanjali.
From sk239 at st-andrews.ac.uk Fri Mar 15 17:51:18 2019
From: sk239 at st-andrews.ac.uk (Stefan Kohl)
Date: Fri, 15 Mar 2019 17:51:18 +0000
Subject: [GAP Forum] A request for finding a group
In-Reply-To:
References:
Message-ID:
Dear Zohreh,
First observe that we are looking for perfect groups of order 2^6 * |PSL(2,8)| = 64 * 504 = 32256. Since 18^2*98 = 31752 is not much smaller than 32256, some scepticism regarding the existence of such groups with 98 characters of degree 18 seems in order. Anyway, let's continue. -- We can check how many perfect groups of this order there are, up to isomorphism:
gap> NrPerfectGroups(32256); # Order 32256 is covered by the data
2 # in GAP's Perfect Groups Library
So we know that there are precisely two groups we need to have a look at. We get them from the said library, represented as permutation groups (this being most convenient here):
gap> G := PerfectGroup(IsPermGroup,32256,1);
L2(8) 2^6
gap> H := PerfectGroup(IsPermGroup,32256,2);
L2(8) N 2^6
Now we can compute the lists of normal subgroups of both groups ...
gap> normsG := NormalSubgroups(G);
[ Group(()), , L2(8) 2^6 ]
gap> normsH := NormalSubgroups(H);
[ Group(()), , L2(8) N 2^6 ]
... and have a look at the quotients:
gap> StructureDescription(G/normsG[2]);
"PSL(2,8)"
gap> StructureDescription(H/normsH[2]);
"PSL(2,8)"
So far, both groups fulfil our criteria. -- But now let's compute the character degrees of our two groups:
gap> CharacterDegrees(G);
[ [ 1, 1 ], [ 7, 4 ], [ 8, 1 ], [ 9, 3 ], [ 63, 8 ] ]
gap> CharacterDegrees(H);
[ [ 1, 1 ], [ 7, 4 ], [ 8, 1 ], [ 9, 3 ], [ 63, 8 ] ]
As we see, none of the groups has an irreducible character of degree 18. Therefore -- unless I have misread the conditions -- a group with the desired properties does not exist.
Hope this helps,
Stefan
________________________________
From: zohreh sayanjali
Sent: Friday, March 15, 2019 3:22:09 PM
To: GAP Forum
Subject: [GAP Forum] A request for finding a group
Dear GAP Forum,
I am trying to figure out if there is any perfect group G whose normal
minimal subgroup, say N, is an elementary abelian 2-group of order 2^6,
G/N is isomorphic to L2(8) and cd(G) = {1, 18, 9, 8, 7}, where the number
of irreducible characters whose degrees are 18 is 98.
Unfortunately, I do not know how to construct such a group and figure out
about its character degrees. I would really appreciate it if you help me to
find them, if there exists any.
Regards,
zohreh sayanjali.
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
From zohrehsayanjali at gmail.com Fri Mar 15 19:09:26 2019
From: zohrehsayanjali at gmail.com (zohreh sayanjali)
Date: Fri, 15 Mar 2019 22:39:26 +0330
Subject: [GAP Forum] thank you
Message-ID:
Dear Prof. Kohl
It was very nice of you to answer my email promptly. I really appreciate
your clear and accurate guidance.
*Actually, we tried to find perfect groups of order 2^9.7.9 using some
commands similar to what you used. But it seems like our GAP does not have
a group with that order in its library. Because of that we asked you. It is
strange. Anyway thanks again for your help. *
Regards
*Zohreh sayanjali*
From zohrehsayanjali at gmail.com Sat Mar 16 19:43:43 2019
From: zohrehsayanjali at gmail.com (zohreh sayanjali)
Date: Sat, 16 Mar 2019 23:13:43 +0330
Subject: [GAP Forum] thanks a lot
Message-ID:
Dear Prof Kohl,
I take in GAP the following command:
gap> names:= AllCharacterTableNames( Size, 32256, IsPerfect, true );
and GAP answers me [].
That's why I could not decide on the existence or absence of a group.
Anyway, thank you Very much for answering me. That was a relief.
