Numerical Invariants of a Plane

The order of the plane P.

The cardinality v of the point--set V of the plane P.

The cardinality v of the line--set L of the plane P.

The p-rank of the plane P of order p^t.

The p-rank of the plane P.

We demonstrate some of the above functions with the plane PG_2(8).

> P := FiniteProjectivePlane(8);
> NumberOfLines(P);
73
> Order(P);
8
> pRank(P);
28
> pRank(P, 2);
28
> pRank(P, 3);
72
> pRank(P, 5);
73