Hi Leonard, I suppose your definition of a Unix system includes Windows with Cygwin installed, and with GAP installed via the Cygwin route, right?
Best, Dima On 23 March 2010 01:53, Leonard Soicher <l.h.soic...@qmul.ac.uk> wrote: > Dear Forum, > > I would suggest making use of the DESIGN package and its > function to compute the automorphism group of a block > design, as illustrated in the logfile, below. > The DESIGN package uses GRAPE for this computation, which > in turn makes use of Brendan McKay's nauty package, and so > this will only work on a Unix system on which GAP, GRAPE > and DESIGN have been fully installed. > > Regards, > Leonard > > gap> LoadPackage("design"); > > Loading GRAPE 4.3 (GRaph Algorithms using PErmutation groups), > by l.h.soic...@qmul.ac.uk. > > ----------------------------------------------------------------------------- > Loading DESIGN 1.4 (The Design Package for GAP) > by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/). > ----------------------------------------------------------------------------- > true > gap> st:=[ [ 2, 4, 11 ], [ 7, 10, 12 ], [ 3, 8, 10 ], [ 2, 6, 12 ], [ 3, 6, > 13 ], [ >> 1, 6, 10 ], [ 5, 11, 13 ], [ 1, 2, 3 ], >> [ 3, 4, 9 ], [ 5, 7, 8 ], [ 3, 7, 11 ], [ 4, 8, 12 ], [ 1, 8, 13 ], [ 5, >> 6, 9 ], [ 9, 12, 13 ], [ 1, 7, 9 ], >> [ 2, 5, 10 ], [ 2, 7, 13 ], [ 2, 8, 9 ], [ 6, 8, 11 ], [ 9, 10, 11 ], [ 4, >> 10, 13 ], [ 1, 11, 12 ], [ 1, 4, 5 ], >> [ 4, 6, 7 ], [ 3, 5, 12 ] ];; > gap> S:=BlockDesign(13,st); > rec( isBlockDesign := true, v := 13, > blocks := [ [ 1, 2, 3 ], [ 1, 4, 5 ], [ 1, 6, 10 ], [ 1, 7, 9 ], > [ 1, 8, 13 ], [ 1, 11, 12 ], [ 2, 4, 11 ], [ 2, 5, 10 ], [ 2, 6, 12 ], > [ 2, 7, 13 ], [ 2, 8, 9 ], [ 3, 4, 9 ], [ 3, 5, 12 ], [ 3, 6, 13 ], > [ 3, 7, 11 ], [ 3, 8, 10 ], [ 4, 6, 7 ], [ 4, 8, 12 ], [ 4, 10, 13 ], > [ 5, 6, 9 ], [ 5, 7, 8 ], [ 5, 11, 13 ], [ 6, 8, 11 ], [ 7, 10, 12 ], > [ 9, 10, 11 ], [ 9, 12, 13 ] ] ) > gap> AllTDesignLambdas(S); > [ 26, 6, 1 ] > gap> G:=AutomorphismGroup(S); > Group([ (1,7,9)(2,11,4)(5,13,10)(6,8,12), (4,11)(5,12)(6,10)(7,9)(8,13) ]) > gap> Size(G); > 6 > gap> > > On Mon, Mar 22, 2010 at 11:36:12AM -0600, Alexander Hulpke wrote: >> >> >> Dear Forum, >> >> Mbg Nimda asked: >> >> > I'm trying to determine the automorphism group of Steiner(2,3,13) but I get >> > a memory exceeded error. >> > Here is the session: >> > >> > gap> st; >> > [ [ 2, 4, 11 ], [ 7, 10, 12 ], [ 3, 8, 10 ], [ 2, 6, 12 ], [ 3, 6, 13 ], [ >> > 1, 6, 10 ], [ 5, 11, 13 ], [ 1, 2, 3 ], >> > [ 3, 4, 9 ], [ 5, 7, 8 ], [ 3, 7, 11 ], [ 4, 8, 12 ], [ 1, 8, 13 ], [ 5, >> > 6, 9 ], [ 9, 12, 13 ], [ 1, 7, 9 ], >> > [ 2, 5, 10 ], [ 2, 7, 13 ], [ 2, 8, 9 ], [ 6, 8, 11 ], [ 9, 10, 11 ], [ 4, >> > 10, 13 ], [ 1, 11, 12 ], [ 1, 4, 5 ], >> > [ 4, 6, 7 ], [ 3, 5, 12 ] ] >> > gap> >> > gap> >> > gap> g:=SymmetricGroup(13); >> > Sym( [ 1 .. 13 ] ) >> > gap> h:=Stabilizer(g,st,OnSetsSets); >> >> First, `st' should be sorted to be a set: >> st:=Set(st); >> >> Then, alas, the OnSetsSets action only does a naive orbit algorithm, and has >> no backtrack implementation. The stabilizer calculation therefore needs to >> form the whole orbit, which is unlikely to succeed. >> >> The best way to deal with this would be to use the GRAPE package, encode the >> steiner system in a graph and use the graph automorphism function. >> >> Alternatively (as 13 choose 3= 286 is still small), you could take the >> action on 3-sets, and in this action compute a set stabilizer (a single set >> stabilizer has a backtrack implementation and therefore much faster): >> >> gap> comb:=Combinations([1..13],3);; >> gap> act:=ActionHomomorphism(g,comb,OnSets,"surjective"); >> <action epimorphism> >> >> Now translate st to a set of points in this action of degree 286 >> gap> stp:=Set(List(st,x->Position(comb,x))); >> [ 1, 22, 42, 47, 56, 64, 83, 90, 99, 106, 107, 126, 137, 145, 149, 153, 175, >> 191, 199, 205, 210, 229, 239, 262, 277, 282 ] >> >> stabilize, and transfer back to S13: >> gap> u:=Stabilizer(Image(act),stp,OnSets); >> <permutation group of size 6 with 2 generators> >> gap> u:=PreImage(act,u); >> Group([ (4,11)(5,12)(6,10)(7,9)(8,13), (1,9)(2,4)(5,8)(6,13)(10,12) ]) >> >> I hope this helps, >> >> Alexander Hulpke >> >> -- Colorado State University, Department of Mathematics, >> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA >> email: hul...@math.colostate.edu, Phone: ++1-970-4914288 >> http://www.math.colostate.edu/~hulpke >> >> >> >> >> _______________________________________________ >> 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 > -- Dmitrii Pasechnik ----- DISCLAIMER: Any text following this sentence does not constitute a part of this message, and was added automatically during transmission. 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