"Source: Text/Incidence/Plane.text";
"Line: 2484";
"Date: Fri Sep 26 12:10:10 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Incidence/Plane.text, line: 2484
// Example: H154E14 ()
print "Example: H154E14";
ei := GetEchoInput();
SetEchoInput(true);
BaerDerivation := function(q)
//---------------------------
// Construct an affine plane by the technique of derivation using 
// Baer subplanes
   Fq2< w > := FiniteField(q^2);
   V := VectorSpace(Fq2, 3);
   Plane, Pts, Lns := FiniteProjectivePlane(V);
   G, Y := CollineationGroup(Plane);
   Subplane := SubfieldSubplane(Plane, GF(q));
   LineInf := Lns![1, 0, 0];

   BaerSeg := Points(Subplane) meet LineInf;
   StabSeg := Stabilizer(G, Y, BaerSeg);
   BaerLines := Orbit(StabSeg, Y, Points(Subplane) diff BaerSeg);
   AffLines := BaerLines join { Set(l) diff LineInf : l in Lns | 
                               (BaerSeg meet l) eq {} };
   return FiniteAffinePlane< SetToIndexedSet(&join(AffLines)) | Setseq(AffLines) 
                                            : Check := false >;
end function; /*BaerDerivation*/
SetEchoInput(ei);
