Bill Allombert on Wed, 25 Sep 2013 13:04:58 +0200 |
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Re: halving points on elliptic curve |
On Wed, Sep 25, 2013 at 12:15:48PM +0200, Bill Allombert wrote: > 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 []. I just fixed this bug in PARI 2.6.2. No we get *** unused characters: ...2*x^2+2*e.b4*x+e.b6);v=[]; for(i=1,6,print(i *** ^-------------------- (=A0 is a non-breaking space. Normal spaces are removed in error messages, so the space there is a cue it must be a special space). Cheers, Bill.