Kind regards,
Zohreh
From mbg.nimda at gmail.com Sun Mar 17 13:10:38 2019
From: mbg.nimda at gmail.com (Mbg Nimda)
Date: Sun, 17 Mar 2019 14:10:38 +0100
Subject: [GAP Forum] Quotient of the ring Z_77 by an ideal
Message-ID:
What is wrong with the following sequence of commands in GAP, trying to
form the quotient of the ring Z/77Z by the ideal generated by 7Z ?
gap> R := ZmodnZ(77);
(Integers mod 77)
gap> o := One(R);
ZmodnZObj( 1, 77 )
gap> i := o*7;
ZmodnZObj( 7, 77 )
gap> I := Ideal(R, [i]);
gap> R/I;
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound Error, no 1st choice method found for
`NaturalHomomorphismByIdeal' on 2 arguments at /proc/cygdrive/E/gap-
4.10.0/lib/methsel2.g:250 called from
NaturalHomomorphismByIdeal( R, I ) at /proc/cygdrive/E/gap-
4.10.0/lib/ringhom.gi:648 called from
( )
called from read-eval loop at *stdin*:12
type 'quit;' to quit to outer loop
brk>
From williamgiuliano00 at gmail.com Wed Mar 20 11:12:51 2019
From: williamgiuliano00 at gmail.com (William Giuliano)
Date: Wed, 20 Mar 2019 11:12:51 +0000
Subject: [GAP Forum] Identify a finitely presented group
Message-ID:
Dear Forum,
I have a finitely presented group
G = fp group on the generators [ f1, f2, x, f3, f4, y ]
(file attached) which I constructed in such a way that:
- < f1, f2, x > is [ 1344, 814 ];
- < f1, f2 > is [ 192, 956 ];
- < f3, f4, y > is [ 576, 8282 ];
- < f3, f4 > is [ 192, 1494 ];
- < f1, f2, f3, f4 > is the Mathieu Group M12;
I would like to identify G somehow, or just know if it the trivial group or
not. I tried to simplify its presentation (also in MAGMA), but it seems it
is not enough. The only thing I know is that it's perfect.
Any advice on how to tackle this kind of problem more efficiently?
Thank you ver much,
William
-------------- next part --------------
free:=FreeGroup("f1", "f2", "x", "f3", "f4", "y");;
AssignGeneratorVariables(free);;
g:=free/[ (f2^-1*f1^-1)^2, f2^6, f1^8, f2*f1^-1*f2^-1*f1^2*f2^2*f1^3, (f2^2*f1*f2^-1*f1^-1)^2, f2*f1^2*f2^-1*f1^2*(f2*f1^-1)^2, f3^3, (f4^-1*f3)^4, (f3^-1*f4^-1*f3^-1*f4)^2,
