[GAP Forum] Fwd: stabilizer problem

[John McDermott]

Begin forwarded message:

> From: Alexander Hulpke <hulpke at math.colostate.edu>
> Date: 28 February 2005 18:30:42 GMT
> To: gap-forum at gap-system.org
> Subject: Re: stabilizer problem
>
> Dear Gap Forum,
>
> Mathieu Dutour wrote:
>
>> I am computing with Integral Matrix Groups in GAP.
>
>> The action of the matrix Group on this set is
>   [...]
>> Using that action, I want to use function Stabilizer
>   [...]
>> However, in some cases, the computation fails by lack of
>> memory (for example in dimension 15 with the symmetry group
>> of Lambda15 of order 41287680) Those cases arise when the
>> stabilizer groups to be computed are small.
>
> Unless the group is a permutation group acting on points, sets, 
> elements or
> subgroups (in which case a backtrack algorithm is used) the 
> calculation of a
> stabilizer (or representative) usually works by enumerating the orbit.
>
> If the stabilizer is small this orbit is large and this can cause you
> running out of memory.
>
> The only way around it (apart from getting more memory or recoding to 
> save
> storage space) is to reduce the stabilizer computation into smaller 
> steps by
> finding an intermediate subgroup U such that Stab<U<G.
>
> Typically such an U can be found as stabilizer under another 
> ``coarser''
> action. Sometimes it can be written down from the structure of the 
> domain
> (say a subspace stabilizer in GL), sometimes it is found by 
> considering an
> action that is not necessarily faithful (projective action, reduction 
> modulo
> a prime or similar). Which action to use concretely will depend very 
> much on
> the concrete case.
>
> In your situation, considering reduction modulo a prime that does not 
> occur
> in the denominators might be a first approach.
>
> Best wishes,
>
>    Alexander Hulpke
>
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
> http://www.math.colostate.edu/~hulpke
>
>
--
John McDermott
Computing Officer & Purchase Officer
School of Computer Science
University of St Andrews
North Haugh, St Andrews, Fife
KY16 9SX

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