In this chapter we will present the categories of finite projective and affine planes.
The category names for projective and affine planes are PlaneProj and PlaneAff respectively. Within each of these categories we have what we will call classical planes --- those which are defined by a vector space of dimension 2 (for affine planes) or 3 (for projective planes).
Some functions documented here apply to all types of planes, others are specific to projective, affine or classical planes. It should be clear which is the case for each entry.
A point of a plane is considered to be a special object, and so points are given their own special type, PlanePt, in Magma. This allows the points of a plane to be defined over any type of Magma object, and also improves the efficiency of the code.
A special structure called the point--set acts as the parent structure for points. A point is created by coercing an appropriate Magma object into the point--set. It is also possible the get the i-th point, or a random point, from the point--set.
Similarly, lines of a plane have a special type PlaneLn, and the line--set acts as their parent structure. Lines can be created by coercing a suitable object into the line--set, or by asking for the i-th line, or a random line, from the line--set.