Return a k-arc for the plane P.

Return a complete k-arc for the plane P (if one exists).

True if the set of points C is an arc, i.e. no three points of C are collinear.

True if the k-arc C is complete.

Given five points p, q, r, s, t belonging to a classical projective plane of order n > 3 and being in general position, construct the unique conic that passes through them.

Conic(S) : { PlanePt } -> SetEnum

Given a set S of five points belonging to a classical projective plane of order n > 3 and being in general position, construct the unique conic that passes through them.

Given five points p, q, r, s, t belonging to a classical projective plane of order n > 3 that are in general position, return the quadratic form defining the conic containing the five points.

QuadraticForm(S) : { PlanePt } -> RngMPolElt

Given a set S of five points belonging to a classical projective plane of order n > 3 that are in general position, return the quadratic form defining the conic containing the five points.

Given an arc A in the plane P, and a point p on A, return a tangent to A at p.

Given an arc A in the plane P, return the set of tangent lines to A. A tangent is a line of P that has intersection of cardinality one with A.

Given an arc A in the plane P, return the set of secant lines to A. A secant is a line of P that has intersection of cardinality two with A.

AllPassants(A) : { PlanePt } -> { PlaneLn }

Given an arc A in the plane P, return the set of external lines to A. An external line is a line of P that has trivial intersection with A.

Given a conic C in the projective plane P, which is defined over a field having even characteristic, return the knot of the conic C, i.e the interstection point of the tangents to C.

Given a conic C in the projective plane P, which is defined over a field having odd characteristic, return the exterior points of C, i.e. the points of P that lie on two tangents of C.

Given a conic C in the projective plane P, which is defined over a field having odd characteristic, return the interior points of C, i.e. the points of P that do not lie on any tangent of C.

> P, V, L := ProjectivePlane(16); 
> oval := kArc(P, 18);
> pts := Points(P) diff oval;
> lns := ExternalLines(oval);
> I := IncidenceStructure< SetToIndexedSet(pts) | [l meet pts : l in lns] >;
> D := Design(Dual(I), 2); 
> print D;
2-(120, 8, 1) Design with 255 blocks