"Source: Text/Incidence/Plane.text";
"Line: 2633";
"Date: Fri Sep 26 12:10:10 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Incidence/Plane.text, line: 2633
// Example: H154E15 ()
print "Example: H154E15";
ei := GetEchoInput();
SetEchoInput(true);
P, V, L := FiniteProjectivePlane< 13 |
    {1, 2, 3, 4}, {1, 5, 6, 7}, {1, 8, 9, 10},
    {1, 11, 12, 13}, {2, 5, 8, 11}, {2, 6, 9, 12},
    {2, 7, 10, 13}, {3, 5, 9, 13}, {3, 6, 10, 11},
    {3, 7, 8, 12}, {4, 5, 10, 12}, {4, 6, 8, 13},
    {4, 7, 9, 11} >;
p := V!3;
l := L.1;
G := CentralCollineationGroup(P, p, l);
G;
g := G.1;
g;
is_cent_coll, centre, axis := IsCentralCollineation(P, g);
is_cent_coll;
assert $1;
centre eq p;
assert $1;
axis eq l;
assert $1;
lines := {m : m in Lines(P) | p in m};
m := Random(lines);
m;
m ^ G;
SetEchoInput(ei);
