# 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: invar (ex-1297f0)`

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

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

```