f4^8, (f4^2*f3^-1)^2*f4^-2*f3^-1, (f4^2*f3)^3, (f3^-1*f4^-1*f3*f4^2)^2, (f4^2*f3*f4*f3^-1)^2, (f3*f4^-1*f3^-1*f4^2)^2, (f4^2*f3^-1*f4*f3)^2,
f4^-1*f3*f4*f3^-1*f4^-1*f3*f4^-1*f3^-1*f4*f3*f4^-1*f3^-1, f1*(f3^-1*f4^-1*f3^-1)^4*(f3^-1*f4*f3^-1)^3, f2*f1^-1*f2*(f3^-1*f4^-1*f3^-1)^2*f3^-1*f4*f3^-2*f4^-1*f3^-1,
f2^3*(f3^-1*f4*f3^-1)^4*(f3^-1*f4^-1*f3^-1)^2*f3^-1*f4*f3^-1*f4^-1, (f2^-2*f3)^10, (f2^-2*f4*f3^-1*f4^-1*f3*f4)^10,
(x*f2^-1*(f1^-2*f2*f1^-1)^2*f1^-1*f2^-1*f1^-1)^7, (x*f1^-1*f2*f1^-2)^7, (x*f1*f2*f1^-4)^8, (x*f2*f1^-2*f2^-1)^3, (x*f1^2*f2^-1*f1)^
7, (x*f1^4*f2^-1*f1^-1)^8, (x*f2*f1^2*f2^-1)^6, (x*f2^-3*f1^-2*f2*f1^-2*f2^-1*f1^-1)^3, (x*f2^-4*f1^-2*f2*f1^-1)^6, (x*f2^-3*f1^-3)^6, (x*f1^-3*f2^3)^
3, (x*f2^-4*(f1^-2*f2*f1^-1)^2)^3, (x*f2^-4*f1^-2*f2*f1^2*f2^-1)^6, (x*f2^2)^6, (x*f2^-1*f1^-2*f2*f1^2*f2^2)^3, (x*f2^-1*f1^-2*f2*f1*f2*f1^-2*f2^-1*f1^-1)^
7, (x*f1^4)^7, (x*f1^-2*f2^-1*f1)^7, (x*f2^-1*f1^-1)^8, (x*f2^-1*f1^-2*f2*f1^-2)^6, (x*f1*f2^-1*f1^2*f2^2)^7, (x*f2^-1*(f1^-2*f2*f1^-1)^2*f1^-1)^
8, (x*f1^2*f2^-1*f1^2*f2)^3, (x*f2^-2*(f2^-1*f1)^2*f1*f2)^3, (x*f2^-3*f1^2*f2*f1^-2*f2^-1*f1^-1)^6, (x*f1*f2^3)^3, (x*f2^-3*f1)^6, (x*f2^-3*f1^4*f2^-1)^
6, (x*(f1^-1*f2)^2*f2^2)^6, (x*f2^-1*f1^-4*f2^3)^3, (x*f1^2*f2^-1*f1^2*f2^3)^3, (x*f2^-1*f1^2*f2)^8, (x*f2*f1^2*f2^-1*f1^2)^8, (x*f1^-1*f2)^7, (x*f1*f2*f1^-2)^
6, (x*f2^-1*f1^-1*(f1^-1*f2)^2*f1^-2*f2^-1*f1^-1)^7, (x*f1*f2^-1*f1^2*f2^2*f1^-2)^7, (x*f1^4*f2^-1*f1)^3, (x*f1^2)^7, (x*f2^-1*f1^-2*f2)^
8, (x*f1^-2*f2*f1^-2*f2^-1)^8, (x*f1^-1*f2*f1^-4)^7, (x*f2^-1*f1)^6, (x*f1^-2)^7, (x*f1^2*f2^-1*f1^-1)^7, (x*f2^-1*f1^-2*f2*f1^-3*f2)^
3, (x*f1*f2^-1*f1^2*f2^2*f1^-2*f2^-1*f1^-1)^7, (x*f2^-4*f1^-2*f2*f1^-3*f2^-1*f1)^8, (x*f1*f2^-1*f1^2)^6, (x*f2^-3*f1^4*f2)^8, (x*f1^2*f2*f1^-1)^
3, (x*f2^-3*f1^4*f2*f1^-2)^7, (x*f1*f2^-2*f1^-1*(f1^-1*f2)^2*f2^2)^7, (x*f1*f2^-1)^7, (x*f2^-3*f1*f2^2)^7, (x*f2^-4*f1^-2*f2*f1^-1*f2^-1*f1^-1)^3, (x*f2*f1^-3)^
7, (x*f2^-3*f1^-2*f2*f1^-2)^6, (x*f1^-1*f2^-1)^7, (x*f2^-4*f1^-2*f2*f1^-1*f2^-1*f1)^7, (x*f2^-3*f1^-2*f2)^7, (x*f2^-1*f1^-2*f2*f1*f2^-1)^8, (x*f2*f1^-1)^
8, (x*f2^-3*f1^3)^2, (x*f1^-1*f2^3)^2, (x*f1^-1*f2^-1*f1^2*f2^4)^8, (x*f2^-3*f1^4*f2*f1^-2*f2^-1*f1^-1)^8, (x*f1*f2^-1*f1*(f1*f2)^2*f2)^
