True if the points p and q are equal, otherwise false.

True if the points p and q are not equal, otherwise false.

True if the lines l and m are equal, otherwise false.

True if the lines l and m are not equal, otherwise false.

True if point p lies on the line l, otherwise false.

True if point p does not lie on the line l, otherwise false.

Given a subset S of the point set of the plane P and a line l of P, return true if the subset S of points lies on the line l, otherwise false.

Given a subset S of the point set of the plane P and a line l of P, return true if the subset S of points does not lie on the line l, otherwise false.

The unique point common to the lines l and m.

The i-th coordinate of the point p, which must be from a classical plane. If p is from a projective plane, then i must satisfy 1 <= i <= 3; if p is from an affine plane, then i must satisfy 1 <= i <= 2.

l[i] : PlaneLn, RngIntElt -> FldFinElt

The i-th coordinate of the line l, which must be from a classical plane. The integer i must satisfy 1 <= i <= 3. Recall that in a classical plane <a:b:c> (where a, b, c in K) represents the line given by the equation ax + by + cz = 0 in a projective plane or ax + by + c = 0 in an affine plane.

True if the set S of points of the plane P are collinear, otherwise false. If the points are collinear, the line which they define is also returned.

True if the set R of lines of the plane P are concurrent, otherwise false. If the lines are concurrent, their common point is returned as a second value.

The pencil of lines passing through the point p.

The set of points contained in the line l.

The set of underlying points contained in the line l of a plane P (i.e. the elements of the set have their "real" types; they are no longer a "PlanePt" of P).

Rep(l) : PlaneLn -> PlanePt

Given a line l of the plane P, return a representative point of P which is incident with l.

Given a line l of the plane P, return a random point of P which is incident with l.

The slope of the line l of a classical affine plane P.

True if the line l is parallel to the line m in the affine plane P.

The parallel class containing the line l of an affine plane P.

The partition into parallel classes of the lines of the affine plane P.

True if the set S of points of a plane P contains a quadrangle.