ellPoint(List,EllipticCurveW) -- A method for defining point on an elliptic curve.

Synopsis

• Function: ellPoint

• Usage:

  ellPoint(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:
  • an instance of the type EllPointW

Description

Returns the point of projective coordinates { L#0 : L#1 : L#2 } 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 : P=ellPoint({1,5,1},E)

o2 = The point ({1, 5, 1}( is not on the((Elliptic Curve defined by Y^2 + 1
     ------------------------------------------------------------------------
     XY + 3 Y = X^3 + 2 X^2 + 4 X + 6( over(GF 29 .))).)))