policies

[Leonard Soicher]

Dear Developers,

I record here some policies for my GAP Writer (which is well on its way
to being able to write (almost) all of the external representation
excluding the statistical properties):

>
>Other areas (not exclusive) where we need to specify policies:
>
>    - how far to go with <block_concurrences>

The GAP Writer writes <block_concurrences> for k=1 and (unless there is
only one block) k=2. In both cases, preimages are collapsed to
<preimage_cardinality>s.  In other words, the information given are the
sizes of the blocks, the number of blocks of each size, the sizes of the
pairwise intersections of blocks, and the number of pairs of blocks
giving each intersection size.

>
>    - how far to go with <point_concurrences>
>	depending whether the design is t_design or not.
>

If the block design is not a t-design with t>=2 the GAP Writer writes
<point_concurrences> for k=1 and (unless there is only one point) k=2.
In both cases, the full preimage is given (which may be <entire_domain/>).
In other words, we give the replication number for each point and the
pairwise point concurrences.  

If the given block design  D  *is* a t-design with t>=2 the GAP Writer
writes <point_concurrences> for k=1,2,...,maximum t for which D is a
t-design.  Here, full preimages are given and they are all, of course,
<entire_domain/>.

I have tried to write (without being *too* verbose) the information of
interest to statisticians and to t-design theorists. 

More GAP Writer policy:

Information about resolutions is written iff the given block design
D has a component D.resolutions (usually made by the function 
MakeResolutionsComponent in the Design package). The Writer itself 
does not attempt to compute resolutions (the GAP Writer 
computes much of the other info it writes). Hence, the exact
info on resolutions which is written depends on what (if anything)
is stored in  D.resolutions.

For automorphism groups of resolutions, the GAP Writer does not write
the (optional) <automorphism_group_properties>, which have nowhere near
the interest that these properties have for the automorphism group of
the block design itself. To include these properties for each
resolution would be a waste of space. Of course, when the automorphism
group of a resolution is known, the GAP Writer gives its degree, order,
and a list of generators (acting on points).

Regards,  Leonard.