[GAP Forum] The stability of group libraries

[Leonard Soicher]

Dear Alexander K., Stefan, Dima, Alexander H., Derek,  and GAP-Forum,

Thank you for the useful replies.

> - In the library of transitive groups, the actual permutation groups 
> (but not the generators used) are guaranteed to be stable. So you could refer 
> to a particular point set and a particular group in a combinatorial construction.
>

Good.

> 
> - The *new* library of primitive groups, release with GAP 4.2, guarantees a stable 
> numbering  [...] but does not guarantee a fixed S_n representative or particular generators.
> 

It would be better if the actual permutation groups in the library of 
primitive groups could be guaranteed to be stable.
Why would this not be possible? 

Finally, the guarantees (or their lack, or any cautions) for specific libraries should be 
documented in the GAP reference manual. 

Thanks,
Leonard 

________________________________________
From: Derek Holt <D.F.Holt at warwick.ac.uk>
Sent: 28 January 2015 16:54
To: Alexander Hulpke
Cc: Leonard Soicher; forum at gap-system.org
Subject: Re: [GAP Forum] The stability of group libraries

Dear Alexander, dear Forum,

On Wed, Jan 28, 2015 at 09:02:12AM -0700, Alexander Hulpke wrote:
> Dear Leonard, Dear Forum,
>
> > I would like to know what the policy is concerning the groups
> > in the the very useful GAP libraries of transitive permutation groups and
> > of primitive permutation groups (and any other group library you wish to comment on)
> > as regards to any possible changes wihen changes are made in GAP. In particular,
> > were the actual groups in the library, their GeneratorsOfGroup, and their indexing
> > within the library fixed in perpetuity when the library was initially made available in GAP4,
> > and if not, what is the mechanism to alert users to any changes? This is important
> > for being able to repeat, check, report on, and extend results made using specific
> > groups in a given  library.
>
> We guarantee the following for the most prominent group libraries. (Guarantees are not exactly the same, as the construction processes differ).
>
> - In the library of small groups, the numbering of isomorphism types is guaranteed to be stable. Actual group generators, or the PC presentations used could theoretically change (though there is no intention to do so, unless it would reflect a deeper mathematical understanding, and if this happened I'd expect an explicit announcement in the release notes.)
>
> - In the library of transitive groups, the actual permutation groups (but not the generators used) are guaranteed to be stable. So you could refer to a particular point set and a particular group in a combinatorial construction.
>
> - The *old* library of primitive groups had in fact an unstable numbering, dependent on the implementation of the subgroup lattice algorithm. This library was therefore retired with the release of GAP 4.2.
>
> - The *new* library of primitive groups, release with GAP 4.2, guarantees a stable numbering (which for degree up to 50 is compatible with lists published in the literature), but does not guarantee a fixed S_n representative or particular generators.
>
> (To the best of my knowledge the numbering of groups is compatible with other systems that provide such libraries.)

Magma has the same numbering for the small groups and transitive groups
databases, but a completely different numbering for the primitive groups.
I believe that the divergence resulted originally as a result of errors
(missing groups) in the old list, which were rectified in different ways.

It seems very unlikely indeed that there are errors in either the small groups
or the transitive groups databases, because they have been independently
checked, but I guess that if a mistake were to be found then that might
force a chage in numbering.

Derek.

> There is no mechanism for explicitly alerting users of changes in the non-guaranteed properties. A change in the guaranteed properties would presumably mean that the library was retired and replaced with a new library.
>
> Needless to say, any such promises are only worth as much as the promiser, as anyone who endowed a chantry before 1545 can tell you.
>
> Best,
>
>   Alexander
>
>
>
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