Numerical Invariants of a Plane

Order(P): Plane -> RngIntElt

The order of the plane \(P\).

NumberOfPoints(P): Plane -> RngIntElt

# V: PlanePtSet -> RngIntElt

The cardinality \(v\) of the point–set \(V\) of the plane \(P\).

NumberOfLines(P): Plane -> RngIntElt

# L: PlaneLnSet -> RngIntElt

The cardinality \(v\) of the line–set \(L\) of the plane \(P\).

pRank(P): Plane -> RngIntElt

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

pRank(P, p): Plane, RngIntElt -> RngIntElt

The \(p\)-rank of the plane \(P\).

Example: Numerical Invariants of PG(2,8) (ex-1297f0)

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

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