# isOnEllCurve(List,EllipticCurveW) -- A method to check if a point is on an elliptic curve.

## Synopsis

• Function: isOnEllCurve
• Usage:
isOnEllCurve(L,E)
• Inputs:
• L, a list, the projective coordinates of the point
• E, an instance of the type EllipticCurveW, the elliptic curve on which the point lies
• Outputs:

## Description

Tells whether the point of projecive coordinates { L#0 : L#1 : L#2 } is on the elliptic curve E

 i1 : E=ellCurve({1,2,3,4,6},GF(29)) o1 = Elliptic Curve defined by Y^2 + 1 XY + 3 Y = X^3 + 2 X^2 + 4 X + 6( over(GF 29 .)) o1 : EllipticCurveW i2 : isOnEllCurve({1,5,1},E) o2 = false