Enumeration of Points

In this section the descriptions will refer to a point set \(H\), which is either the \(H\) in the signature or the base point set of the elliptic curve \(E\) in the signature.

Points(E): CrvEll -> {@ PtEll @}

Points(H): SetPtEll -> {@ PtEll @}

RationalPoints(E): CrvEll -> {@ PtEll @}

RationalPoints(H): SetPtEll -> {@ PtEll @}

Returns the set of rational points of the point set \(H\) or of the base point set of the elliptic curve \(E\), including the point at infinity.

Random(E): CrvEll -> PtEll

Random(H): SetPtEll -> PtEll

Returns a random rational point of the point set \(H\) or of the base point set of the elliptic curve \(E\). Every rational point has a roughly equal chance of being selected, including the point at infinity.