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Numerical Invariants of a Plane

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
The p-rank of the plane P.

Example Plane_invar (H57E6)

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

> P := ProjectivePlane(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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