[GAP Forum] StructureDescription Revisited

[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 <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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> >
>
>
>