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 y² = 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.