"Source: Text/Incidence/Plane.text";
"Line: 1117";
"Date: Fri Sep 26 12:10:10 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Incidence/Plane.text, line: 1117
// Example: H154E7 ()
print "Example: H154E7";
ei := GetEchoInput();
SetEchoInput(true);
A := FiniteAffinePlane(3); 
P := ProjectiveEmbedding(A); 
P;
A2 := FiniteAffinePlane(P, Random(LineSet(P)));
A2;
iso, map := IsIsomorphic(A, A2);
is_iso, map := IsIsomorphic(A, A2);
is_iso;
assert $1;
map;
K<w> := GF(4);
A, AP, AL := FiniteAffinePlane(K);
P, PP, PL, f := ProjectiveEmbedding(A);
AP.5;
AP.5 @ f;
linf := PL.#PL;
linf;
SetSeed(1, 3);
p := Random(PP);    
p in linf;
assert not $1;
p @@ f;
l := Random(PL);
l eq linf;
assert not $1;
l @@ f;
$1 @ f eq l;
assert $1;
SetEchoInput(ei);
