Re: halving points on elliptic curve

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Wed, Sep 25, 2013 at 01:03:00AM -0700, somayeh didari wrote:
> thanks for your help, I wrote this program, which take elliptic curve e over the rational points and a point Q in e and returns (1/2)Q:
> halve(e,Q)={
> x_0=Q[1];
> Half=[];
> f=x^4-e.b4*x^2-2*e.b6*x-e.b8-x_0*(4*x^3+e.b2*x^2+2*e.b4*x+e.b6);
> g=factor(f);
> v=[];
>  for(i=1,#g~,
  ^
Actually the character below is a 8bit char which is not valid in GP script
indeed this is from the quoted-printable we received:
+e.b2*x^2+2*e.b4*x+e.b6);=0Ag=3Dfactor(f);=0Av=3D[];=0A=A0for(i=3D1,#g~,=0A=
                                                       ^^^
=A0 is a 8bit char.

Unfortunately due to a bug in GP, all 8bit chars are treated as end of string,
so your function is truncated at this point. So Half is always [].

Cheers,
Bill.