8, (x*f2^-2*(f2^-1*f1)^2*f1*f2^2*f1^-1)^2, (x*f2^-4*f1^-2)^8, (x*f1^2*f2^2)^2, (x*f2^-2)^8, (x*f1^-2*f2*f1^-1)^3, (x*f2*f1^-4*f2^3)^
8, (x*f2^-1*f1^-2*f2*f1^-1*f2^-1)^6, (x*f2*f1^-2*f2^3)^7, (x*f2^-2*f1^-2)^7, (x*f2*f1^3*f2^-1*f1^2*f2)^7, (x*f1^5*f2^-1)^7, (x*f2^-3*f1^2*f2*f1^-2)^
3, (x*f1^3*f2^-1)^7, (x*f2^-2*(f2^-1*f1)^2)^6, (x*f2^-3*f1^-1*f2^2)^7, (x*f2^-3*f1^2*f2)^7, (x*f2^-2*(f2^-1*f1)^2*f1^2)^7, (x*f1^4*f2*f1^-1)^
8, (x*f2^-1*f1^-2*f2*f1^-3*f2^-1)^8, (x*f1^3*f2^3)^4, (x*f2^-3*f1^-1)^4, (x*f2^-2*f1^-2*f2^-1*f1^-1)^8, (x*f2^-4*f1^-2*f2*f1)^
8, (x*f2^-2*(f2^-1*f1)^2*f1*f2*f1*f2^-1)^8, (x*f2^-3*f1^2*f2^-1)^4, (x*f2^-1*f1^-2*f2^3)^8, (x*f2^-4*f1^-1*(f1^-1*f2)^2*f1^-1)^4, (x*f2^-3*f1^4)^
7, (x*f2^-4*f1^-2*f2*f1*f2*f1^-2*f2^-1*f1^-1)^7, (x*f2^-2*(f2^-1*f1)^2*f1*f2^2)^7, (x*f1*f2^4)^8, (x*f2^-3*f1^4*f2*f1^-2*f2^-1)^6, (x*f2^-3*f1^-2*f2^-1*f1)^
7, (x*f2^-4*f1^-1)^8, (x*f2^-4*f1^-2*f2*f1^-2)^3, (x*f1^2*f2*f1^-2*f2^-1*f1^-1)^3, (x*f1*f2^-1*f1^2*f2)^6, (x*f1)^3, (x*f2*f1*(f1*f2^-1)^2*f1^2*f2)^
6, (x*f2^-1*f1^-4)^3, (x*f1^-1*f2*f1^-1)^3, (x*f1^4*f2^-1)^6, (x*f1^2*f2^-1*f1^2)^6, (x*f2^-4*(f1^-2*f2*f1^-1)^2*f1^-1*f2^-1*f1^-1)^7, (x*f2^-3)^
7, (x*f2^-3*f1^2*f2^-1*f1)^7, (x*f2^-3*f1^4*f2^-1*f1^-1)^8, (x*f2^-2*(f2^-1*f1)^2*f1*f2*f1^-1)^3, (x*f1^-1*f2*f1^-2*f2^3)^7, (x*f2^-4*f1^-2*f2*f1*f2*f1^-2)^
8, (x*f2^-2*f1^-2*f2^-1)^6, (x*f2^-1*f1^-2*f2*f1^-1)^3, (x*f1^-2*f2*f1^-2*f2^-1*f1^-1)^6, (x*f2^-1*f1^-2*f2*f1*f2*f1^-2*f2^-1)^6, (x*f1^-3)^3, (x*f2^-1)^
6, (x*f1*f2*f1*f2^-1*f1^2*f2)^3, (x*f2^-1*(f1^-2*f2*f1^-1)^2)^3, (x*f1^2*f2^-1*f1^-2)^6, (x*f2^-3*f1^-2*f2*f1^-2*f2^-1)^8, (x*f2^-4*f1^-2*f2)^
8, (x*f2^-3*f1^2*f2^-1*f1^-1)^7, (x*f1*f2*f1^-2*f2^3)^3, (x*f2^-2*(f2^-1*f1)^2*f1*f2^2*f1^-2*f2^-1*f1^-1)^7, (x*f1^-1*f2^4)^7, (x*f2^-4*f1)^6, (x*f2^-3*f1^-2)^
7, (x*f2^-4*f1^-2*f2*f1^-4)^8, (x*f2^-3*f1^2*f2*f1^-2*f2^-1)^8, (x*f2^-1*f1^-1*f2^-1*f1^2*f2^4)^7, (x*f1*f2*f1^2*f2^3)^3, (x*f2^-3*f1^2)^
7, (x*f2^-3*f1^-2*f2^-1*f1^-1)^7, (x*f2^-4*f1^-2*f2*f1*f2)^6, (x*f2^-4*f1^-1*(f1^-1*f2)^2*f1^-2*f2^-1*f1^-1)^7, (x*f2*f1^-4)^8, (x*f2^-4*f1^-2*f2*f1^-1*f2^-1)^
