[GAP Forum] StructureDescription Revisited

[Nilo de Roock]

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 <ndroock1 at gmail.com>:
> 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 <jack at ms.uky.edu>:
> > 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.
> > >
> > > <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. )
> > > </EXAMPLE>
> > >
> > > 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
> > >
> > > _______________________________________________
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> > >
> >
> >
> >
>