Translation Planes

The following functions may be used to construct translation planes by derivation. The original code is due to Jenny Key.

BaerDerivation(q2): RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet

An affine plane constructed by the technique of derivation with respect to a Baer subplane, where \(q2\) is an even power of a prime.

BaerSubplane(P): PlaneProj -> PlaneProj, PlanePtSet, PlaneLnSet

A Baer subplane of the projective plane \(P\).

OvalDerivation(q: parameters): RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet

HallOval: BoolElt                    Default: false
Print   : BoolElt                    Default: false

A translation plane from PG\((2, q)\), where \(q\) is a power of 2, computed by derivation with respect to an oval. By default, the oval chosen is that defined by the points of the conic \(y^2 = xz\) together with the nucleus, in PG\((2, q)\). In the case \(q = 16\), a Hall oval in the plane may be requested by assigning the parameter HallOval the value true. If the parameter Print is assigned the value true, then some information is printed during the computation.