The methods in this chapter do not deal with relative difference sets. Instead, they help studying projective planes. So if you have a relative difference set, you must first generate the projective plane it defines (if it does).
Projective planes are always assumed to consist of positive integers (as points) and sets of integers (as blocks). The incidence relation is assumed to be the element relation. The blocks of a projective plane must be sets.
The following methods generate a record characterising the projective
plane. As most of the functions in this chapter need this data, the
record returned by ElationPrecalc
or ElationPrecalcSmall
is the
recommended representation of projective planes.
ElationPrecalc(
blocks ) F
ElationPrecalcSmall(
blocks ) F
Given the blocks blocks of a projective plane,
ElationPrecalc(
blocks )
returns a record conatining
ElationPrecalcSmall(
blocks )
returns a record which
does only contain .points, .blocks and .jblock. Hence the name.
In the following sections, some of the functions have two versions.
The versions which have a Small
appended to it's name do not depend
on the data generated by ElationPrecalc
, but rather on the data
structure provided by ElationPrecalcSmall
. The Small
versions are
generally much slower than the other ones.
DualPlane(
blocks ) O
For a projective plane given by blocks, DualPlane(
blocks )
returns
a record containing a set of blocks defining the dual plane and a List
image containing the same blocks such that image[p] is the image of the
point p under duality.
It is not tested, if the design defined by blocks is actually
a projective plane.
ProjectiveClosureOfPointSet(
points,
maxsize,
data ) O
Let P be a projective plane given by the record data as returned by
ElationPrecalcSmall
. Let points be a set of points (integers). Then
ProjectiveClosureOfPointSet
returns the projective colsure of points
in P (the smallest subplane of P containing the points points).
The closure is returned as a list of points.
If maxsize ≠ 0, calculations are stopped if the closure is known to
have at least maxsize points and data.points is returned.
Observe that this is a ``small'' function, in the sense that it does not
need the data from ElationPrecalc
but merely the data generated by
ElationPrecalcSmall
.
[Up] [Previous] [Next] [Index]
RDS manual