Dear GAP Forum,
On 7 Jun 2011, at 01:56, Piyush garg wrote:
> I am very tahnkful to Peter, Stefan and Steve for helping me out.
> Now I am able to do this through GeneratorsOfGroup and SmallGeneratingSet ,
> but I am still getting the error message for MinimalGeneratingSet (thats ok,
> i will keep it on hold for moment).
As I said, the next version will give a better error message, but we don't have
a way to
compute a minimal cardinality generating set efficiently for non-solvable
groups.
>
> I have two more doubts :
> ## How to get the matrices from the output generated by GeneratorsOfGroup
> for the Special Linear Group; like for SL(2,17) :
> s:=SL(2,17);
> gens:=GeneratorsOfGroup(s);
> [ [ [ Z(17), 0*Z(17)], [ 0*Z(17), Z(17)^15 ] ],
> [ [ Z(17)^8, Z(17)^0], [Z(17)^8, 0*Z(17)] ] ]
>
> this is the output we are getting, now hwo to get the matrices from it which
> can generate the whole set of SL(2,17) ?? (with the elements' values from 0
> to 16.)
>
Well, this is two matrices that generate the whole of SL(2,17), but not
represented in the way you want.
You can visualize them in the form you want using Display
gap> Display(gens[1]);
3 .
. 6
gap> Display(gens[2]);
16 1
16 .
where the . represents zero, Alternatively you need to use the IntFFE function
to convert
elements of the Galois field of order 17 into integers. Because you have list
of matrices -- ie a list of lists of lists, you do it as follows:
gap> intgens := List(gens, m -> List(m, r-> List(r, IntFFE)));
[ [ [ 3, 0 ], [ 0, 6 ] ], [ [ 16, 1 ], [ 16, 0 ] ] ]
I don't know if this is appropriate format for matlab, but if it is, you can
write it to a file by
gap> PrintTo( "sl17gens", intgens);
If you have further problems, I'd suggest asking on the GAP support mailing
list, rather than the forum.
We will report back here any advice of wider interest
Yours
Steve Linton
> ## How can we store this output of matrices in a file and make use of
> them in Matlab program ??
> like storing the matrices now generated in a 3d-array and then later using
> them in Matlab.
>
> Thank you again for helping me out.
>
> Regards,
> Piyush Garg.
>
>
> On Mon, Jun 6, 2011 at 7:51 PM, Stephen Linton
> <s...@cs.st-andrews.ac.uk>wrote:
>
>> Dear GAP Forum,
>>
>> As Peter has already reported, if you simply want a generating set then
>> GeneratorsOfGroup is the appropriate function.
>> As you will see from the documentation (try ?GeneratorsSmallest for
>> instance), the functions you called: GeneratorsSmallest and
>> MinimalGeneratingSet
>> make much stronger promises about the result, which GAP has to do much more
>> work to achieve.
>>
>> An intermediate choice is SmallGeneratingSet, which tries heuristically to
>> reduce the size of the set it returns, but makes no firm promises.
>>
>> The error message from MinimalGeneratingSet is confusing, but, in fact GAP
>> has no way to compute this function for general groups. In the next release
>> you will get the rather more helpful error message:
>>
>> Error, `MinimalGeneratingSet' currently assumes that the group must be
>> solvable.
>> In general, try `SmallGeneratingSet' instead, which returns a generating
>> set that is small but not of guarateed smallest cardinality
>>
>> It is also possible, looking at the error message that you have mixed up g
>> and G. Remember that GAP is case-sensitive.
>>
>> Yours
>>
>> Steve Linton
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