6, (x*f2)^8, (x*f2^-3*f1^-2*f2*f1^-1)^3, (x*f2*f1^-2)^7, (x*f2*f1^2)^7, (x*f2^-3*f1^5*f2^-1)^7, (x*f1^5*f2^2)^7, (x*f1*f2^-1*f1)^3, (x*f1^-1*f2^2)^
7, (x*f1^2*f2*f1^-2)^6, (x*f2^-3*f1^3*f2^-1)^7, (x*f1*f2^-1*f1^3)^7, (x*f1^2*f2)^7, (x*f2*f1^-5*f2^3)^8, (x*f2*f1^-1*f2^3)^8, (x*f1^-1)^
4, (x*f1*f2^-1*f1^2*f2^2*f1^-2*f2^-1)^4, (x*f2^-1*f1^-2*f2*f1)^8, (x*f2*f1^-2*f2^-1*f1^-1)^8, (x*f2^-1*f1^2)^8, (x*f2^-1*f1^-1*(f1^-1*f2)^2*f1^-1)^
4, (x*f1^-3*f2*f1^-1)^8, (x*f1^2*f2^-1)^4, (x*f1^4*f2)^8, (x*f2^-3*f1^2*f2*f1^-1)^3, (x*f2^-1*f1^-2*f2*f1^-3*f2^-1*f1)^8, (x*f2^-2*(f2^-1*f1)^2*f1)^
6, (x*(f1*f2^-1)^2*f1^2*f2)^7, (x*f1^4*f2*f1^-2)^7, (x*f1*f2^2)^7, (x*f2^-3*f1*f2^-1)^7, (x*f1^-2*f2*f1^-2)^3, (x*f2^-2*f1)^7, (x*f2^-1*f1^-2*f2*f1^-1*f2^-1*f1^-1)^
6, (x*f1^3*f2^2)^7, (x*f1^-2*f2)^7, (x*f2^-1*f1^-2*f2*f1^-1*f2^-1*f1)^7, (x*f2^-2*f1^-1)^8, (x*f2^-2*f1^-5)^8, (x*f2^-1*f1^-1*(f1^-1*f2)^2*f1^-2*f2^-1)^2, (x*f1^3)^
2, (x*f1*f2*f1^2*f2^-1)^8, (x*f2^-1*f1^-2*f2*f1^-3)^8, (x*f2^-1*f1^-2)^8, (x*f1^-2*f2^-1)^2, (x*f1^-1*f2*f1*f2^-1*f1^2*f2)^8, (x*f1*f2^-1*f1^2*f2^2*f1^-1)^2,
y^3, (y^-1 * f4 * f3)^2, f4^2 * y^-1 * f3^-1 * y* f3, f4 * f3 * y * f3^-1 * y^-1 * f4, (f4^-1 * f3^-1 * y)^2, f4^8, (f4^-1 * f3)^4, f4^-2 * y^-1 * f4^-1 * f3 * y^-1 * f4^-1 * f3, (f4^-1 * y^-1)^4, (f4^-1 * y^-1 * f4 * y^-1)^2, (f3 * f4 * f3 * f4^-1)^2, f4 * y * f4^-1 * y^-1 * f3^-1 * f4 * y * f4^-1 * f3, f4^-1 * y^-1 * f4 * y * f3 * f4^-1 * y^-1 * f4 * f3^-1,
y * f4^-1 * y^-1 * f4^-1 * f3^-1 * f4^-1 * f3^-1 * f4^-1 * y * f4^2, f4^-1 * f3 * f4^-1 * y^-1 * f4 * y * f4 * f3^-1 * f4 * y * f4 * f3^-1, y^-1 * f4^-1 * y * f3^-1 * f4^2 * f3^-1 * y^-1 * f4^-2 * f3^-1 * f4 * f3 * f4^-1 * y^-1 * f3 * f4^-1, f3^-1 * f4 * y^-1 * f4 * f3^-1 * f4 * y^-1 * f4 * f3^-1 * f4 * y^-1 * f4 * f3^-1 * f4 * f3 * f4^-2 * f3 * f4, (f3 * y)^12];;
From minghuiliu2006 at gmail.com Sat Mar 23 21:02:48 2019
From: minghuiliu2006 at gmail.com (Minghui Liu)
Date: Sat, 23 Mar 2019 17:02:48 -0400
Subject: [GAP Forum] Symmetrising presented group from a given presentation
Message-ID:
Dear GAP users,
I have the following question on inputting symmetrised relations in a group.
