The Set of Points and Set of Lines

It may sometimes be desirable to have an explicitly enumerated set of the points or lines of a plane, as opposed to the point–set and line–set, which aren’t true Magma sets. The following functions have been provided for this purpose.

Points(P): Plane -> { PlanePt }

An indexed set \(E\) whose elements are the points of the plane \(P\). Note that this creates a standard indexed set and not the point–set of \(P\), in contrast to the function PointSet.

Lines(P): PlaneLnSet -> { PlaneLn}

An indexed set containing the lines of the plane \(P\). In contrast to the function LineSet, this function returns the collection of lines of \(P\) in the form of a standard indexed set.