From sal at dcs.st-and.ac.uk Mon Jan 2 16:08:18 2006 From: sal at dcs.st-and.ac.uk (Steve Linton) Date: Thu Jan 5 13:04:32 2006 Subject: [GAP Forum] Fw: [GAP Support] Itanium Message-ID: <20060102160818.577e85ea@localhost.localdomain> Dear GAP Forum, Dima Pasechnik reported problems compiling GAP for the Itanium processor. This is a known problem, see http://www.gap-system.org/Faq/Hardware-OS/hardware-os8.html If anyone wants to work on this, I can give you some more clues, but that page summarises the issue. A non-optimising compile usually works (but very slowly). Steve -- Steve Linton School of Computer Science & Centre for Interdisciplinary Research in Computational Algebra University of St Andrews Tel +44 (1334) 463269 http://www.dcs.st-and.ac.uk/~sal Fax +44 (1334) 463278 From welcometn at yahoo.fr Tue Jan 3 12:57:37 2006 From: welcometn at yahoo.fr (Saber) Date: Thu Jan 5 13:04:32 2006 Subject: [GAP Forum] colored tetrahedron Message-ID: <20060103125737.23179.qmail@web26801.mail.ukl.yahoo.com> Dear GAP-Forum, i want to give all the possibilities to color the nodes (up to 4 colors) of a regular tetrahedron: 1) related to the symmetric group $S_4$. 2) related to the alternating group $A_4$. is there any idea to draw this in (x)gap? thanks in advance, Saber. ___________________________________________________________________________ Nouveau : t?l?phonez moins cher avec Yahoo! Messenger ! D?couvez les tarifs exceptionnels pour appeler la France et l'international. T?l?chargez sur http://fr.messenger.yahoo.com From wdj at usna.edu Wed Jan 4 12:53:06 2006 From: wdj at usna.edu (David Joyner) Date: Thu Jan 5 13:04:32 2006 Subject: [GAP Forum] guava 2.5 beta2 Message-ID: <43BBC532.2010500@usna.edu> Hello GAP people: I have posted a second beta version of GUAVA 2.5 on the GAP webpage http://cadigweb.ew.usna.edu/~wdj/gap/GUAVA/ (it is the link guava2.5.tar.gz near the top). Because of the function Peter Mayr and I wrote (see below), one major difference is that SONATA must be loaded to install GUAVA. This doesn't bother me but might bother others. Opinions or comments on this? Here are the changes: Version 2.5: (1-2006) o Fixed undesired feature in Decodeword (spotten by Cayanne McFarlane). o Added MinimumWeightWords to manual; modified GAP code for MinimumWeightWords to speed it up. o Modified CheckMatCode to "Set" *mutable* generator and check matrices. o Added BitFlipDecoder, a fast decoder for LDPC codes, written with Gordon McDonald. o Added GuavaVersion and guava_version o Added FerrorDesignCode, written with Peter Mayr at Linz (one of the SONATA authors). This requires SONATA. o Miscellaneous additions to the GUAVA manual. Again, if there are problems, please email me. Modulo installation problems which might arise, this is the planned next release. - David Joyner From kohl at mathematik.uni-stuttgart.de Mon Jan 9 14:56:50 2006 From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl) Date: Mon Jan 9 14:57:03 2006 Subject: [GAP Forum] RCWA 1.3 Message-ID: <43C279B2.8040304@mathematik.uni-stuttgart.de> Dear Forum, This is to announce the release of RCWA 1.3. The RCWA package provides methods for computing in certain infinite permutation groups acting on the integers. Since the initial release of version 1.0 in spring last year, significant functionality has been added. As usual, the RCWA package is available at http://www.gap-system.org/Packages/rcwa.html. Wishing you fun and success using this package, Stefan Kohl From bob.heffernan at gmail.com Mon Jan 9 18:25:29 2006 From: bob.heffernan at gmail.com (Robert Heffernan) Date: Mon Jan 9 18:26:38 2006 Subject: [GAP Forum] computing automorphism groups Message-ID: <6d9a83e90601091025u1e22c2bcsf74a5f536ba50a42@mail.gmail.com> Hi, I'm computing the automorphism groups of finite groups (particularly,finite perfect groups) but GAP seems to be taking an awful long timeto do this. For example, the following has been running for several hours now: A:=AutomorphismGroup(PerfectGroup(168,1)); The machine I am running this on is quite decently specced. Also, Istarted gap with the following:gap -o 1000Mto give GAP plenty of memory to work with. Should I be expecting such a delay? thank you,Bob From hulpke at math.colostate.edu Mon Jan 9 18:40:01 2006 From: hulpke at math.colostate.edu (Alexander Hulpke) Date: Mon Jan 9 18:40:28 2006 Subject: [GAP Forum] computing automorphism groups In-Reply-To: <6d9a83e90601091025u1e22c2bcsf74a5f536ba50a42@mail.gmail.com> References: <6d9a83e90601091025u1e22c2bcsf74a5f536ba50a42@mail.gmail.com> Message-ID: <2F415FC2-8945-4C10-84BF-F63DD6736EB1@math.colostate.edu> Dear GAP Forum, Rober Heffernan wrot: > I'm computing the automorphism groups of finite groups > (particularly,finite perfect groups) but GAP seems to be taking an > awful long timeto do this. > For example, the following has been running for several hours now: > A:=AutomorphismGroup(PerfectGroup(168,1)); > The machine I am running this on is quite decently specced. Also, > Istarted gap with the following:gap -o 1000Mto give GAP plenty of > memory to work with. PerfectGroup returns by default a finitely presented group. An automorphism group calculation for these is likely to be very inefficient. If you use a permutation representation instead you are likely to get a much better performance: A:=AutomorphismGroup(PerfectGroup(IsPermGroup,168,1)); Best wishes, Alexander Hulpke From vdabbagh at math.carleton.ca Tue Jan 10 05:21:47 2006 From: vdabbagh at math.carleton.ca (Vahid Dabbaghian-Abdoly) Date: Tue Jan 10 05:23:54 2006 Subject: [GAP Forum] Repsn 2.0. package release Message-ID: Dear GAP Forum, I am pleased to announce the release of Repsn 2.0. The modifications include: - computing constituents of reducible representations. - computing a block diagonal representation equivalent to a given reducible representation. - improving the search method for finding character subgroups. - a bugfix in the extending representation functions. The Repsn package is available at the following pages; http://www.gap-system.org/Packages/repsn.html http://www.math.carleton.ca/~vdabbagh/gap/repsn.html Please send bug reports, suggestions and other comments to vdabbagh@math.carleton.ca. Best wishes, Vahid Dabbaghian-Abdoly From alice at maths.uwa.edu.au Wed Jan 11 10:48:19 2006 From: alice at maths.uwa.edu.au (Alice C. Niemeyer) Date: Wed Jan 11 10:48:52 2006 Subject: [GAP Forum] colored tetrahedron In-Reply-To: <20060103125737.23179.qmail@web26801.mail.ukl.yahoo.com> References: <20060103125737.23179.qmail@web26801.mail.ukl.yahoo.com> Message-ID: Dear Saber, It is currently not possible to draw tetrahedra in different colours using Xgap. You might have to find a different graphical package to do this. However, you can use GAP to count the number of different colourings of a tetrahedron for the groups A_n or S_n. You can find an exposition of the basic ideas on the GAP web site under Documentation -> Teaching -> Lectures and Workshops by Alice Niemeyer -> Lecture 3. Accompanying these lectures are also some GAP functions. Another reference is N. G. de Bruijn, in {\it Selecta Mathematica, III}, 1--26. Heidelberger Taschenb\"ucher, 86, Springer, Berlin, 1971; All the best, Alice Niemeyer. =*=*=*=*=*=*=*=*=*=*=*=M=*=*=*=*M*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Alice C. Niemeyer =@\___) =@\ School of Mathematics & Statistics alice@maths.uwa.edu.au \_ ( ( \ University of Western Australia +61-8-6488 3890 .| .| .|_(\_) Nedlands, WA 6009, Australia. =*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* WWW: http://www.maths.uwa.edu.au/~alice/ On Tue, 3 Jan 2006, Saber wrote: >Dear GAP-Forum, > >i want to give all the possibilities to color the >nodes (up to 4 colors) of a regular tetrahedron: >1) related to the symmetric group $S_4$. >2) related to the alternating group $A_4$. > >is there any idea to draw this in (x)gap? > > >thanks in advance, >Saber. > > > > > > >___________________________________________________________________________ >Nouveau : t?l?phonez moins cher avec Yahoo! Messenger ! D?couvez les tarifs exceptionnels pour appeler la France et l'international. >T?l?chargez sur http://fr.messenger.yahoo.com > >_______________________________________________ >Forum mailing list >Forum@mail.gap-system.org >http://mail.gap-system.org/mailman/listinfo/forum > > > From raghu_juliet at rediffmail.com Thu Jan 12 07:56:03 2006 From: raghu_juliet at rediffmail.com (raghunathan) Date: Thu Jan 12 10:43:12 2006 Subject: [GAP Forum] Class structure identification of symmetric groups Message-ID: <20060112075603.19345.qmail@webmail30.rediffmail.com> Hello GAP forum, Is there a way to find the different classes of permutations corresponding to different columns of the character table of a symmetric group? For ex., The character table of S3 is displayed by GAP as 2 1 1 . 3 1 . 1 1a 2a 3a 2P 1a 1a 3a 3P 1a 2a 1a X.1 1 -1 1 X.2 2 . -1 X.3 1 1 1 Is there a way to relate the symbols displayed just above the table i.e., 1a 2a 3a etc., to the different classes (1)(2)(3),(1)(2,3) &(1,2,3) of SymmetricGroup(3)? Thanks, Raghunathan,R. ? From welcometn at yahoo.fr Thu Jan 12 15:24:28 2006 From: welcometn at yahoo.fr (Saber) Date: Thu Jan 12 15:24:58 2006 Subject: [GAP Forum] colored tetrahedron In-Reply-To: Message-ID: <20060112152428.82236.qmail@web26815.mail.ukl.yahoo.com> Dear Alice Niemeyer, thank you very much for your help. i have added a link to your program. Saber Mbarek Algebra und Number Theory University of Siegen, Germany www.math.uni-siegen.de/~mbarek --- "Alice C. Niemeyer" a ?crit?: > Dear Saber, > > It is currently not possible to draw tetrahedra in > different colours > using Xgap. You might have to find a different > graphical package to do > this. > > However, you can use GAP to count the number of > different colourings > of a tetrahedron for the groups A_n or S_n. You can > find an exposition > of the basic ideas on the GAP web site under > Documentation -> Teaching -> Lectures and Workshops > by Alice Niemeyer -> > Lecture 3. > Accompanying these lectures are also some GAP > functions. > > Another reference is > N. G. de Bruijn, in {\it Selecta Mathematica, III}, > 1--26. Heidelberger > Taschenb\"ucher, 86, Springer, Berlin, 1971; > > All the best, Alice Niemeyer. > > > =*=*=*=*=*=*=*=*=*=*=*=M=*=*=*=*M*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* > Alice C. Niemeyer =@\___) =@\ School of > Mathematics & Statistics > alice@maths.uwa.edu.au \_ ( ( \ University of > Western Australia > +61-8-6488 3890 .| .| .|_(\_) Nedlands, WA > 6009, Australia. > =*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* > WWW: http://www.maths.uwa.edu.au/~alice/ > > On Tue, 3 Jan 2006, Saber wrote: > > >Dear GAP-Forum, > > > >i want to give all the possibilities to color the > >nodes (up to 4 colors) of a regular tetrahedron: > >1) related to the symmetric group $S_4$. > >2) related to the alternating group $A_4$. > > > >is there any idea to draw this in (x)gap? > > > > > >thanks in advance, > >Saber. > > > > > > > > > > > > > >___________________________________________________________________________ > >Nouveau : t?l?phonez moins cher avec Yahoo! > Messenger ! D?couvez les tarifs exceptionnels pour > appeler la France et l'international. > >T?l?chargez sur http://fr.messenger.yahoo.com > > > >_______________________________________________ > >Forum mailing list > >Forum@mail.gap-system.org > >http://mail.gap-system.org/mailman/listinfo/forum > > > > > > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > ___________________________________________________________________________ Nouveau : t?l?phonez moins cher avec Yahoo! Messenger ! D?couvez les tarifs exceptionnels pour appeler la France et l'international. T?l?chargez sur http://fr.messenger.yahoo.com From laurent.bartholdi at gmail.com Thu Jan 12 18:24:28 2006 From: laurent.bartholdi at gmail.com (Laurent Bartholdi) Date: Thu Jan 12 18:25:51 2006 Subject: [GAP Forum] weird bug with wreath products Message-ID: <1ff637850601121024r3cff4ecbn9d56d784905bc951@mail.gmail.com> hello world, it seems to me that there's a problem with wreath products: GAP4, Version: 4.4.5 of 13-May-05, i686-pc-linux-gnu-gcc gap> G := WreathProduct(CyclicGroup(3),Group((1,2,3),(4,5,6))); gap> Gc := Image(IsomorphismPcGroup(G)); Group([ f1, f2, f3, f4, f5 ]) gap> Size(Gc); 243 gap> G := WreathProduct(CyclicGroup(IsPermGroup,3),Group((1,2,3),(4,5,6))); gap> Gc := Image(IsomorphismPcGroup(G)); Group([ f1, f2, f3, f4, f5, f6, f7, f8 ]) gap> Size(Gc); 6561 -- Laurent Bartholdi \ laurent.bartholdigmailcom EPFL SB SMA IMB MAD \ T?l?phone: +41 21-6930380 CH-1015 Lausanne, Switzerland \ Fax: +41 21-6930385 From thoffman at coastal.edu Thu Jan 12 19:20:15 2006 From: thoffman at coastal.edu (Tom Hoffman) Date: Thu Jan 12 19:23:31 2006 Subject: [GAP Forum] Special unitary groups Message-ID: <1137093615.43c6abef6b711@mail.coastal.edu> Does anyone know how to get a permutation representation of a special unitary group in GAP? The manual says that the command SpecialUnitaryGroup will take a filter as its first argument but when I tried this I got the following GAP4, Version: 4.4.6 of 02-Sep-2005, i686-pc-linux-gnu-gcc gap> SpecialUnitaryGroup(IsPermGroup, 4,2); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `SpecialUnitaryGroupCons' on 3 arguments\ called from SpecialUnitaryGroupCons( arg[1], arg[2], arg[3] ) called from ( ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> Any help would be appreciated. Tom Dr. Thomas R. Hoffman Department of Mathematics and Statistics Coastal Carolina University ----------------------------------------------------------------------- This message was sent from the Coastal Carolina University Mail System. From wdjoyner at comcast.net Thu Jan 12 19:57:50 2006 From: wdjoyner at comcast.net (David Joyner) Date: Thu Jan 12 19:54:57 2006 Subject: [GAP Forum] Special unitary groups In-Reply-To: <1137093615.43c6abef6b711@mail.coastal.edu> References: <1137093615.43c6abef6b711@mail.coastal.edu> Message-ID: <43C6B4BE.2000609@comcast.net> Try |IsomorphismPermGroup:| gap> G:=SpecialUnitaryGroup(4,2); SU(4,2) gap> iso:=IsomorphismPermGroup(G); gap> image:= Image( iso );; For more details, see section 40.2 of the reference manual. ++++++++++++++++++++++ Tom Hoffman wrote: > Does anyone know how to get a permutation representation of a special unitary > group in GAP? The manual says that the command SpecialUnitaryGroup will take a > filter as its first argument but when I tried this I got the following > > GAP4, Version: 4.4.6 of 02-Sep-2005, i686-pc-linux-gnu-gcc > gap> SpecialUnitaryGroup(IsPermGroup, 4,2); > Error, no method found! For debugging hints type ?Recovery from NoMethodFound > Error, no 1st choice method found for `SpecialUnitaryGroupCons' on 3 arguments\ > called from > SpecialUnitaryGroupCons( arg[1], arg[2], arg[3] ) called from > ( ) called from read-eval-loop > Entering break read-eval-print loop ... > you can 'quit;' to quit to outer loop, or > you can 'return;' to continue > brk> > > Any help would be appreciated. > Tom > > > Dr. Thomas R. Hoffman > Department of Mathematics and Statistics > Coastal Carolina University > > ----------------------------------------------------------------------- > This message was sent from the Coastal Carolina University Mail System. > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > > From holmespe at for.mat.bham.ac.uk Thu Jan 12 20:33:37 2006 From: holmespe at for.mat.bham.ac.uk (Petra Holmes) Date: Thu Jan 12 20:34:01 2006 Subject: [GAP Forum] Special unitary groups In-Reply-To: <1137093615.43c6abef6b711@mail.coastal.edu> Message-ID: When you know that SU(n,q) is isomorphic to PSU(n,q) (such as in your example SU(4,2)) then you can use PSU instead, which always arrives as a perm group. On Thu, 12 Jan 2006, Tom Hoffman wrote: > > Does anyone know how to get a permutation representation of a special unitary > group in GAP? The manual says that the command SpecialUnitaryGroup will take a > filter as its first argument but when I tried this I got the following > > GAP4, Version: 4.4.6 of 02-Sep-2005, i686-pc-linux-gnu-gcc > gap> SpecialUnitaryGroup(IsPermGroup, 4,2); > Error, no method found! For debugging hints type ?Recovery from NoMethodFound > Error, no 1st choice method found for `SpecialUnitaryGroupCons' on 3 arguments\ > called from > SpecialUnitaryGroupCons( arg[1], arg[2], arg[3] ) called from > ( ) called from read-eval-loop > Entering break read-eval-print loop ... > you can 'quit;' to quit to outer loop, or > you can 'return;' to continue > brk> > > Any help would be appreciated. > Tom > > > Dr. Thomas R. Hoffman > Department of Mathematics and Statistics > Coastal Carolina University > > ----------------------------------------------------------------------- > This message was sent from the Coastal Carolina University Mail System. > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > From Frank.Luebeck at math.rwth-aachen.de Thu Jan 12 23:17:02 2006 From: Frank.Luebeck at math.rwth-aachen.de (Frank =?iso-8859-1?Q?L=FCbeck?=) Date: Thu Jan 12 23:18:05 2006 Subject: [GAP Forum] Class structure identification of symmetric groups In-Reply-To: <20060112075603.19345.qmail@webmail30.rediffmail.com> References: <20060112075603.19345.qmail@webmail30.rediffmail.com> Message-ID: <20060112231702.GA4245@math.rwth-aachen.de> On Thu, Jan 12, 2006 at 07:56:03AM +0000, raghunathan wrote: > Hello GAP forum, > Is there a way to find the different classes of permutations > corresponding to different columns of the character table of a > symmetric group? > For ex., > The character table of S3 is displayed by GAP as > 2 1 1 . > 3 1 . 1 > > 1a 2a 3a > 2P 1a 1a 3a > 3P 1a 2a 1a > > X.1 1 -1 1 > X.2 2 . -1 > X.3 1 1 1 > Is there a way to relate the symbols displayed just above the table > i.e., 1a 2a 3a etc., to the different classes (1)(2)(3),(1)(2,3) &(1,2,3) > of SymmetricGroup(3)? Dear Raghunathan, dear Forum, In general it can be difficult to identify the conjugacy classes of a given group in GAP with the columns of its abstract character table. But for symmetric groups GAP can compute the character table, using the labeling of conjugacy classes and irreducible characters by partitions: gap> t := CharacterTable("Symmetric", 7); CharacterTable( "Sym(7)" ) gap> ClassParameters(t); [ [ 1, [ 1, 1, 1, 1, 1, 1, 1 ] ], [ 1, [ 2, 1, 1, 1, 1, 1 ] ], [ 1, [ 2, 2, 1, 1, 1 ] ], [ 1, [ 2, 2, 2, 1 ] ], [ 1, [ 3, 1, 1, 1, 1 ] ], [ 1, [ 3, 2, 1, 1 ] ], [ 1, [ 3, 2, 2 ] ], [ 1, [ 3, 3, 1 ] ], [ 1, [ 4, 1, 1, 1 ] ], [ 1, [ 4, 2, 1 ] ], [ 1, [ 4, 3 ] ], [ 1, [ 5, 1, 1 ] ], [ 1, [ 5, 2 ] ], [ 1, [ 6, 1 ] ], [ 1, [ 7 ] ] ] The i-th entry of ClassParameters(t) describes the class of the i-th column of t: its second component gives the cycle type of the elements in this class. There is a similar CharacterParameters(t). Remark: If G is a group in GAP then 'CharacterTable(G);' returns a table which can be asked for 'IdentificationOfConjugacyClasses', e.g.: gap> G := SymmetricGroup(20); Sym( [ 1 .. 20 ] ) gap> t := CharacterTable(G); CharacterTable( Sym( [ 1 .. 20 ] ) ) gap> IdentificationOfConjugacyClasses(t); [ 1 .. 627 ] But for bigger G GAP may not be able to compute the character table. Nevertheless, in this particular case of symmetric groups, GAP knows that it can use the efficient function mentioned above to compute the table. With best regards, Frank Luebeck -- /// Dr. Frank L?beck, Lehrstuhl D f?r Mathematik, Templergraben 64, /// \\\ 52062 Aachen, Germany \\\ /// E-mail: Frank.Luebeck@Math.RWTH-Aachen.De /// \\\ WWW: http://www.math.rwth-aachen.de/~Frank.Luebeck/ \\\ From raghu_juliet at rediffmail.com Fri Jan 13 10:18:36 2006 From: raghu_juliet at rediffmail.com (raghunathan) Date: Fri Jan 13 10:19:09 2006 Subject: [GAP Forum] Class structure identification of symmetric groups Message-ID: <20060113101836.26675.qmail@webmail50.rediffmail.com> >Dear Raghunathan, dear Forum, > >In general it can be difficult to identify the conjugacy classes of a given >group in GAP with the columns of its abstract character table. > >But for symmetric groups GAP can compute the character table, using the >labeling of conjugacy classes and irreducible characters by partitions: > >gap> t := CharacterTable("Symmetric", 7); >CharacterTable( "Sym(7)" ) >gap> ClassParameters(t); >[ [ 1, [ 1, 1, 1, 1, 1, 1, 1 ] ], [ 1, [ 2, 1, 1, 1, 1, 1 ] ], > [ 1, [ 2, 2, 1, 1, 1 ] ], [ 1, [ 2, 2, 2, 1 ] ], [ 1, [ 3, 1, 1, 1, 1 ] ], > [ 1, [ 3, 2, 1, 1 ] ], [ 1, [ 3, 2, 2 ] ], [ 1, [ 3, 3, 1 ] ], > [ 1, [ 4, 1, 1, 1 ] ], [ 1, [ 4, 2, 1 ] ], [ 1, [ 4, 3 ] ], > [ 1, [ 5, 1, 1 ] ], [ 1, [ 5, 2 ] ], [ 1, [ 6, 1 ] ], [ 1, [ 7 ] ] ] > >The i-th entry of ClassParameters(t) describes the class of the i-th column >of t: its second component gives the cycle type of the elements in this class. > >There is a similar CharacterParameters(t). > >Remark: If G is a group in GAP then 'CharacterTable(G);' returns a table >which can be asked for 'IdentificationOfConjugacyClasses', e.g.: > >gap> G := SymmetricGroup(20); >Sym( [ 1 .. 20 ] ) >gap> t := CharacterTable(G); >CharacterTable( Sym( [ 1 .. 20 ] ) ) >gap> IdentificationOfConjugacyClasses(t); >[ 1 .. 627 ] > >But for bigger G GAP may not be able to compute the character table. >Nevertheless, in this particular case of symmetric groups, GAP knows that >it can use the efficient function mentioned above to compute the table. > >With best regards, > > Frank Luebeck Respected Dr.Frank Luebeck and GAP Forum, Thank you very much for ur valuable suggestion regarding class structures of symmetric groups which can be correlated to numerical partitions of the degree of the symmetric groups.But, for a wreath product group as simple as S2[S2] whose conjugacy classes' structures as given by GAP is as gap> > [ ()^G, (3,4)^G, (1,2)(3,4)^G, (1,3)(2,4)^G, (1,3,2,4)^G ] has two classes of permutations each with two cycles of length two (1,2)(3,4) and (1,3)(2,4). Also, the sequential commands, gap>s:=SymmetricGroup(2);;w:=WreathProduct(s,s);;t:=CharacterTable(w);;ClassParameters(t); did not work.Is there a way to overcome this problem by relating the abstract symbols usually displayed above any character table given by GAP as 1a 2a 2b...etc., which in the case of S4 is as follows to the class structures? 2 3 2 3 . 2 3 1 . . 1 . 1a 2a 2b 3a 4a 2P 1a 1a 1a 3a 2b 3P 1a 2a 2b 1a 4a X.1 1 -1 1 1 -1 X.2 3 -1 -1 . 1 X.3 2 . 2 -1 . X.4 3 1 -1 . -1 X.5 1 1 1 1 1 Thanks, Raghunathan,R., M.Sc.Chemistry, Department of Chemistry, Indian Institute of Technology Madras, Chennai-36, India. From Goetz.Pfeiffer at NUIGalway.ie Fri Jan 13 12:44:50 2006 From: Goetz.Pfeiffer at NUIGalway.ie (Goetz Pfeiffer) Date: Fri Jan 13 12:45:12 2006 Subject: [GAP Forum] Class structure identification of symmetric groups In-Reply-To: <20060113101836.26675.qmail@webmail50.rediffmail.com> References: <20060113101836.26675.qmail@webmail50.rediffmail.com> Message-ID: <20060113124450.GA12957@schmidt.nuigalway.ie> Dear Raghunathan, dear Forum, the function 'CharacterTableWreathSymmetric' constructs the character table of the wreath product of a group G with the symmetric group on n points from the character table of G and supplies it with lists of partitions as labels for the classes (and the characters). The underlying algorithm is described in Character Tables of Weyl Groups in GAP. Bayreuther Math. Schr. 47 (1994), 165-222. (http://schmidt.nuigalway.ie/~goetz/pub/ctweyl.html) Goetz Pfeiffer On Fri, Jan 13, 2006 at 10:18:36AM +0000, raghunathan wrote: > Respected Dr.Frank Luebeck and GAP Forum, > Thank you very much for ur valuable suggestion regarding class structures of symmetric groups which can be correlated to numerical partitions of the degree of the symmetric groups.But, for a wreath product group as simple as S2[S2] whose conjugacy classes' structures as given by GAP is as > > gap> > [ ()^G, (3,4)^G, (1,2)(3,4)^G, (1,3)(2,4)^G, (1,3,2,4)^G ] > > has two classes of permutations each with two cycles of length two (1,2)(3,4) and (1,3)(2,4). Also, the sequential commands, > > gap>s:=SymmetricGroup(2);;w:=WreathProduct(s,s);;t:=CharacterTable(w);;ClassParameters(t); > did not work.Is there a way to overcome this problem by relating the abstract symbols usually displayed above any character table given by GAP as 1a 2a 2b...etc., which in the case of S4 is as follows to the class structures? > > 2 3 2 3 . 2 > 3 1 . . 1 . > > 1a 2a 2b 3a 4a > 2P 1a 1a 1a 3a 2b > 3P 1a 2a 2b 1a 4a > > X.1 1 -1 1 1 -1 > X.2 3 -1 -1 . 1 > X.3 2 . 2 -1 . > X.4 3 1 -1 . -1 > X.5 1 1 1 1 1 > > Thanks, > Raghunathan,R., > M.Sc.Chemistry, > Department of Chemistry, > Indian Institute of Technology Madras, > Chennai-36, > India. > > > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum ------------------------------------------------------------------------- Goetz.Pfeiffer@NUIGalway.ie http://schmidt.nuigalway.ie/~goetz/ National University of Ireland, Galway. phone +353-91-49-3591 From vdabbagh at math.carleton.ca Mon Jan 16 00:23:06 2006 From: vdabbagh at math.carleton.ca (Vahid Dabbaghian-Abdoly) Date: Mon Jan 16 00:23:24 2006 Subject: [GAP Forum] substitution Message-ID: Dear GAP Forum, I have a dense matrix of large dimensions with entries in the cyclotomic field CF(24) and in this matrix I would like to replace the primitive element E(24) by a prime number p. Do you know any method for this substitution? Best regards, Vahid From sh_fouladi at yahoo.com Mon Jan 16 08:31:16 2006 From: sh_fouladi at yahoo.com (shirin fouladi) Date: Mon Jan 16 08:32:36 2006 Subject: [GAP Forum] find some information Message-ID: <20060116083116.40318.qmail@web53303.mail.yahoo.com> Dear Gap Forum. I Read in mathscinet a summery of this paper: " th.Exarchakos, LA-group.Math.Soc.Japan.33(1981)185-190" but unfortunately this jornal is not available in my country and I couldnot find the e-mail of writer. I am very thankful if anyone tell me any information. Best regards. Shirin fouladi. Faculty of Mathematical Sciences and Computer Engineering University For Teacher Education. --------------------------------- Yahoo! Photos Got holiday prints? See all the ways to get quality prints in your hands ASAP. From laurent.bartholdi at gmail.com Tue Jan 17 14:07:51 2006 From: laurent.bartholdi at gmail.com (Laurent Bartholdi) Date: Tue Jan 17 14:08:11 2006 Subject: [GAP Forum] CanComputeSize Message-ID: <1ff637850601170607u72f6474l931939b2e91a9a43@mail.gmail.com> Hi, I try to understand Size(), HasSize() and CanComputeSize(). It seems very strange to me that gap> l := [];; gap> HasSize(l); false gap> CanComputeSize(l); false isn't there a missing method/attribute here? I would expect that all dense lists have these attributes set. However InstallTrueMethod(CanComputeSize,IsDenseList); doesn't change the results of the code above. My interest is that I want to display an object either by its size (if it exists or is easy to compute) or as an object by itself (in other cases). Thanks, Laurent -- Laurent Bartholdi \ laurent.bartholdigmailcom EPFL SB SMA IMB MAD \ T?l?phone: +41 21-6930380 CH-1015 Lausanne, Switzerland \ Fax: +41 21-6930385 From joachim.neubueser at math.rwth-aachen.de Tue Jan 17 16:23:30 2006 From: joachim.neubueser at math.rwth-aachen.de (Joachim Neubueser) Date: Tue Jan 17 16:23:43 2006 Subject: [jneubues: Re: [GAP Forum] find some information] Message-ID: <20060117162330.GB8114@math.rwth-aachen.de> ----- Forwarded message from jneubues ----- To: shirin fouladi Subject: Re: [GAP Forum] find some information Reply-To: Joachim Neubueser Dear Shirin Fouladi, On Mon, Jan 16, 2006 at 12:31:16AM -0800, you wrote to the GAP Forum: > Dear Gap Forum. > I Read in mathscinet a summery of this paper: > " th.Exarchakos, LA-group.Math.Soc.Japan.33(1981)185-190" > but unfortunately this jornal is not available in my country > and I couldnot find the e-mail of writer. The e-mail address of the writer is texarcha@primedu.uoa.gr The paper is probably available in our library, if you cannot get it from the author, just send me your postal address and I will try to send you a Xerox. But please do understand that the GAP Forum normally is not the address for such requests. With kind regards Joachim Neubueser ---------------------------------------------------------- Prof. em. J. Neubueser LDFM, RWTH Aachen Germany ------------------------------------------------------------ ----- End forwarded message ----- From hulpke at math.colostate.edu Wed Jan 18 16:56:09 2006 From: hulpke at math.colostate.edu (Alexander Hulpke) Date: Wed Jan 18 16:56:25 2006 Subject: [GAP Forum] weird bug with wreath products In-Reply-To: <1ff637850601121024r3cff4ecbn9d56d784905bc951@mail.gmail.com> References: <1ff637850601121024r3cff4ecbn9d56d784905bc951@mail.gmail.com> Message-ID: <238A8206-0C6C-4707-8CDE-AC68382BC7BC@math.colostate.edu> Dear GAP- Forum, On Jan 12, 2006, at 11:24 , Laurent Bartholdi wrote: > > it seems to me that there's a problem with wreath products: > > GAP4, Version: 4.4.5 of 13-May-05, i686-pc-linux-gnu-gcc > gap> G := WreathProduct(CyclicGroup(3),Group((1,2,3),(4,5,6))); > > gap> Gc := Image(IsomorphismPcGroup(G)); > Group([ f1, f2, f3, f4, f5 ]) > gap> Size(Gc); > 243 Thank you for reporting this bug. The problem arises if the group H in G\wr H is not acting transitively. In this case GAP might miss some generators for the base of the product. This will be corrected in the next bugfix, please write me privately if you want a workaround now. Best wishes and many thanks! Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hulpke@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke From thomas.breuer at math.rwth-aachen.de Wed Jan 18 18:07:52 2006 From: thomas.breuer at math.rwth-aachen.de (Thomas Breuer) Date: Wed Jan 18 18:08:34 2006 Subject: [GAP Forum] CanComputeSize Message-ID: <20060118180752.C9667777D4@altair.math.rwth-aachen.de> Dear GAP Forum, Laurent Bartholdi wrote > I try to understand Size(), HasSize() and CanComputeSize(). It seems very > strange to me that > > gap> l := [];; > gap> HasSize(l); > false > gap> CanComputeSize(l); > false > > isn't there a missing method/attribute here? I would expect that all dense > lists have these attributes set. However > > InstallTrueMethod(CanComputeSize,IsDenseList); > > doesn't change the results of the code above. > > My interest is that I want to display an object either by its size (if > it exists or > is easy to compute) or as an object by itself (in other cases). According to the GAP Reference Manual, - the operation `Size' is applicable to domains and lists (see Chapter "Collections"), - the filter `HasSize' is `true' for an object if the `Size' value is known (See Section "Setter and Tester for Attributes"), and - the filter `CanComputeSize' indicates whether it is not too complicated to compute the `Size' value of a domain (see Section "Tests for the Availability of Methods"). The term ``known'' in the second item means that it is very cheap to get the value when `Size' is called (see Section "Attributes"); except perhaps in special cases, this means that the object actually stores its `Size' value, and that the object lies in the filter `IsAttributeStoringRep'; then this value has been computed using `Size' or has been set using `SetSize'. In principle, it would be possible to set `HasSize' to `true' for internally represented lists; currently this is not the case. `CanComputeSize' was not designed as a filter for lists. Again, in principle it could be set automatically also for internally represented lists. The implication from `IsDenseList' to `CanComputeSize' does not work for internally represented lists because these lists do not carry around their individual types: Only a small number of types is supported for these lists, and `CanComputeSize' is not involved in these types. Thanks to Laurent for these suggestions how to improve the behaviour of GAP. (I am not sure whether these rather technical questions are of general interest for the GAP Forum. Perhaps the address support@gap-system.org would be more appropriate.) All the best, Thomas From thomas.breuer at math.rwth-aachen.de Wed Jan 18 18:26:01 2006 From: thomas.breuer at math.rwth-aachen.de (Thomas Breuer) Date: Wed Jan 18 18:26:27 2006 Subject: [GAP Forum] substitution Message-ID: <20060118182601.6401E777D4@altair.math.rwth-aachen.de> Dear GAP Forum, Vahid Dabbaghian-Abdoly wrote > I have a dense matrix of large dimensions with entries in the cyclotomic > field CF(24) and in this matrix I would like to replace the primitive > element E(24) by a prime number p. > Do you know any method for this substitution? If only one value shall be replaced by another value and all other values in the matrix shall remain unchanged, a short solution is the following. mat:= ...; # the matrix, i.e., list of lists old:= ...; # the value that shall be replaced new:= ...; # the value that shall replace it replace:= function( value ) if value = old then return new; fi; return value; end; List( mat, row -> List( row, replace ) ); Another possible interpretation of replacement would be that all entries of the given matrix over `CF(24)' shall be replaced by the images under a linear map (or a ring homomorphism that is defined by the image of `E(24)'). The replacement by a prime mentioned in the question is not of that kind, but if one is interested in this then one can use the GAP function `CoeffsCyc' to compute the (rational) coefficients of an element `x' in `CF(n)' w.r.t. a basis of `CF(n)' that consists of certain powers of `E(n)'. `CoeffsCyc( x, n )' is a list of length `n' in which the entry at position `i' is the coefficient of `E(n)^i'. (See "CoeffsCyc" in the GAP Reference Manual, more about the basis used can be found in the manual section "Integral Bases of Abelian Number Fields".) All the best, Thomas From dutour at liga.ens.fr Thu Jan 19 07:42:32 2006 From: dutour at liga.ens.fr (Mathieu Dutour) Date: Thu Jan 19 09:38:15 2006 Subject: [GAP Forum] Function demand Message-ID: <20060119074232.GA25528@orge.ens.fr> Dear Gap forum, there are two functions, which are reasonably basic, which would perhaps be useful to have in GAP: ---Pfaffian of an antisymmetric matrix. ---sylvester inertia coefficients of a symmetric matrix. I can contribute myself those functions, but the code may not be up to the standard of GAP. Mathieu -- Mathieu Dutour Sikiric Researcher in Math Tel. (+972)2 65 84 103 and Computer Science Fax. (+972)2 56 30 702 Einstein Institute of Mathematics E-mail: Mathieu.Dutour@ens.fr Hebrew University of Jerusalem http://www.liga.ens.fr/~dutour Israel From r_n_tsai at yahoo.com Fri Jan 20 21:22:28 2006 From: r_n_tsai at yahoo.com (R.N. Tsai) Date: Fri Jan 20 21:22:46 2006 Subject: [GAP Forum] universal enveloping algebras Message-ID: <20060120212228.53035.qmail@web33704.mail.mud.yahoo.com> Dear gap forum, I'm having difficulty in manipulating elements of the universal enveloping algebra of a Lie algebra. This simple example brings out the problem : Test:=function()local L,UL,g,x,d,t,e,f,h,a1,a2,a3,M,emb; L:=SimpleLieAlgebra("A",1,Rationals); UL:=UniversalEnvelopingAlgebra(L); g:=GeneratorsOfAlgebraWithOne(UL); d:=g[1];x:=g[2];t:=g[3]; a1:=d*x-x*d;Print(" [d,x] ",a1,"\n"); e:=x+d;f:=x-d;h:=f*e; a2:=h*e-e*h;Print(" [h,f] ",a2,"\n"); a3:=h*f-f*h;Print(" [h,e] ",a3,"\n"); M:=FreeMagmaRing(Rationals,UL); emb:=Embedding(UL,M); end; when executed this gives : gap> Read("Test.g"); gap> Test(); [d,x] [(1)*x.3] [h,f] [(-4)*x.1+(-2)*x.1*x.3+(4)*x.2+(-2)*x.2*x.3] [h,e] [(-2)*x.1*x.3+(2)*x.2*x.3] Error, this case will eventually be handled by the Vector Enumerator which is not available yet called from OperationAlgebraHomomorphism( A, [ [ Zero( A ) ] ], OnRight ) called from IsomorphismMatrixFLMLOR( A ) called from IsFiniteDimensional( V ) called from IsFinite( V ) called from GeneratorsOfMagma( M ) called from ... Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> If there's another way to map the generators of UL such that : x -> x d -> d t -> 1 so that [d,x]=1 and not [d,x]=t, then this would suffice for what I'm doing. I am running "GAP4, Version 4.4.6 of 02-Sep-2005, i686-pc-cygwin-gcc" Thanks for you help. R.N. --------------------------------- Yahoo! Photos ? Showcase holiday pictures in hardcover Photo Books. You design it and we?ll bind it! From degraaf at science.unitn.it Mon Jan 23 09:52:24 2006 From: degraaf at science.unitn.it (Willem De Graaf) Date: Mon Jan 23 09:52:49 2006 Subject: [GAP Forum] universal enveloping algebras In-Reply-To: <20060120212228.53035.qmail@web33704.mail.mud.yahoo.com> References: <20060120212228.53035.qmail@web33704.mail.mud.yahoo.com> Message-ID: <43D4A758.3050109@science.unitn.it> Dear R.N. Tsai, You asked > > If there's another way to map the generators of UL such that : > x -> x > d -> d > t -> 1 > so that [d,x]=1 and not [d,x]=t, then this would suffice for what I'm doing. >I am running "GAP4, Version 4.4.6 of 02-Sep-2005, i686-pc-cygwin-gcc" > Thanks for you help. > > > As far as I am aware, there is currently no way in GAP for doing this, because there are no constructions of algebras with generators that satisfy the ralations you indicate. Also, I am not exactly sure what you want. There is no algebra homomorphism that does the indicated thing: in the universal enveloping algebra we also have the relation dt-td=-2d. So if you map t to 1 by an algebra homomorphism, then you have to map d to 0. All the best, Willem de Graaf From r_n_tsai at yahoo.com Tue Jan 24 00:45:10 2006 From: r_n_tsai at yahoo.com (R.N. Tsai) Date: Tue Jan 24 00:46:10 2006 Subject: [GAP Forum] universal enveloping algebras In-Reply-To: <43D4A758.3050109@science.unitn.it> Message-ID: <20060124004510.14425.qmail@web33701.mail.mud.yahoo.com> Dear gap forum and Willem, Thanks for your response. Maybe my example made things more complicated instead of clarifying them. I was hoping to find an equivalent to "CoefficientsAndMagmaElements" that would work with universal enveloping algebras; with that I could map the algebra elements to anything I want. Fortunately I was pointed by email to gap code written by Jan Draisma that defines Weyl Algebras. This actually provides the ability to do the calculations I had in mind in a much better setting so I'll switch to using that. Thanks again for your help and for Jan Draisma for very useful code. R.N. --------------------------------- What are the most popular cars? Find out at Yahoo! Autos From ms-swissoft at arcor.de Thu Jan 26 16:22:33 2006 From: ms-swissoft at arcor.de (Michael Schweitzer) Date: Thu Jan 26 16:22:45 2006 Subject: [GAP Forum] How to identify a group Message-ID: <000601c62294$b772dc20$2101a8c0@SWISSOFT> Dear forum members, given a group G of order n (given by generators). Is GAP able to identify the group by name or as the group of symmetries of some geometric object? For example: I define G such that G is isomorphic to A5. Can I ask GAP: which group is G? And GAP answers: A5- which is, for example, the symmetry group of the icosahedron. That is, does GAP contain a database of finite groups of small orders ( < several hundrets, say) which includes information about the transformation group aspect: this group, among other things, is the symmetry group of X or operates in a natural manner on X (I know that GAP does contain a database of small groups - but is this kind of information stored there?). The group in question is of order 432 with generators g1 := (4,6,5)(7,8,9) and g2 := (1,7,2,4,6,9,5,3) Regards, Michael Schweitzer Michael Schweitzer Alt-Heiligensee 51 A 13503 Berlin email: ms-swissoft@arcor.de From klin at cs.bgu.ac.il Thu Jan 26 17:39:50 2006 From: klin at cs.bgu.ac.il (Mikhail Klin) Date: Thu Jan 26 17:39:37 2006 Subject: [GAP Forum] How to identify a group In-Reply-To: <000601c62294$b772dc20$2101a8c0@SWISSOFT> Message-ID: Dear Michael, GAP may identify your group or as a group of order 432, or as a transitive group of degree 9, however it does not have requested catalogues of symmetries of geometrical or combinatorial structures. In fact, your group is the automorphism group of the affine plane of order 3. Moreover, this plane has is in a sense most famous labelling. Best regards, Mikhail ******************************************************************** Dr. Mikhail Klin Department of Mathematics Ben-Gurion University of the Negev P.O.Box 653, Beer Sheva 84105, Israel Tel: (0)8/6477-802 (office) (0)8/641-37-15 (home) Fax: +972-(0)8/6477-648 e-mail: klin@cs.bgu.ac.il On Thu, 26 Jan 2006, Michael Schweitzer wrote: > Dear forum members, > > given a group G of order n (given by generators). Is GAP > able to identify the group by name or as the > group of symmetries of some geometric object? > > For example: I define G suchthat G is isomorphic to A5. Can I ask GAP: > which group is G? And GAP answers: A5- which is,for example, > the symmetry group of the icosahedron. > > That is, does GAP contain a database of finite groups of > small orders ( < several hundrets, say) which includes > information about the transformation group aspect: this > group, among other things, is the symmetry group of X or > operates in a natural manner on X (I know that GAP > does contain a database of small groups - but is this kind > of information stored there?). > > The group in question is of order 432 with generators > > g1 := (4,6,5)(7,8,9) andg2 := (1,7,2,4,6,9,5,3) > > > Regards, > Michael Schweitzer > > > Michael Schweitzer > Alt-Heiligensee 51 A > 13503 Berlin > email: ms-swissoft@arcor.de > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > From ndroock1 at gmail.com Fri Jan 27 09:46:02 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Fri Jan 27 09:46:18 2006 Subject: [GAP Forum] How to identify a group In-Reply-To: <000601c62294$b772dc20$2101a8c0@SWISSOFT> References: <000601c62294$b772dc20$2101a8c0@SWISSOFT> Message-ID: gap> G:=Group((4,6,5)(7,8,9),(1,7,2,4,6,9,5,3)); Group([ (4,6,5)(7,8,9), (1,7,2,4,6,9,5,3) ]) gap> Size(G); 432 gap> StructureDescription(G); "(((C3 x C3) : Q8) : C3) : C2" 2006/1/26, Michael Schweitzer : > Dear forum members, > > given a group G of order n (given by generators). Is GAP > able to identify the group by name or as the > group of symmetries of some geometric object? > > For example: I define G such that G is isomorphic to A5. Can I ask GAP: > which group is G? And GAP answers: A5- which is, for example, > the symmetry group of the icosahedron. > > That is, does GAP contain a database of finite groups of > small orders ( < several hundrets, say) which includes > information about the transformation group aspect: this > group, among other things, is the symmetry group of X or > operates in a natural manner on X (I know that GAP > does contain a database of small groups - but is this kind > of information stored there?). > > The group in question is of order 432 with generators > > g1 := (4,6,5)(7,8,9) and g2 := (1,7,2,4,6,9,5,3) > > > Regards, > Michael Schweitzer > > > Michael Schweitzer > Alt-Heiligensee 51 A > 13503 Berlin > email: ms-swissoft@arcor.de > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > From ndroock1 at gmail.com Fri Jan 27 09:48:59 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Fri Jan 27 09:49:05 2006 Subject: [GAP Forum] How to identify a group In-Reply-To: References: <000601c62294$b772dc20$2101a8c0@SWISSOFT> Message-ID: Sorry for the noise on the list, this reply was meant for my archive. 2006/1/27, Nilo de Roock : > gap> G:=Group((4,6,5)(7,8,9),(1,7,2,4,6,9,5,3)); > Group([ (4,6,5)(7,8,9), (1,7,2,4,6,9,5,3) ]) > gap> Size(G); > 432 > gap> StructureDescription(G); > "(((C3 x C3) : Q8) : C3) : C2" > > 2006/1/26, Michael Schweitzer : > > Dear forum members, > > > > given a group G of order n (given by generators). Is GAP > > able to identify the group by name or as the > > group of symmetries of some geometric object? > > > > For example: I define G such that G is isomorphic to A5. Can I ask GAP: > > which group is G? And GAP answers: A5- which is, for example, > > the symmetry group of the icosahedron. > > > > That is, does GAP contain a database of finite groups of > > small orders ( < several hundrets, say) which includes > > information about the transformation group aspect: this > > group, among other things, is the symmetry group of X or > > operates in a natural manner on X (I know that GAP > > does contain a database of small groups - but is this kind > > of information stored there?). > > > > The group in question is of order 432 with generators > > > > g1 := (4,6,5)(7,8,9) and g2 := (1,7,2,4,6,9,5,3) > > > > > > Regards, > > Michael Schweitzer > > > > > > Michael Schweitzer > > Alt-Heiligensee 51 A > > 13503 Berlin > > email: ms-swissoft@arcor.de > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > From ndroock1 at gmail.com Mon Jan 30 23:07:03 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Mon Jan 30 23:10:29 2006 Subject: [GAP Forum] Unexpected behaviour on StructureDescription() Message-ID: Hello GAP Forum, The command StructureDescription(DirectProduct(CyclicGroup(5),SymmetricGroup(4))); generated the following response: gap> StructureDescription(DirectProduct(CyclicGroup(5),SymmetricGroup(4))); #I default `IsGeneratorsOfMagmaWithInverses' method returns `true' for [ Tuple( [ f1, () ] ) ] #I default `IsGeneratorsOfMagmaWithInverses' method returns `true' for [ Tuple( [ of ..., (1,2,3,4) ] ) ] #I default `IsGeneratorsOfMagmaWithInverses' method returns `true' for [ Tuple( [ of ..., (1,2) ] ) ] Error, lies not in group defined by called from ExponentsOfPcElement( pcgs, elm ) called from IN_LIST_DEFAULT( elm, list ) called from Enumerator( D ) called from called from func( elm ) called from ... Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> I have never seen such a response from GAP. I use GAP mainly for "educational algebra" i.e.: only very small, known groups - Is this expected GAP behaviour?? If so how should I interpret the message? Thanks in advance for an answer to my question. Kind Regards, nilo de roock From greg.gamble at math.rwth-aachen.de Thu Feb 2 14:32:09 2006 From: greg.gamble at math.rwth-aachen.de (Greg Gamble) Date: Thu Feb 2 14:32:35 2006 Subject: [GAP Forum] Package updates: ANUPQ 3.0, ACE 5.0 Message-ID: <20060202143208.GA16789@math.rwth-aachen.de> Dear GAP Forum, This is to announce the release of ANUPQ 3.0 and ACE 5.0. Both packages are available from the GAP website: http://www.gap-system.org and my websites: http://www.math.rwth-aachen.de/~Greg.Gamble/ (Aachen, Germany) http://www.maths.uwa.edu.au/~gregg/ (Perth, Australia) http://www.itee.uq.edu.au/~gregg/ (Brisbane, Australia) There is no urgency for users to upgrade either package. The new versions are *not* backward-compatible to versions of GAP prior to GAP 4.4. Thus, users of these packages must *not* upgrade if they are still using GAP 4.3 (and must continue to use ANUPQ 2.2 and ACE 4.1), though such users are strongly encouraged to upgrade their GAP to version 4.4, in which case it makes sense to upgrade ACE and ANUPQ at the same time. Neither package contains new features nor fixes any outstanding bugs (the previous versions of ACE and ANUPQ are not known to contain any bugs). These new versions of the packages update them fully to GAP 4.4; all obsolete pre-GAP 4.4 code has been removed. While GAP continues to support `ReadPkg' (and, in the case of ANUPQ, `PrimeOfPGroup') users of ANUPQ and ACE may continue to use ANUPQ 2.2 and ACE 4.1, safely. In the case of ANUPQ, the `IsPqIsomorphicPGroup' has been improved thanks to suggestions from Marco Costantini and Jack Schmidt. Users installing ANUPQ are urged to use testPq to check for correct installation (and can be confident they do have a correct installation if it responds as described in the README). For ACE also, one of the internal functions has been simplified (by removing GAP 4.2 compatibility). Users doing a ReadTest of the tst/aceds.tst file of the package should be aware that if the only difference is one of timing then their installation is quite ok (a cputime of 0 just means the relevant instruction took less than 5ms). Regards, Greg Gamble From greg.gamble at math.rwth-aachen.de Tue Feb 7 06:01:19 2006 From: greg.gamble at math.rwth-aachen.de (Greg Gamble) Date: Wed Feb 8 14:29:07 2006 Subject: [GAP Forum] Example package updated Message-ID: <20060207060119.GB32735@math.rwth-aachen.de> Dear GAP Forum, This is to announce the release of version 2.0 of the Example package. The Example package is intended as a prototype/template of a GAP package that hopefully new package writers will find useful. The package complements the detailed instructions found in the Reference Manual (chapter 74) and the Extending GAP Manual (chapter 4), links to which, along with other useful information, can be found by following the `Packages' then `For Authors' links at the GAP website: http://www.gap-system.org Also on the `Packages' page(s) is a link to the Example package. This new version of the Example package is fully up-to-date with respect to the new package loading mechanism of GAP 4.4, and removes all obsolete code. New GAP package writers are urged to base their package on this new version of the Example package and not older versions of the package. Comments exist in the package files to explain the changes from GAP 4.3 to GAP 4.4. The `Authorhints' link from the `Packages' -> `For Authors' page described above, has a section `How to adjust a package after the release of GAP 4.4?' that provides details of these changes. The new version of the Example package can be downloaded directly from http://www.gap-system.org/Packages/example.html or the package homepage: http://www.math.rwth-aachen.de/~Greg.Gamble/Example/ (Aachen, Germany) or its Australian mirrors: http://www.maths.uwa.edu.au/~gregg/Example/ (Perth) http://www.itee.uq.edu.au/~gregg/Example/ (Brisbane) Regards, Greg Gamble for the GAP Group From kohl at mathematik.uni-stuttgart.de Wed Feb 8 15:54:29 2006 From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl) Date: Wed Feb 8 15:54:35 2006 Subject: [GAP Forum] Unexpected behaviour on StructureDescription() In-Reply-To: References: Message-ID: <43EA1435.6020709@mathematik.uni-stuttgart.de> Dear Forum, Nilo de Roock wrote: > The command > > StructureDescription(DirectProduct(CyclicGroup(5),SymmetricGroup(4))); > > generated the following response: > > gap> StructureDescription(DirectProduct(CyclicGroup(5),SymmetricGroup(4))); > #I default `IsGeneratorsOfMagmaWithInverses' method returns `true' for > [ Tuple( [ f1, () ] ) ] This is due to a problem in a method in the package CRISP. In the meantime the author of this package has fixed this bug. Remedies are: - upgrade to CRISP 1.3, or - use StructureDescription(DirectProduct(CyclicGroup(IsPermGroup,5), SymmetricGroup(4))); or StructureDescription(DirectProduct(CyclicGroup(5), SymmetricGroup(IsPcGroup,4))); instead or - start GAP without autoloading of packages. Hope this helps, Stefan Kohl --------------------------------------------------------------------------- Stefan Kohl Institut f?r Geometrie und Topologie Pfaffenwaldring 57 Universit?t Stuttgart 70550 Stuttgart / Germany E-mail: kohl@mathematik.uni-stuttgart.de Web: http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/ --------------------------------------------------------------------------- From ndroock1 at gmail.com Fri Feb 10 09:11:34 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Fri Feb 10 09:12:13 2006 Subject: [GAP Forum] "(C4 x C2) : C2" Message-ID: Hello GAP Forum, Could someone please explain why AllGroups(16)[3] and AllGroups(16)[13] both return "(C4 x C2) : C2" on the function StructureDescription? Thanks in advance, nilo From ken.w.smith at cmich.edu Fri Feb 10 16:41:54 2006 From: ken.w.smith at cmich.edu (Ken W Smith) Date: Fri Feb 10 16:42:08 2006 Subject: [GAP Forum] "(C4 x C2) : C2" In-Reply-To: References: Message-ID: <2d4ac61a0e3c30dbdae57cb083631ad4@cmich.edu> Hi Nilo, Both groups are semidirect products of a normal subgroup isomorphic to C4 x C2 with a subgroup of order 2. (More explicitly, according to some notes of mine, group [16,3] is generated by elements x, y, z where x has order 4, y and z have order 2, x and y commute (thus = C4 x C2), y and z commute and zxz=xy. Group [16,13] is generated by x, y, z with orders 4, 2, 2, respectively where xy=yx, xz=zx, zyz=x^2y.) ken --- On Feb 10, 2006, at 4:11 AM, Nilo de Roock wrote: > Hello GAP Forum, > > Could someone please explain why AllGroups(16)[3] and > AllGroups(16)[13] both return "(C4 x C2) : C2" on the function > StructureDescription? > > Thanks in advance, > nilo > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > > --- Ken W. Smith, Professor of Mathematics, Central Michigan University 989-854-0185 (Cell) http://www.cst.cmich.edu/users/smith1kw Address for 2005-06: 22 Chase Gayton Terrace, Apt 1518 Richmond, VA 23238-6526 From ndroock1 at gmail.com Sat Feb 11 12:56:35 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Sat Feb 11 12:56:47 2006 Subject: [GAP Forum] StructureDescription Revisited Message-ID: Hello GAP forum, I have posted some questions regarding StructureDescription() recently, thank you for all answers. ( It came a bit as a shock to me but I now understand that non-isomorphic groups can have the same structure description. So yes the answers have been -very- helpful. I have also updated to the latest GAP releases, both kernel and packages. ) I am however still a bit uncertain about how I should interpret the answers of StructureDescription() and what is the best (simplest) method of finding the structure of a group. Let me give an example. I am doing some experiments regarding generating sets of matrices and the structure of the group they generate. I use for example the following function: testG:=function(a,b) local M1; M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [ E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]]; return (Group(M1)); end; I noticed the (for me...) interesting result that StructureDescription(testG(8,1)) = QD16 StructureDescription(testG(8,3)) =C3 X QD16 StructureDescription(testG(8,5))= C5 X QD16 For other numbers however... StructureDescription(testG(8,2))= GAP Error* StructureDescription(testG(8,4))= GAP Error* StructureDescription(testG(8,7))= GAP Error* *="... Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called fro\ m..." ( I interpreted the errors as "does not generate a group", or a bug in StructureDescription() for which a fix is due...) Size(testG(8,1))= 16 Size(testG(8,2))= 64 Size(testG(8,3))= 48 Size(testG(8,4))= 128 Size(testG(8,5))= 80 Size(testG(8,6))= 192 Size(testG(8,7))= 112 So there -are- groups generated. But which ones? ( Starting from Size(testG(4,7*11))= 176 computation time increased noticably. ) In this particular example I would very much like to know which group is generated in testG(8,2). Can GAP give an answer to that? Will the forthcoming update in StructureDescription() address this issue(if an issue at all)? More in general, am I perhaps using StructureDescription() in a wrong way or am I expecting too much from the command? Thanks in advance for any advice. nilo From rm43 at evansville.edu Sat Feb 11 13:18:52 2006 From: rm43 at evansville.edu (Robert F. Morse) Date: Sat Feb 11 13:19:09 2006 Subject: [GAP Forum] StructureDescription Revisited In-Reply-To: References: Message-ID: <43EDE43C.8050605@evansville.edu> Nilo de Roock wrote: > Hello GAP forum, > > I have posted some questions regarding StructureDescription() > recently, thank you for all answers. ( It came a bit as a shock to me > but I now understand that non-isomorphic groups can have the same > structure description. So yes the answers have been -very- helpful. I > have also updated to the latest GAP releases, both kernel and > packages. ) > > I am however still a bit uncertain about how I should interpret the > answers of StructureDescription() and what is the best (simplest) > method of finding the structure of a group. Dear Nilo, One safe approach is to find an isomorphic permutation group for the group in question and then attempt to find the structural description. Hence for your examples: gap> g8_2 := Image(IsomorphismPermGroup(testG(8,2))); gap> StructureDescription(g8_2); "(C8 x C4) : C2" gap> g8_4 := Image(IsomorphismPermGroup(testG(8,4))); gap> StructureDescription(g8_4); "(C16 x C4) : C2" gap> g8_7 := Image(IsomorphismPermGroup(testG(8,7))); gap> StructureDescription(g8_7); "C7 x QD16" Regards, Robert F. Morse From max at quendi.de Sat Feb 11 14:21:53 2006 From: max at quendi.de (Max Horn) Date: Sat Feb 11 14:22:01 2006 Subject: [GAP Forum] StructureDescription Revisited In-Reply-To: References: Message-ID: Am 11.02.2006 um 13:56 schrieb Nilo de Roock: > Hello GAP forum, > [...] > > *="... Error, no method found! For debugging hints type ?Recovery from > NoMethodFound > Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments > called fro\ > m..." > ( I interpreted the errors as "does not generate a group", or a bug in > StructureDescription() for which a fix is due...) To me this seems like a bug... > > Size(testG(8,1))= 16 > Size(testG(8,2))= 64 > Size(testG(8,3))= 48 > Size(testG(8,4))= 128 > Size(testG(8,5))= 80 > Size(testG(8,6))= 192 > Size(testG(8,7))= 112 > So there -are- groups generated. But which ones? You can work around the problem by first converting to e.g. a permutation group. gap> G:=testG(8,2);; gap> phi:=IsomorphismPermGroup(G); gap> StructureDescription(Image(phi)); "(C8 x C4) : C2" Hope that helps! Max From R.W.Barraclough at qmul.ac.uk Fri Feb 10 18:08:23 2006 From: R.W.Barraclough at qmul.ac.uk (Richard Barraclough) Date: Mon Feb 13 10:38:24 2006 Subject: [GAP Forum] "(C4 x C2) : C2" In-Reply-To: <2d4ac61a0e3c30dbdae57cb083631ad4@cmich.edu> Message-ID: Hi Nilo, As you have noticed, the 'shape' of a group, i.e., what you get from StructureDescription(), does not determine the isomorphism type of the group. There are two split extensions of (4 x 2) by 2, the action of the outer 2 on the normal 4x2 is different. With Ken's notation we have ( x ) : . Now, 4x2 has two cyclic subgroups of order 4, one generated by x that we can see clearly, the other generated by xy. In case [16,3] z acts to swap these. 4x2 has three cyclic subgroups of order 2, generators are x^2, y and x^2y. In case [16,3] z acts to swap with . Notice that this fixes the two subgroups of order 4 You can't swap any other pair of order 2 subgroups. For example, y -> x^2 -> xyxy = x^2 -> x^2 -> ... which is nonsense. It is also impossible to do both of these swaps at once: The first requires you to swap x with xy, the second forces you to swap x with x^3y. Therefore these are the only two groups of shape (4x2):2. I seem to remember that "Groups for Undergraduates" by J. Moody determines all of the groups of order up . I expect there are many other references. Richard. > Hi Nilo, > Both groups are semidirect products of a normal subgroup isomorphic to > C4 x C2 with a subgroup of order 2. > > (More explicitly, according to some notes of mine, group [16,3] is > generated by elements x, y, z where x has order 4, y and z have order > 2, x and y commute (thus = C4 x C2), y and z commute and zxz=xy. > Group [16,13] is generated by x, y, z with orders 4, 2, 2, respectively > where xy=yx, xz=zx, zyz=x^2y.) > > ken > --- > On Feb 10, 2006, at 4:11 AM, Nilo de Roock wrote: > >> Hello GAP Forum, >> >> Could someone please explain why AllGroups(16)[3] and >> AllGroups(16)[13] both return "(C4 x C2) : C2" on the function >> StructureDescription? >> >> Thanks in advance, >> nilo >> >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >> >> > --- > Ken W. Smith, Professor of Mathematics, Central Michigan University > 989-854-0185 (Cell) > http://www.cst.cmich.edu/users/smith1kw > Address for 2005-06: > 22 Chase Gayton Terrace, Apt 1518 > Richmond, VA 23238-6526 > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum From ally at dcs.gla.ac.uk Mon Feb 13 15:12:08 2006 From: ally at dcs.gla.ac.uk (Alastair Donaldson) Date: Mon Feb 13 15:12:18 2006 Subject: [GAP Forum] Wreath Product Decomposition Message-ID: Dear Forum members I am trying to write an algorithm which, given a permutation group G acting (not necessarily transitively) on {1,2,.....,n} for some n>0, will determine whether or not G is a wreath product of subgroups H and K. According to a previous posting by Burkhard Hoefling, I think this should be fairly easy: "Wreath products of permutation groups can easily be recognized by looking at their block structure, see `Blocks' in the GAP reference manual. In general, a transitive permutation group G embeds in the wreath product (action of block stabilizer on block) wr (action of G on orbit of block), and you can easily check equality by comparing orders." However, the groups which crop up in my application domain do not tend to act transitively. As an example, consider the group G := Group( [ (1,2), (2,3), (1,4)(2,5)(3,6)(19,20), (26,27), (28,29), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(19,21)(20,22)(25,30)(26,31)(27,32)(28,33)(29,34)(40,41), (7,13)(8,14)(9,15)(10,16)(11,17)(12,18)(21,23)(22,24)(30,35)(31,36)(32,37)(33,38)(34,39)(41,42) ]); I have worked out that this decomposes in several possible ways as H wr K, one of which is H := Group([ (33,34), (31,32), (11,12), (8,9), (10,11,12), (7,8,9), (7,10)(8,11)(9,12)(21,22) ]); and K := Group([ (7,13)(8,14)(9,15)(10,16)(11,17)(12,18)(21,23)(22,24)(30,35)(31,36)(32,37)(33,38)(34,39)(41,42), (1,7,13)(2,8,14)(3,9,15)(4,10,16)(5,11,17)(6,12,18)(19,21,23)(20,22,24)(25,30,35)(26,31,36)(27,32,37)(28,33,38)(29,34,39)(40,41,42) ] (the group H can then be decomposed further as a direct product, one factor of which is itself a wreath product). I have written a rather complex algorithm which does this decomposition correctly for my example. However, I'm having trouble proving the correctness of my algorithm, which is not nearly as simple as Buckhard's approach of looking at blocks and comparing orders. However, since blocks are not immediately applicable when the group does not act transitively, I'm not sure how to extend his suggested approach. Any ideas would be greatly appreciated -Alastair From barracrw at for.mat.bham.ac.uk Mon Feb 13 18:51:23 2006 From: barracrw at for.mat.bham.ac.uk (Richard Barraclough) Date: Mon Feb 13 22:01:48 2006 Subject: [GAP Forum] Wreath Product Decomposition In-Reply-To: Message-ID: Dear Alastair, Transitive imprimitive permutation groups can be decomposed as wreath products. All intransitive permutation groups are imprimitive: The orbits are the blocks. I guess that's not what you had in mind though. The usual way of dealing with permutation groups is to write them as a direct product of transitive permutation groups, then deal with the transitive groups separately. You probably then want at least one transitive constituent in order to be imprimitive. Here are some calculations. gens := [ (1,2), (2,3), (1,4)(2,5)(3,6)(19,20), (26,27), (28,29), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(19,21)(20,22)(25,30)(26,31)(27,32)(28,33)( 29,34)(40,41), (7,13)(8,14)(9,15)(10,16)(11,17)(12,18)(21,23)(22,24)(30,35)(31,36)(32,37)(3 3,38)(34,39)(41,42) ]; gp := Group(gens); orbs := Orbits(gp); gpsGens := []; gps := []; for i in [1..Length(orbs)] do gpsGens[i] := List([1..Length(gens)], j -> RestrictedPerm( gens[j], orbs[i])); gps[i] := Group(gpsGens[i]); od; gp is the direct product of the gps You can now investigate them using GAP's built in functions, which have already been proved correct. looks relatively interesting. gap> Order(gps[1]); 2239488 gap> # looks relatively interesting gap> IsTransitive(gps[1]); true gap> IsPrimitive(gps[1]); false So that may be all you need. You can write gps[1] as a wreath product as follows: gap> bl := MaximalBlocks(gps[1],MovedPoints(gps[1])); [ [ 1, 2, 3, 4, 5, 6 ], [ 7, 8, 9, 10, 11, 12 ], [ 13, 14, 15, 16, 17, 18 ] ] # (Explained in Chapter 39 of the Ref. Manual.) gap> H := Stabilizer(gps[1], bl[1], OnSets); gap> HH := Group(List(GeneratorsOfGroup(H), g -> RestrictedPerm(g,bl[1]))); gap> K := Action(gps[1],bl,OnSets); Group([ (1,2,3), (2,3) ]) gap> wr := WreathProduct(HH,K); By construction, wr embeds in gps[1]. (I've assumed that gps[1] is acting the same way on each block.) Burkhard Hoefling suggests comparing orders: gap> Order(gps[1]); 2239488 gap> Order(wr); 2239488 They're the same, therefore the groups are isomorphic. gap> # This will take a while and is probably not a good idea unless you're gap> # _really_ sceptical gap> iso := IsomorphismGroups(wr,gps[1]); Once you've done this for all the gps you have gp as a direct product of wreath products, say (H1 wr K1) x (H2 wr K2) x ... x (Hn wr Kn) You can then write this as a subgroup of the wreath product (H1 x H2 x ... x Hn) wr (K1 x K2 x ... x Kn) but that seems a bit silly because it needs many more points to support its action. If you're interested in the actual algorithms, I seem to remember Greg Butler's 'Fundamental algorithms for permutation groups' being easy reading (if your library has it). Richard. ------------- Richard Barraclough School of Mathematical Sciences Queen Mary College web: www.maths.qmul.ac.uk/~rwb Mile End Road email: R.W.Barraclough@qmul.ac.uk London E1 4NS On 13/2/06 3:12 pm, "Alastair Donaldson" wrote: > Dear Forum members > > I am trying to write an algorithm which, given a permutation group G > acting (not necessarily transitively) on {1,2,.....,n} for some n>0, will > determine whether or not G is a wreath product of subgroups H and K. > > According to a previous posting by Burkhard Hoefling, I think this should > be fairly easy: > > "Wreath products of permutation groups can easily be recognized by looking > at their block structure, see `Blocks' in the GAP reference manual. In > general, a transitive permutation group G embeds in the wreath > product (action of block stabilizer on block) wr (action of G on > orbit of block), and you can easily check equality by comparing orders." > > However, the groups which crop up in my application domain do not tend to > act transitively. As an example, consider the group > > G := Group( [ (1,2), (2,3), (1,4)(2,5)(3,6)(19,20), (26,27), (28,29), > (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(19,21)(20,22)(25,30)(26,31)(27,32)(28,33)(29 > ,34)(40,41), > (7,13)(8,14)(9,15)(10,16)(11,17)(12,18)(21,23)(22,24)(30,35)(31,36)(32,37)(33, > 38)(34,39)(41,42) > ]); > > I have worked out that this decomposes in several possible ways as H wr K, > one of which is > > H := Group([ (33,34), (31,32), (11,12), (8,9), (10,11,12), (7,8,9), > (7,10)(8,11)(9,12)(21,22) ]); > > and > > K := Group([ > (7,13)(8,14)(9,15)(10,16)(11,17)(12,18)(21,23)(22,24)(30,35)(31,36)(32,37)(33, > 38)(34,39)(41,42), > (1,7,13)(2,8,14)(3,9,15)(4,10,16)(5,11,17)(6,12,18)(19,21,23)(20,22,24)(25,30, > 35)(26,31,36)(27,32,37)(28,33,38)(29,34,39)(40,41,42) ] > > (the group H can then be decomposed further as a direct product, one > factor of which is itself a wreath product). > > I have written a rather complex algorithm which does this decomposition > correctly for my example. However, I'm having trouble proving the > correctness of my algorithm, which is not nearly as simple as Buckhard's > approach of looking at blocks > and comparing orders. However, since blocks are not immediately > applicable when the group does not act transitively, I'm not sure how to > extend his suggested approach. > > Any ideas would be greatly appreciated > > -Alastair > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum From ndroock1 at gmail.com Wed Feb 15 00:13:41 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Wed Feb 15 00:13:56 2006 Subject: [GAP Forum] StructureDescription Revisited In-Reply-To: <60206.12.211.103.182.1139683037.squirrel@webmail.ms.uky.edu> References: <60206.12.211.103.182.1139683037.squirrel@webmail.ms.uky.edu> Message-ID: Thanks, Your reply was very helpful. Since I can also report that while using ...SmallGroup(IdGroup... calculation was measurably faster. In my case: calculations that took >> 10 minutes ( I don't know the actual time, I cancelled after 10 min) are now done in seconds. Kind regards, nilo 2006/2/11, Jack Schmidt : > Howdy, as a quick fix you convert the matrix group to a > representation that is easier for GAP to use: > > for i in [1..10] do > Print(i,": ", > StructureDescription(SmallGroup(IdGroup(testG(8,i)))), > "\n"); > od; > > This should print: > > 1: QD16 > 2: (C8 x C4) : C2 > 3: C3 x QD16 > 4: (C16 x C4) : C2 > 5: C5 x QD16 > 6: C3 x ((C8 x C4) : C2) > 7: C7 x QD16 > 8: (C32 x C4) : C2 > 9: C9 x QD16 > 10: C5 x ((C8 x C4) : C2) > > > The (silly) reason this works is because IdGroup is an older more > mature function which has been tested and fixed for many years to > handle all sorts of groups given to it. StructureDescription is > much newer and does not yet protect itself against hard questions. > > > > On Sat, February 11, 2006 07:56, Nilo de Roock wrote: > > Hello GAP forum, > > > > I have posted some questions regarding StructureDescription() > > recently, thank you for all answers. ( It came a bit as a shock to me > > but I now understand that non-isomorphic groups can have the same > > structure description. So yes the answers have been -very- helpful. I > > have also updated to the latest GAP releases, both kernel and > > packages. ) > > > > I am however still a bit uncertain about how I should interpret the > > answers of StructureDescription() and what is the best (simplest) > > method of finding the structure of a group. Let me give an example. > > > > > > I am doing some experiments regarding generating sets of matrices and > > the structure of the group they generate. I use for example the > > following function: > > > > testG:=function(a,b) > > local M1; > > M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [ > > E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]]; > > return (Group(M1)); > > end; > > > > I noticed the (for me...) interesting result that > > StructureDescription(testG(8,1)) = QD16 > > StructureDescription(testG(8,3)) =C3 X QD16 > > StructureDescription(testG(8,5))= C5 X QD16 > > For other numbers however... > > StructureDescription(testG(8,2))= GAP Error* > > StructureDescription(testG(8,4))= GAP Error* > > StructureDescription(testG(8,7))= GAP Error* > > > > *="... Error, no method found! For debugging hints type ?Recovery from > > NoMethodFound > > Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called > > fro\ > > m..." > > ( I interpreted the errors as "does not generate a group", or a bug in > > StructureDescription() for which a fix is due...) > > > > Size(testG(8,1))= 16 > > Size(testG(8,2))= 64 > > Size(testG(8,3))= 48 > > Size(testG(8,4))= 128 > > Size(testG(8,5))= 80 > > Size(testG(8,6))= 192 > > Size(testG(8,7))= 112 > > So there -are- groups generated. But which ones? > > > > ( Starting from Size(testG(4,7*11))= 176 computation time increased > > noticably. ) > > > > > > In this particular example I would very much like to know which group > > is generated in testG(8,2). Can GAP give an answer to that? Will the > > forthcoming update in StructureDescription() address this issue(if an > > issue at all)? > > > > More in general, am I perhaps using StructureDescription() in a wrong > > way or am I expecting too much from the command? > > > > Thanks in advance for any advice. > > nilo > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > > > From ndroock1 at gmail.com Wed Feb 15 00:22:50 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Wed Feb 15 00:22:56 2006 Subject: [GAP Forum] StructureDescription Revisited In-Reply-To: References: <60206.12.211.103.182.1139683037.squirrel@webmail.ms.uky.edu> Message-ID: Hello Forum, This is a correction on my previous post. I wrote: "...are now done in seconds.", this should be: "are now done in a few minutes, some even in a few seconds." nilo 2006/2/15, Nilo de Roock : > Thanks, > > Your reply was very helpful. Since I can also report that while using > ...SmallGroup(IdGroup... calculation was measurably faster. In my > case: calculations that took >> 10 minutes ( I don't know the actual > time, I cancelled after 10 min) are now done in seconds. > > Kind regards, > nilo > > > 2006/2/11, Jack Schmidt : > > Howdy, as a quick fix you convert the matrix group to a > > representation that is easier for GAP to use: > > > > for i in [1..10] do > > Print(i,": ", > > StructureDescription(SmallGroup(IdGroup(testG(8,i)))), > > "\n"); > > od; > > > > This should print: > > > > 1: QD16 > > 2: (C8 x C4) : C2 > > 3: C3 x QD16 > > 4: (C16 x C4) : C2 > > 5: C5 x QD16 > > 6: C3 x ((C8 x C4) : C2) > > 7: C7 x QD16 > > 8: (C32 x C4) : C2 > > 9: C9 x QD16 > > 10: C5 x ((C8 x C4) : C2) > > > > > > The (silly) reason this works is because IdGroup is an older more > > mature function which has been tested and fixed for many years to > > handle all sorts of groups given to it. StructureDescription is > > much newer and does not yet protect itself against hard questions. > > > > > > > > On Sat, February 11, 2006 07:56, Nilo de Roock wrote: > > > Hello GAP forum, > > > > > > I have posted some questions regarding StructureDescription() > > > recently, thank you for all answers. ( It came a bit as a shock to me > > > but I now understand that non-isomorphic groups can have the same > > > structure description. So yes the answers have been -very- helpful. I > > > have also updated to the latest GAP releases, both kernel and > > > packages. ) > > > > > > I am however still a bit uncertain about how I should interpret the > > > answers of StructureDescription() and what is the best (simplest) > > > method of finding the structure of a group. Let me give an example. > > > > > > > > > I am doing some experiments regarding generating sets of matrices and > > > the structure of the group they generate. I use for example the > > > following function: > > > > > > testG:=function(a,b) > > > local M1; > > > M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [ > > > E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]]; > > > return (Group(M1)); > > > end; > > > > > > I noticed the (for me...) interesting result that > > > StructureDescription(testG(8,1)) = QD16 > > > StructureDescription(testG(8,3)) =C3 X QD16 > > > StructureDescription(testG(8,5))= C5 X QD16 > > > For other numbers however... > > > StructureDescription(testG(8,2))= GAP Error* > > > StructureDescription(testG(8,4))= GAP Error* > > > StructureDescription(testG(8,7))= GAP Error* > > > > > > *="... Error, no method found! For debugging hints type ?Recovery from > > > NoMethodFound > > > Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called > > > fro\ > > > m..." > > > ( I interpreted the errors as "does not generate a group", or a bug in > > > StructureDescription() for which a fix is due...) > > > > > > Size(testG(8,1))= 16 > > > Size(testG(8,2))= 64 > > > Size(testG(8,3))= 48 > > > Size(testG(8,4))= 128 > > > Size(testG(8,5))= 80 > > > Size(testG(8,6))= 192 > > > Size(testG(8,7))= 112 > > > So there -are- groups generated. But which ones? > > > > > > ( Starting from Size(testG(4,7*11))= 176 computation time increased > > > noticably. ) > > > > > > > > > In this particular example I would very much like to know which group > > > is generated in testG(8,2). Can GAP give an answer to that? Will the > > > forthcoming update in StructureDescription() address this issue(if an > > > issue at all)? > > > > > > More in general, am I perhaps using StructureDescription() in a wrong > > > way or am I expecting too much from the command? > > > > > > Thanks in advance for any advice. > > > nilo > > > > > > _______________________________________________ > > > Forum mailing list > > > Forum@mail.gap-system.org > > > http://mail.gap-system.org/mailman/listinfo/forum > > > > > > > > > > From kohl at mathematik.uni-stuttgart.de Wed Feb 15 10:35:52 2006 From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl) Date: Wed Feb 15 10:35:59 2006 Subject: [GAP Forum] StructureDescription Revisited In-Reply-To: References: Message-ID: <43F30408.7050604@mathematik.uni-stuttgart.de> Dear Forum, Nilo de Roock wrote: > I am doing some experiments regarding generating sets of matrices and > the structure of the group they generate. I use for example the > following function: > > testG:=function(a,b) > local M1; > M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [ > E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]]; > return (Group(M1)); > end; > > I noticed the (for me...) interesting result that > StructureDescription(testG(8,1)) = QD16 > StructureDescription(testG(8,3)) =C3 X QD16 > StructureDescription(testG(8,5))= C5 X QD16 > For other numbers however... > StructureDescription(testG(8,2))= GAP Error* > StructureDescription(testG(8,4))= GAP Error* > StructureDescription(testG(8,7))= GAP Error* > > *="... Error, no method found! For debugging hints type ?Recovery from > NoMethodFound > Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called fro\ > m..." > ( I interpreted the errors as "does not generate a group", or a bug in > StructureDescription() for which a fix is due...) Thanks for reporting this! This problem will be fixed in the next update. In the meantime -- as already several people have suggested -- you can use StructureDescription( Image ( IsomorphismPermGroup( ) ) ) instead. Technically, the reason for the error message is that a trivial method for `IsGeneralLinearGroup' for matrix groups in lib/grpmat.gi which is ranked higher than the nontrivial method for generic groups in lib/grpnames.gi calls the operation `IsNaturalGL', for which currently no nontrivial method is available. Thanks again and best wishes, Stefan Kohl --------------------------------------------------------------------------- Stefan Kohl Institut f?r Geometrie und Topologie Pfaffenwaldring 57 Universit?t Stuttgart 70550 Stuttgart / Germany E-mail: kohl@mathematik.uni-stuttgart.de Web: http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/ --------------------------------------------------------------------------- From wdjoyner at comcast.net Thu Feb 16 03:24:39 2006 From: wdjoyner at comcast.net (David Joyner) Date: Thu Feb 16 18:16:47 2006 Subject: [GAP Forum] guava 2.5 Message-ID: <43F3F077.4000801@comcast.net> Hello GAP people: GUAVA 2.5 is now officially released. You can find it on the GAP website or the URL http://cadigweb.ew.usna.edu/~wdj/gap/GUAVA/ New features are described in http://cadigweb.ew.usna.edu/~wdj/gap/GUAVA/CHANGES The main difference is that GUAVA 2.5 requires SONATA 2.3. Recently, Cary Huffman has discovered a number of codes for which AutomorphismGroup fails. This program calls Leon's C code. The error seems to be so serious that Leon's code will have to eventually abandoned (and hopefully replaced by someone's else's some day). - David Joyner From ndroock1 at gmail.com Sat Feb 18 20:19:05 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Sat Feb 18 20:20:07 2006 Subject: [GAP Forum] Bug Report Message-ID: Hello GAP Forum, Below you'll find - GAP output - listing of the GAP program I was running - contents of stackdumpfile I hope this helps. Kind regards, nilo I got the following output... gap> str(testH(3)); "(C12 x C2) : C2" gap> str(testH(9)); "(C36 x C2) : C2" gap> str(testH(27)); 4 [main] gapw95 101740 handle_exceptions: Exception: STATUS_ACCESS_VIOLATI ON 18102 [main] gapw95 101740 open_stackdumpfile: Dumping stack trace to gapw95.e xe.stackdump testH:=function(p) local M, M1, T; # QD16 (8) # M1:=[ [[ 1, 0, 0 ], [0, 0, E(8)^-1 ], [0, E(8), 0 ] ], # [[ 1, 0, 0 ], [0, E(4), 0 ], [0, 0, -E(4) ] ], # [[ 1, 0, 0 ], [0, 0, -1 ], [0, 1, 0 ] ], # [[ 1, 0, 0 ], [0, 1, 0 ], [0, 0, 1 ] ] ]; M1:=[ [[ 1, 0, 0, 0 ], [0, 0, E(p)^-1, 0 ], [0, E(p), 0, 0 ], [0, 0, 0, 1 ] ], [[ 1, 0, 0, 0 ], [0, E(4), 0, 0 ], [0, 0, -E(4), 0 ], [0, 0, 0, 1 ] ], [[ 1, 0, 0, 0 ], [0, 0, -1, 0 ], [0, 1, 0, 0 ], [0, 0, 0, 1 ] ], [[ 1, 0, 0, 0 ], [0, 1, 0, 0 ], [0, 0, 1, 0 ], [0, 0, 0, 1 ] ]]; return (SmallGroup(IdGroup(Group(M1)))); end; Exception: STATUS_ACCESS_VIOLATION at eip=00483218 eax=00000001 ebx=0AAE6098 ecx=00000000 edx=0A4A8FF8 esi=10F71F04 edi=0EA3D19C ebp=0022DE48 esp=0022DE00 program=C:\GAP4R4\bin\gapw95.exe, pid 101740, thread main cs=001B ds=0023 es=0023 fs=003B gs=0000 ss=0023 Stack trace: Frame Function Args 0022DE48 00483218 (00000010, 00000000, 00000001, 0DA3434F) 0022DE68 00482B14 (00000002, 00000010, 0E990EBC, 00000000) 0022DEA8 00487552 (368D0D3D, 0A9AED74, 00000002, 0A9AECEC) 0022DED8 004D88B0 (0A66CE54, 0A9ADF38, 0022DF18, 0A070A4C) 0022DF08 0049F6E0 (0A06D150, 0AC644D4, 0A658648, 0A9ADF38) 0022DF98 004BCCC3 (0A093200, 0AC644D4, 0A658648, 0A9ADF38) 0022DFD8 004778AB (000004CC, 0A52A354, 00000504, 000005EC) 0022DFF8 004EDE54 (0000053C, 0B80DA28, 0022E028, 004ECA66) 0022E008 004EC714 (000005EC, 0AAE8D90, 0022E048, 0B80DA28) 0022E028 004ECA66 (00000600, 00000638, 0022E048, 004A4100) 0022E048 004EC9E6 (00000614, 0AAD14A4, 0022E088, 000003B8) 0022E068 004EC9E6 (00000620, 00000005, 0022E098, 00000007) 0022E098 004ED698 (0000062C, 00000714, 0022E0C8, 00000240) 0022E0B8 004EC5D5 (0000063C, 00000009, 0022E0D8, 00000005) 0022E0D8 004EDBC9 (00000664, 0A529E7C, 0022E0F8, 00000004) 0022E0F8 004EC5D5 (00000718, 0000016C, 0022E128, 0047975D) End of stack trace (more stack frames may be present) From ndroock1 at gmail.com Sat Feb 18 20:36:48 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Sat Feb 18 20:38:03 2006 Subject: [GAP Forum] Re: Bug Report In-Reply-To: References: Message-ID: Hello GAP Forum, Two remarks about the bug report I just emailed. 1. Please note that although my GAP program is in C:\GAP4R4\bin\gapw95.exe I only recently updated to the latest releases. 2. str is an alias for StructureDescription (if that wasn't clear from the context already). Kind regards, nilo From andrew_johnson at uk.ibm.com Sun Feb 19 15:43:48 2006 From: andrew_johnson at uk.ibm.com (Andrew Johnson) Date: Sun Feb 19 15:43:57 2006 Subject: [GAP Forum] RepresentativeAction gives error Message-ID: I'm using GAP (gap4r4p6-win.zip) to investigate some permutation groups. group1 := Group([ (1,3)(2,5)(4,7)(6,8), (1,4)(2,6)(3,7)(5,8), (1,5)(2,3)(4,8)(6,7), (2,3,4,5,7,8,6), (3,4,7)(5,6,8) ]); group2 := Group([ (1,3,4,7,2,6,8), (1,8,7,5,3,6,2) ]); group3 := SymmetricGroup([1..8]); RepresentativeAction(group3,group1,group2); gives: Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `ONE' on 1 arguments called from OneOp( elm ) called from One( F ) called from CallFuncList( Refinements.(Rf.func), Concatenation( [ rbase, image ], Rf.args ) ) called from RRefine( rbase, image, false ) called from PBEnumerate( 1, not repr ) called from ... Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue Is this expected? My work around is to use First(AsList(group3),e->group1^e=group2); If this gets too slow, then I might use IsomorphismGroups(group1, group2) to see first of all whether the groups are isomorphic or compare cycle structures of the elements. signature2:= function(g) local cg,c2; cg := ConjugacyClasses(g); c2 := List(cg, c->[CycleStructurePerm(Representative(c)),Size(c)]); return SortedList(c2); end; to weed out groups which are clearly not conjugate. [The reference manual for IsConjugate says 'This command is only a shortcut to RepresentativeOperation.' I presume this should be updated to the prefered name of RepresentativeAction.] Andrew Johnson From teron at udm.ru Wed Feb 22 18:57:54 2006 From: teron at udm.ru (Serge) Date: Wed Feb 22 18:59:26 2006 Subject: [GAP Forum] Question about semigroup and finite-state machine Message-ID: Hello. My problem is simple, but it is very urgent and unfortunately I cannot solve it myself. I have a task: There is a jump table of finite-state machine. I must calculate the semigroup of this FSM. Following information is known: 1. Alphabet of FSM, set of initial and final states are the same 2. Size of jump table is limited to 5*5 As far as I know, semigroup of finite-state machine is the set of congruence classes of its elements. In my case, FSM is representation from A*A to A (f: AA -> A), where A is alphabet, set of initial and final states. I thought that AA means Cartesian product, or in this case second Cartesian power of set A, but I was wrong. So, the first question is: Can anyone explain, how should I treat record AA? According to the definition of congruence relation, x is congruent to y, if they are equivalent and for any t xt is equivalent to yt and tx is equivalent to ty. According to the definition of semigroup of machine, t1 is congruent to t2 if for all a and b from AA f(at1b)=f(at2b), where f is our machine. The second question is: How should I apply machine to the string? My teacher said that at1b is concatenation of strings, but I am still unclear, how to calculate f(at1b). And the last question: My teacher recommends me to use GAP in order to solve this task. But I didn't use GAP earlier. Can you tell me, which advantages I receive, if I will use GAP for this task? Any help is appreciated. Thank you in advance. P.S. Any advices about algorithm are greatly appreciated. _____ Best Regards, Serge. mailto:teron@udm.ru ICQ 315293596 ---------------------------------------------------- ????? ???????? ????? ?? - ??????????? ???????? ??? ????? ?????? - ?????? ????? http://www.mark-itt.ru/MARK-ITT/Contract/current/price.htm From hulpke at math.colostate.edu Fri Feb 24 17:16:34 2006 From: hulpke at math.colostate.edu (Alexander Hulpke) Date: Fri Feb 24 17:16:52 2006 Subject: [GAP Forum] Fwd: [GAP Support] Suggested response: RepresentativeAction gives error References: <7CA77904-F8E4-4095-96FC-EB3E2BAE122A@mac.com> Message-ID: Dear GAP-Forum, Andrew Johnson reported a bug in `RepresentativeAction' for subgroups. Thank you very much. This error will be corrected in the next bugfix. Before going into details of the bug in question, let me take this opportunity to remind everyone of the existence of the email address support@gap-system.org, which is intended for bug reports or to request help with installation problems. The forum email list goes to several hundred people worldwide, most of whom likely are not interested in lengthy error descriptions or stack dumps. Now to the bug in question. What happens is that the conjugacy test in permutation groups contains a special treatment for groups with an elementary abelian regular subgroup (EARNS), as such groups are important in the classification of primitive groups. What is missing is the (easy) check that not just one, but both groups have an EARNS. In the example this was not the case, the error was triggered when trying to use the EARNS of group2. (You can verify this by swapping group2 and group1.) As mentioned this will be corrected in the next bugfix. In case you are testing a larger set of subgroups of S_n (for n<=31) for conjugacy, you might want to look as well as the command `TransitiveIdentification', which uses the classification of transitive subgroups of the symmetric group (known up to degree 31) and which is likely to be much faster. Best wishes, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hulpke@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke From ndroock1 at gmail.com Sun Feb 26 10:44:56 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Sun Feb 26 10:45:23 2006 Subject: [GAP Forum] StructureDescription Message-ID: Hello GAP forum, Forgive for yet another question (...) on this command, perhaps I am using the wrong command for my purpose. When I execute the following command. gap> List(AllGroups(20),StructureDescription); GAP responds with [ "C5 : C4", "C20", "C5 : C4", "D20", "C10 x C2" ] The issue I have here is that "C5:C4" occurs twice in the list. What I am looking for is a command that would recognize that the Frobenius group is in there somewhere. Even if I do... gap> F:=FreeGroup(2); gap> s:=F.1; f1 gap> t:=F.2; f2 gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1]; gap> Size(G); 20 gap> str(G); "C5 : C4" gap> the answer is "C5:C4". I am getting lost on this command, and thus on GAP. Please help. -- met vriendelijke groet, Nilo de Roock From bob.heffernan at gmail.com Sun Feb 26 13:46:10 2006 From: bob.heffernan at gmail.com (Robert Heffernan) Date: Sun Feb 26 13:46:17 2006 Subject: [GAP Forum] StructureDescription In-Reply-To: References: Message-ID: <6d9a83e90602260546l300e247boebb2d1d449125949@mail.gmail.com> On 2/26/06, Nilo de Roock wrote:> The issue I have here is that "C5:C4" occurs twice in the list. What I am> looking for is a command that would recognize that the Frobenius group> is in there somewhere. The semidirect product of two groups is not unique, this is why C5:C4occurs twice. You can ask GAP to construct an explicit isomorphismbetween F and one of the two C5:C4 groups: gap> F:=FreeGroup(2);;gap> s:=F.1;; t:=F.2;;gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1];;gap> StructureDescription(G);"C5 : C4"gap> IsomorphismGroups(G,SmallGroup(20,1));failgap> IsomorphismGroups(G,SmallGroup(20,3));[ f1, f2 ] -> [ f1, f3 ] So, as you can see, F is isomorphic to SmallGroup(20,3). I hope this helps. From ndroock1 at gmail.com Sun Feb 26 16:39:12 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Sun Feb 26 16:39:29 2006 Subject: [GAP Forum] Unexpected Behaviour in Size() Message-ID: Hello GAP forum, I created the free group ( i got this spec. for the group from a textbook-exercise ): gap> F:=FreeGroup(3); gap> x:=F.1; f1 gap> y:=F.2; f2 gap> z:=F.3; f3 gap> G:=F/[y^3*z^15,x^4*y^7*z^3,x^8,y^14,z^18]; Then when I wanted to now the size of the group, GAP became a bit of erratic. gap> Size(G); #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit user interrupt at firstFree := app[6]; called from TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from CosetTableFromGensAndRels( fgens, grels, List( trial, UnderlyingElement ) ) called from Attempt( gens ) called from FinIndexCyclicSubgroupGenerator( G, infinity ) called from ( ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> quit; #I Options stack has been reset gap> G:=F/[y^3*z^15,x^4*y^7*z^3,x^8*y^14*z^18]; gap> Size(G); #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit #I Coset table calculation failed -- trying with bigger table limit exceeded the permitted memory (`-o' command line option) at g[2 * limit] := 0; called from TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from CosetTableFromGensAndRels( fgens, grels, List( trial, UnderlyingElement ) ) called from Attempt( trial ) called from Attempt( gens ) called from FinIndexCyclicSubgroupGenerator( G, infinity ) called from ... Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> Sorry but, any idea what's wrong in this case? Thanks on beforehand for any advice. -- met vriendelijke groet, Nilo de Roock From dima at ntu.edu.sg Sun Feb 26 18:08:25 2006 From: dima at ntu.edu.sg (Dima Pasechnik) Date: Sun Feb 26 18:09:50 2006 Subject: [GAP Forum] Unexpected Behaviour in Size() In-Reply-To: Message-ID: Dear Forum, On 2/27/06 12:39 AM, "Nilo de Roock" wrote: > Hello GAP forum, > > I created the free group ( i got this spec. for the group from a > textbook-exercise ): > gap> F:=FreeGroup(3); > > gap> x:=F.1; > f1 > gap> y:=F.2; > f2 > gap> z:=F.3; > f3 > gap> G:=F/[y^3*z^15,x^4*y^7*z^3,x^8,y^14,z^18]; > > > Then when I wanted to now the size of the group, GAP became a bit of > erratic. > That's a huge group for sure (as you can gather, using PQuotient, that it's at least 2^97) Can it be ininite? Anyhow, enumerating conjugacy classes modulo the trivial subgroup (that's what Size will try to do) is out of the question. -- Dima Pasechnik http://www.ntu.edu.sg/home/dima/ From hulpke at mac.com Sun Feb 26 18:21:56 2006 From: hulpke at mac.com (Alexander Hulpke) Date: Sun Feb 26 18:22:29 2006 Subject: [GAP Forum] Unexpected Behaviour in Size() In-Reply-To: References: Message-ID: <15FD609B-88E8-45F2-81C5-BC8B74E31162@mac.com> Dear GAP-Forum, Nilo de Roock wrote: On Feb 26, 2006, at 9:39 AM, Nilo de Roock wrote: > Hello GAP forum, > > I created the free group ( i got this spec. for the group from a > textbook-exercise ): > gap> F:=FreeGroup(3); > > gap> x:=F.1; > f1 > gap> y:=F.2; > f2 > gap> z:=F.3; > f3 > gap> G:=F/[y^3*z^15,x^4*y^7*z^3,x^8,y^14,z^18]; > > > Then when I wanted to now the size of the group, GAP became a bit > of erratic. I would not call this erratic. This is the expected behaviour, as there are fundamental difficulties on algorithmic methods for finitely presented groups. (The so-called ``word problem''.) You might want to read the AMS notices article by 'Akos Seress (notices.ps on the page http://www.math.ohio-state.edu/~akos/ ) or the recent ``Handbook of Computational Group Theory'' by Holt et. al. for methods used and some of the fundamental problems arising. GAP issues warnings that it is performing a lot (probably more than you expected) work, and still does not have a result. This is an indication that you might needs lots of memory or would be on the way of overloading your computer without ever getting a result -- GAP is trying to stop you doing something you don't really want. In your case, GAP tries to compute the size of an fp group by calculating the index of a cyclic subgroup and rewriting the presentation. However an easy calculation (abelian invariants of G') shows that your group is infinite and cannot have any cyclic subgroup of finite index. Best wishes, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hulpke@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke From dfh at maths.warwick.ac.uk Sun Feb 26 20:49:06 2006 From: dfh at maths.warwick.ac.uk (Derek Holt) Date: Sun Feb 26 20:50:54 2006 Subject: [GAP Forum] Unexpected Behaviour in Size() In-Reply-To: <15FD609B-88E8-45F2-81C5-BC8B74E31162@mac.com> References: <15FD609B-88E8-45F2-81C5-BC8B74E31162@mac.com> Message-ID: <20060226204906.GA4036@maths.warwick.ac.uk> Dear GAP-Forum, On Sun, Feb 26, 2006 at 11:21:56AM -0700, Alexander Hulpke wrote: > Dear GAP-Forum, > > Nilo de Roock wrote: > > On Feb 26, 2006, at 9:39 AM, Nilo de Roock wrote: > > >Hello GAP forum, > > > >I created the free group ( i got this spec. for the group from a > >textbook-exercise ): > >gap> F:=FreeGroup(3); > > > >gap> x:=F.1; > >f1 > >gap> y:=F.2; > >f2 > >gap> z:=F.3; > >f3 > >gap> G:=F/[y^3*z^15,x^4*y^7*z^3,x^8,y^14,z^18]; > > > > > >Then when I wanted to now the size of the group, GAP became a bit > >of erratic. > > I would not call this erratic. > > This is the expected behaviour, as there are fundamental difficulties > on algorithmic methods for finitely presented groups. (The so-called > ``word problem''.) > You might want to read the AMS notices article by 'Akos Seress > (notices.ps on the page http://www.math.ohio-state.edu/~akos/ ) > or the recent ``Handbook of Computational Group Theory'' by Holt et. > al. for methods used and some of the fundamental problems arising. > > GAP issues warnings that it is performing a lot (probably more than > you expected) work, and still does not have a result. This is an > indication that you might needs lots of memory or would be on the way > of overloading your computer without ever getting a result -- GAP is > trying to stop you doing something you don't really want. > > In your case, GAP tries to compute the size of an fp group by > calculating the index of a cyclic subgroup and rewriting the > presentation. However an easy calculation (abelian invariants of G') > shows that your group is infinite and cannot have any cyclic subgroup > of finite index. Another way to show that the group is infinite is to use rewriting systems. The MakeConfluent command succeeds quickly, and by inspecting the rules in the confluent system, we find that G = < x,y,z | z^3=y, y^2=1, x^4=1, yz=zy >, so G is the free product of the cyclic groups and or orders 6 and 4. In fact it is not difficult to establish that with a hand calculation, which was probably what was intended in the textbook exercise! I guess in a perfect world, asking whether a finitely presented group was finite or infinite would automatically trigger these types of calculations (coset enumeration, abelian invariants of finite index subgroups, rewriting systems) each being tried in succession (or perhaps in parallel) for progressively longer times. Derek Holt. From dutour at liga.ens.fr Thu Feb 23 05:17:19 2006 From: dutour at liga.ens.fr (Mathieu Dutour) Date: Mon Feb 27 10:16:54 2006 Subject: [GAP Forum] A strange error Message-ID: <20060223051719.GA24588@orge.ens.fr> Hi all, I got the following error with gap 4.4.6: gap> RepresentativeAction(Group(()), [1], [2], OnSets); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for epresentativeActionOp' on 3 arguments called from RepresentativeActionOp( G, d[1], e[1] ) called from RepresentativeActionOp( G, d, e, act ) called from ( ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> The following commands work as expected. RepresentativeAction(Group(()), [1], [1], OnSets); RepresentativeAction(Group(()), [1], [1,3], OnSets); RepresentativeAction(Group(()), [1,3], [2,3], OnSets); Mathieu -- Mathieu Dutour Sikiric Researcher in Math Tel. (+972)2 65 84 103 and Computer Science Fax. (+972)2 56 30 702 Einstein Institute of Mathematics E-mail: Mathieu.Dutour@ens.fr Hebrew University of Jerusalem http://www.liga.ens.fr/~dutour Israel From hulpke at math.colostate.edu Mon Feb 27 20:05:31 2006 From: hulpke at math.colostate.edu (Alexander Hulpke) Date: Mon Feb 27 20:06:21 2006 Subject: [GAP Forum] A strange error In-Reply-To: <20060223051719.GA24588@orge.ens.fr> References: <20060223051719.GA24588@orge.ens.fr> Message-ID: Dear GAP-Forum, On Feb 22, 2006, at 22:17 , Mathieu Dutour wrote: > I got the following error with gap 4.4.6: > gap> RepresentativeAction(Group(()), [1], [2], OnSets); Thank you for the error report. This will be corrected in the next bugfix. (Let me know in private, if you want a temporary patch.) Best wishes, Alexander Hulpke PS: I would like to take the opportunity to once more remind everyone of the `support@gap-system.org' email address for reporting errors which likely are of little interest to the whole list. From ndroock1 at gmail.com Mon Feb 27 21:05:51 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Mon Feb 27 21:07:01 2006 Subject: [GAP Forum] StructureDescription In-Reply-To: <200602261339.19621.costanti@science.unitn.it> References: <200602261339.19621.costanti@science.unitn.it> Message-ID: Hello Marco, Thank you very much for your help. And, yes I will use the support address in the future for this sort of questions. Since GAP is Open Source anyway, is it possible to subscribe to the support-list? These lists usually become the best knowledgebase around, at least for the other software I work with. ( The only thing that's preventing me from reading the GAP source code is the language, C instead Java. Well, Java wasn't around when it all started. ) Although I am still fairly new to GAP I think it's fair to say that the feedback and answers on this list are both excellent and friendly. Isn't that' a rather unique combination in the field? kind regards, nilo de roock 2006/2/26, Marco Costantini : > Dear Nilo de Roock, > > (Warning: > this answer is a draft, and has not yet been discussed with other people > of the GAP Support Group. More detailed information may (or may not) > arrive later. Feel free to write again if you need more help. For any > remark concerning this mail, please do not reply to me, but write to > support@gap-system.org .) > > We offer to react as well as we can to questions, requests for help with > problems, or complaints that you may have. However, for the sake of the whole > user community of GAP, we ask you to separate these into two different > categories. > > GAP Support. We would like to deal with those topics that are more or less > local to you, that is, are likely not of interest to most of the other GAP > users by direct correspondence with you. Please send letters about such local > problems and questions also to the address support@gap-system.org. > > GAP Forum. On the other hand, the GAP Forum should be reserved for > discussions about problems that are likely to interest many of the GAP users. > It would also be welcome if you could occasionally tell other users in the > GAP Forum about interesting applications you have made of GAP. > > > On Sunday 26 February 2006 11:44, Nilo de Roock wrote: > > Hello GAP forum, > > > > Forgive for yet another question (...) on this command, perhaps I am using > > the wrong command for my purpose. When I execute the following command. > > > > gap> List(AllGroups(20),StructureDescription); > > > > GAP responds with > > [ "C5 : C4", "C20", "C5 : C4", "D20", "C10 x C2" ] > > > > The issue I have here is that "C5:C4" occurs twice in the list. > > Yes, in fact StructureDescription is not injective, an two of the groups with > 20 elements have a similar structure. > > > What I am > > looking for is a command that would recognize that the Frobenius group > > is in there somewhere. > > > > > > Even if I do... > > > > gap> F:=FreeGroup(2); > > > > gap> s:=F.1; > > f1 > > gap> t:=F.2; > > f2 > > gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1]; > > > > gap> Size(G); > > 20 > > gap> str(G); > > "C5 : C4" > > gap> > > > > the answer is "C5:C4". > > > > > > I am getting lost on this command, and thus on GAP. Please help. > > A possibility is simply > > gap> IdGroup(G); > [ 20, 3 ] > > that is, G is the 3rd group in AllGroups(20) . > > Another possibility is to use StructureDescription only to restrict to some of > the groups, and then to proceed with something else. For instance > > gap> G_20_1 := SmallGroup(20,1); > > gap> G_20_3 := SmallGroup(20,3); > > > After using StructureDescription you know that the other groups with 20 > elements are not isomorphic to your G. > > After that you can use: > > gap> IsomorphismGroups( G_20_1, G ); > fail > gap> IsomorphismGroups( G_20_3, G ); > [ f1, f2, f3 ] -> [ f1^5, f1^2, f2 ] > > you can also use: > > gap> Length( ConjugacyClasses( G ) ); > 5 > gap> Length( ConjugacyClasses( G_20_1 ) ); > 8 > gap> Length( ConjugacyClasses( G_20_3 ) ); > 5 > > you can also use anything else analogous. > > All the best, > Marco Costantini > From wdjoyner at comcast.net Mon Feb 27 12:08:22 2006 From: wdjoyner at comcast.net (David Joyner) Date: Tue Feb 28 02:57:38 2006 Subject: [GAP Forum] GAP's impact on mathematics Message-ID: <4402EBB6.50406@comcast.net> Hello: Although the GAP website has a bibliography, and an examples page http://www.gap-system.org/Doc/Examples/examples.html , I was looking for a page summarizing some of the problems GAP has helped resolve. What are some interesting problems in mathematics that GAP was instrumental in resolving? Has GAP resolved any famous conjectures? Work on Riemann surfaces using "braid", based on Thomas Breuer's ideas, comes to mind as an example. Unfortunately, that isn't even mentioned, as far as I could see. Anyone else have any favorite applications of GAP? - David Joyner From aodabas at ogu.edu.tr Tue Feb 28 16:47:35 2006 From: aodabas at ogu.edu.tr (=?iso-8859-9?Q?Alper_Odaba=FE?=) Date: Tue Feb 28 16:47:22 2006 Subject: [GAP Forum] elements of algebra Message-ID: <001101c63c86$ad5a0540$a8838cc1@ogu209> Good day. I have some (maybe stupid) questions: How can I get all elements of given algebra? For elements a,b in group G the command a^b in GAP computes (b^-1ab). How can I compute it in algebra case. is GAP best way in Commutative Algebra??? or CoCoA, Magma Thank you. Alper From kohl at mathematik.uni-stuttgart.de Thu Mar 2 12:14:33 2006 From: kohl at mathematik.uni-stuttgart.de (Stefan Kohl) Date: Thu Mar 2 12:14:37 2006 Subject: [GAP Forum] elements of algebra In-Reply-To: <001101c63c86$ad5a0540$a8838cc1@ogu209> References: <001101c63c86$ad5a0540$a8838cc1@ogu209> Message-ID: <4406E1A9.5000000@mathematik.uni-stuttgart.de> Dear Forum, Alper Odaba? wrote: > Good day. > I have some (maybe stupid) questions: > How can I get all elements of given algebra? If your algebra is finite, then you can use `AsList'. E.g.: gap> A := FullMatrixAlgebra(GF(2),2); ( GF(2)^[ 2, 2 ] ) gap> AsList(A); [ [ , ], [ ... (rest of output omitted for saving space) ... ] > For elements a,b in group G the command a^b in GAP computes (b^-1ab). How can I compute it in algebra case. In general you cannot. The reason for this is simply that in general not all elements of an algebra are invertible. > is GAP best way in Commutative Algebra??? or CoCoA, Magma I feel that I am not a neutral person in this respect, thus prefer to leave commenting on this to other people. Hope this helps, Stefan Kohl From hulpke at math.colostate.edu Thu Mar 2 18:15:55 2006 From: hulpke at math.colostate.edu (Alexander Hulpke) Date: Thu Mar 2 18:17:04 2006 Subject: [GAP Forum] Serious bug in `PolynomialReduction' Message-ID: <9B0852C4-F263-4392-AB2A-42222D3D7237@math.colostate.edu> Dear GAP Forum, A user has reported a serious bug in the code for polynomial reduction (thus also affecting Groebner bases), which may return wrong results without warning. (See below for an example) This bug will be corrected in the forthcoming next bugfix. If you are using Groebner bases and need a temporary workaround already now, you can download the file http://www.math.colostate.edu/~hulpke/workaround.gi Read this file in with *Reread* (not Read, as it overwrites some library functions) We apologize for this problem! Alexander Hulpke Example with correct output: x:=X(Rationals,"x");; y:=X(Rationals,"y");; a:=X(Rationals,"a");; c:=X(Rationals,"c");; s:=X(Rationals,"s");; L:=[(a+c)*s-x,(a+c)*c-y,s^2+c^2-1];; ReducedGroebnerBasis(L,MonomialLexOrdering([x,y,a,c,s])); [ c^2+s^2-1, -a*c+s^2+y-1, -a*s-c*s+x ] (2nd polynomial was wrong!) -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hulpke@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke From anvita21 at usa.com Fri Mar 3 05:11:01 2006 From: anvita21 at usa.com (Anvita) Date: Fri Mar 3 05:14:16 2006 Subject: [GAP Forum] Coefficients of constant polynomials Message-ID: <20060303051101.4C0A0BA44C@ws3-2.us4.outblaze.com> Dear Forum, When I apply the function "CoefficientsOfUnivariatePolynomial" to the unit polynomial I get the result [ 1 ], as expected: ----------------------------------------------- gap> R:=PolynomialRing(Integers,["x"]); PolynomialRing(..., [ x ]) gap> i:=One(R); 1 gap> CoefficientsOfUnivariatePolynomial(i); [ 1 ] ----------------------------------------------- For the zero polynomial, however, it returns an empty set: ----------------------------------------------- gap> o:=Zero(R); 0 gap> CoefficientsOfUnivariatePolynomial(o); [ ] ----------------------------------------------- Why isn't the result [ 0 ] ? Could this be a bug? Thank you Anvita -- ___________________________________________________ Play 100s of games for FREE! http://games.mail.com/ From alexander.konovalov at gmail.com Fri Mar 3 10:55:43 2006 From: alexander.konovalov at gmail.com (Alexander Konovalov) Date: Fri Mar 3 10:57:17 2006 Subject: [GAP Forum] LAGUNA 3.3.2 Message-ID: <5b6b8f6c0603030255u47926866iafa7cdb4ef2bd20@mail.gmail.com> Dear GAP Forum, this is to announce the availability of the new version of the LAGUNA package. The LAGUNA package provides functionality for calculation of the normalized unit group of the modular group algebra of the finite p-group and for investigations of Lie algebras associated with group algebras. LAGUNA 3.3.2 was released on March 01, 2006 and it is available from the following pages: - http://ukrgap.exponenta.ru/laguna.htm - http://www.gap-system.org/Packages/laguna.html and also in a merged archive of all currently redistributed GAP packages available from http://www.gap-system.org/Download/index.html The new version resolves a problem in compatibility with GAP methods for Lie algebras and essentially improves performance for computation of the normalized unit group in abelian case. Sincerely yours, Alexander Konovalov From hulpke at mac.com Fri Mar 3 16:07:39 2006 From: hulpke at mac.com (Alexander Hulpke) Date: Fri Mar 3 16:09:22 2006 Subject: [GAP Forum] Coefficients of constant polynomials In-Reply-To: <20060303051101.4C0A0BA44C@ws3-2.us4.outblaze.com> References: <20060303051101.4C0A0BA44C@ws3-2.us4.outblaze.com> Message-ID: <571DE562-15CE-4DA9-A6B3-BD626AE7B173@mac.com> Dear Forum, `Anvita21' wrote: > When I apply the function "CoefficientsOfUnivariatePolynomial" to the > > unit polynomial I get the result [ 1 ], as expected: > > > > For the zero polynomial, however, it returns an empty set: Yes. the zero polynomial is stored by an empty coefficient list, as there are no nonzero coefficients. > Why isn't the result [ 0 ] ? Because storing the zero polynomial that way would require extra treatment in some arithmetic routines (e.g. multiplication). > > Could this be a bug? No. This is intended. Best wishes, Alexander Hulpke > ___________________________________________________ > Play 100s of games for FREE! http://crappy.advertising.dump/ From alexk at mcs.st-and.ac.uk Sat Mar 4 10:21:39 2006 From: alexk at mcs.st-and.ac.uk (Alexander Konovalov) Date: Sat Mar 4 10:08:17 2006 Subject: [GAP Forum] LAGUNA 3.3.2 Message-ID: Dear GAP Forum, this is to announce the availability of the new version of the LAGUNA package. The LAGUNA package provides functionality for calculation of the normalized unit group of the modular group algebra of the finite p-group and for investigations of Lie algebras associated with group algebras. LAGUNA 3.3.2 was released on March 01, 2006 and it is available from the following pages: - http://ukrgap.exponenta.ru/laguna.htm - http://www.gap-system.org/Packages/laguna.html and also in a merged archive of all currently redistributed GAP packages available from http://www.gap-system.org/Download/index.html The new version resolves a problem in compatibility with GAP methods for Lie algebras and essentially improves performance for computation of the normalized unit group in abelian case. Sincerely yours, Alexander Konovalov From dn2447 at yahoo.com Sat Mar 4 21:19:04 2006 From: dn2447 at yahoo.com (D N) Date: Sat Mar 4 21:22:58 2006 Subject: [GAP Forum] Character group and semi-direct product Message-ID: <20060304211904.41058.qmail@web37406.mail.mud.yahoo.com> Hello All, Let G be a finite group and H be a finite left G-module. Let H^ := Hom(H, C*) denote the character group of H. Then, H^ is a right G-module: (\rho \dot g)(h) := \rho(g \dot h) for \rho \in H^, g \in G and h \in H. Let G' := H^ : G (semi-direct product of H^ and G). My question is: how to construct the group G' in GAP? Any help is greatly appreciated. Thanks, DN --------------------------------- Relax. Yahoo! Mail virus scanning helps detect nasty viruses! From anvita21 at usa.com Mon Mar 6 02:03:43 2006 From: anvita21 at usa.com (Anvita) Date: Mon Mar 6 02:05:17 2006 Subject: [GAP Forum] Re: Coefficients of constant polynomials Message-ID: <20060306020343.3221A21B32F@ws3-5.us4.outblaze.com> >> If the function "CoefficientsOfUnivariatePolynomial" is applied to the >> unit polynomial, the result is [ 1 ], as expected: >> ... >> For the zero polynomial, however, it returns an empty set: > >Yes. the zero polynomial is stored by an empty coefficient list, as >there are no nonzero coefficients. > If the zero polynomial is stored as an empty list then why does the function "UnivariatePolynomial" return an error with an empty list as the second argument? --------------------------------------------------------------------------------------- gap> p:=UnivariatePolynomial(Integers,[]); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `UnivariatePolynomial' on 2 arguments called from ( ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> --------------------------------------------------------------------------------------- Anvita -- ___________________________________________________ Play 100s of games for FREE! http://games.mail.com/ From hulpke at mac.com Mon Mar 6 02:33:14 2006 From: hulpke at mac.com (Alexander Hulpke) Date: Mon Mar 6 02:36:27 2006 Subject: [GAP Forum] Re: Coefficients of constant polynomials In-Reply-To: <20060306020343.3221A21B32F@ws3-5.us4.outblaze.com> References: <20060306020343.3221A21B32F@ws3-5.us4.outblaze.com> Message-ID: <8DF3C528-F950-4FDE-9938-547FF57F411B@mac.com> Dear Gap Forum, Someone called `Anvita' wrote: > >>> If the function "CoefficientsOfUnivariatePolynomial" is applied >>> to the >>> unit polynomial, the result is [ 1 ], as expected: >>> ... >>> For the zero polynomial, however, it returns an empty set: >> >> Yes. the zero polynomial is stored by an empty coefficient list, as >> there are no nonzero coefficients. >> > > If the zero polynomial is stored as an empty list then why does the > function > "UnivariatePolynomial" return an error with an empty list as the > second > argument? That is an oversight. (The conditions on coefficients is to be a list of ring elements, the empty list does not qualify and needs to be treated specially.) Thank you for spotting this. It will be corrected in a future release. As a workaround you can issue the command: InstallOtherMethod( UnivariatePolynomial, "ring,empty cof",true, [ IsRing, IsEmpty ], 0, function( ring, cofs ) return LaurentPolynomialByCoefficients( ElementsFamily(FamilyObj (ring)),cofs, 0, 1 ); end ); Best wishes, Alexander Hulpke From ndroock1 at gmail.com Mon Mar 6 07:04:57 2006 From: ndroock1 at gmail.com (Nilo de Roock) Date: Mon Mar 6 07:07:39 2006 Subject: [GAP Forum] Re: GAP issue In-Reply-To: References: Message-ID: Thanks Ignat, This idea about IdGroup() was also in most of the other replies and yes, it helps. I suppose that if StructureDescription() was perfect we wouldn't be doing Group Theory in the first place. ;-) Kind regards, nilo 2006/3/5, ignat soroko : > Hello, Nilo, > > I read some of your questions in GAP forum and I'd like to suggest a solution. > > You like the function StructureDescription. This is a wonderful > function, but it gives only a rough idea what the group is. It does > not determine the group up to isomorphism. What determines the group > up to isomorphism, is IdGroup() function. Type IdGroup(G) and you will > get a pair [ord, nr]. That means that G is isomorphic to the group > number nr among all groups of order ord, that is to > SmallGroup(ord,nr);. > > Thus to determine a group up to isomorphism one should use IdGroup(). > And to get some idea what is the structure of the group, one can use > StructureDescription(). > > Hope this helps. > > Ignat > From dn2447 at yahoo.com Mon Mar 6 18:31:46 2006 From: dn2447 at yahoo.com (D N) Date: Mon Mar 6 18:35:58 2006 Subject: [GAP Forum] Character group and semi-direct product Message-ID: <20060306183146.86690.qmail@web37411.mail.mud.yahoo.com> Dear GAP Forum, Actually, I found (quite inefficient though) a way to do this. My apologies if the question and the follow-up is too trivial to post on this forum. Let H be any Abelian group. The irreducible characters of H can be obtained by typing "Display(Irr(CharacterTable(H)));" Form diagonal matrices with rows of the above output. The group generated by these diagonal matrices is of course isomorphic to the character group H^. Putting the required action on H^ and forming the semidirect product is quite straight-forward. Thanks, DN D N wrote: Hello All, Let G be a finite group and H be a finite left G-module. Let H^ := Hom(H, C*) denote the character group of H. Then, H^ is a right G-module: (\rho \dot g)(h) := \rho(g \dot h) for \rho \in H^, g \in G and h \in H. Let G' := H^ : G (semi-direct product of H^ and G). My question is: how to construct the group G' in GAP? Any help is greatly appreciated. Thanks, DN --------------------------------- Relax. Yahoo! Mail virus scanning helps detect nasty viruses! _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum --------------------------------- Relax. Yahoo! Mail virus scanning helps detect nasty viruses! __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com From dn2447 at yahoo.com Wed Mar 8 20:11:53 2006 From: dn2447 at yahoo.com (D N) Date: Wed Mar 8 20:12:43 2006 Subject: [GAP Forum] Having trouble with cohomolo package Message-ID: <20060308201153.4761.qmail@web37406.mail.mud.yahoo.com> Dear GAP Forum, I get the following message: gap> Read("cohomolo.tst"); Function: number of arguments must be 2 (not 5) at Cohomology( chr, true, false, false, TmpName( ) ); called from ( ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can replace the argument list via 'return ;' to continue brk> What is going on here? DN --------------------------------- Relax. Yahoo! Mail virus scanning helps detect nasty viruses! From l.h.soicher at qmul.ac.uk Thu Mar 9 14:26:13 2006 From: l.h.soicher at qmul.ac.uk (Leonard Soicher) Date: Thu Mar 9 14:26:49 2006 Subject: [GAP Forum] Groups and Computation 2006 - A Leedham-Green Fest Message-ID: <20060309142613.GA6441@mrcpc02.maths.qmul.ac.uk> Groups and Computation 2006 A Leedham-Green Fest We are pleased to announce a one-day conference to celebrate Charles Leedham-Green's contributions to mathematics on the occasion of his retirement. 10th July 2006, starting at 10.30 School of Mathematical Sciences Queen Mary, University of London The main speakers are: Bettina Eick, Eamonn O'Brien, and Aner Shalev (tbc) There is a registration fee of 10 pounds to cover refreshments and lunch. There will also be a celebratory dinner on the evening of July 10th at L'Oasis, costing 20 pounds. Places are limited, and are available on a first-come first-served basis. Should you wish to attend, please mail a cheque or postal order in GBP, payable to "Queen Mary, University of London", covering the registration fee and dinner (if applicable), to: Dr S. McKay Groups and Computation 2006 School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS U.K. Please include your name and email address. We shall contact you by email with more information in due course, including menu choices for the dinner. If you have any queries, please email S.McKay@qmul.ac.uk Some accommodation will be available in the new Queen Mary student village. If you wish to stay for one or more nights, it is important to book as soon as possible. You can book online at www.qmulholidays.co.uk If you experience any problems with this, then phone +44(0)20-7882-3642. We look forward to seeing you at Queen Mary! Sue McKay, Leonard Soicher, Peter Cameron From aodabas at ogu.edu.tr Thu Mar 9 15:10:17 2006 From: aodabas at ogu.edu.tr (=?iso-8859-9?Q?Alper_Odaba=FE?=) Date: Thu Mar 9 15:09:48 2006 Subject: [GAP Forum] Automorphism of Algebra Message-ID: <004201c6438b$93383f90$be838cc1@ogu209> Hi all, I have a question for algebra , Let A and B algebras. Suppose that B acts on A, is there a algebra homomorphism B --> Aut(A) ?? has GAP any function Automorphism of commutative algebras?? gap> G:=Group((1,2,3,4));; gap> A:=GroupRing(GF(3),G);; gap> Automorphism(A); Variable: 'Automorphism' must have a value gap> AutomorphismAlgebra(A); Variable: 'AutomorphismAlgebra' must have a value gap> Automorphisms(A); Variable: 'Automorphisms' must have a value gap> Automorphism(A); Variable: 'Automorphism' must have a value gap> AutomorphismOfAlgebra(A); Variable: 'AutomorphismOfAlgebra' must have a value gap> AutomorphismRing(A); Variable: 'AutomorphismRing' must have a value gap> AutomorphismOfRing(A); Variable: 'AutomorphismOfRing' must have a value thanks. Alper From sal at dcs.st-and.ac.