Let G be a group generated by x_1, x_2, x_3, x_4 with one relation for
example x_1*x_2*x_3^(-1)*x_4^(-2). Now I wish to let the symmetric group
S_4 on 4 letters acts on this relation and therefore obtain a total of
4!=24 relators. For example, one of the obtained relator is
x_2*x_3*x_4^(-1)*x_1^(-2). Is there any easy way for me to write all 24
relators in GAP?
Thank you!
Minghui
From sk239 at st-andrews.ac.uk Sat Mar 23 21:26:45 2019
From: sk239 at st-andrews.ac.uk (Stefan Kohl)
Date: Sat, 23 Mar 2019 21:26:45 +0000
Subject: [GAP Forum] Symmetrising presented group from a given
presentation
In-Reply-To:
References:
Message-ID:
Dear Minghui,
You can proceed as follows:
gap> F := FreeGroup(4);
gap> x := GeneratorsOfGroup(F);
[ f1, f2, f3, f4 ]
gap> S4 := SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> w := x[1]*x[2]*x[3]^-1*x[4]^-2; # your sample word
f1*f2*f3^-1*f4^-2
gap> rels := List(AsList(S4),g->MappedWord(w,x,Permuted(x,g))); # the 24 relators
[ f1*f2*f3^-1*f4^-2, f1*f2*f4^-1*f3^-2, f1*f3*f2^-1*f4^-2, f1*f4*f2^-1*f3^-2,
f1*f3*f4^-1*f2^-2, f1*f4*f3^-1*f2^-2, f2*f1*f3^-1*f4^-2, f2*f1*f4^-1*f3^-2,
f3*f1*f2^-1*f4^-2, f4*f1*f2^-1*f3^-2, f3*f1*f4^-1*f2^-2, f4*f1*f3^-1*f2^-2,
f2*f3*f1^-1*f4^-2, f2*f4*f1^-1*f3^-2, f3*f2*f1^-1*f4^-2, f4*f2*f1^-1*f3^-2,
f3*f4*f1^-1*f2^-2, f4*f3*f1^-1*f2^-2, f2*f3*f4^-1*f1^-2, f2*f4*f3^-1*f1^-2,
f3*f2*f4^-1*f1^-2, f4*f2*f3^-1*f1^-2, f3*f4*f2^-1*f1^-2, f4*f3*f2^-1*f1^-2 ]
Does this help you?
Best regards,
Stefan
-----------------------------------------------------------------------------
Dr. Stefan Kohl, https://stefan-kohl.github.io/
-----------------------------------------------------------------------------
________________________________
From: Minghui Liu
Sent: Saturday, March 23, 2019 10:02:48 PM
To: forum at gap-system.org
Subject: [GAP Forum] Symmetrising presented group from a given presentation
Dear GAP users,
I have the following question on inputting symmetrised relations in a group.
Let G be a group generated by x_1, x_2, x_3, x_4 with one relation for
example x_1*x_2*x_3^(-1)*x_4^(-2). Now I wish to let the symmetric group
S_4 on 4 letters acts on this relation and therefore obtain a total of
4!=24 relators. For example, one of the obtained relator is
x_2*x_3*x_4^(-1)*x_1^(-2). Is there any easy way for me to write all 24
relators in GAP?
Thank you!
Minghui
_______________________________________________
Forum mailing list
Forum at gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum