Subsections

• Arithmetic in a Group of Points
• Predicates on Points

The sum of points P, Q in E[K].

The negative of the point Q in E[K].

P - Q : GeomECElt, GeomECElt -> GeomECElt

The difference P + ( - Q) of points P, Q in E[K].

P * m : GeomECElt, RngIntElt -> GeomECElt

The multiple m.P=P.m of the point P in E[K], and integer m. Here m.P = P + ... + P for positive m, the identity point for m=0 and m.( - P) for negative m.

IsIdentity(P) : GeomECElt -> BoolElt

True if and only if P is the identity point on the elliptic curve that is its parent, false otherwise.

True if and only if P and Q are points on the same elliptic curve and have the same coordinates.