# 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`

```magma
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.