Defining the Elliptic Curve E.

First we define the elliptic curve E, projectively and then take the three affine equations. The affine equations we will actually use in the rest of this document will be f(x,y) and g(u,z).

Defining the function for the elliptic curve E.

> diamond:= (X,Y,Z) -> Z*Y^2 - X^3 - X*Z^2*c1 - Z^3*c2;

Next come up with the three affine equations....

> f:= (x,y) -> diamond(x,y,1);

> g:= (u,z) -> diamond(u,1,z);

> h:= (y,z) -> diamond(1,y,z);

>