cino hilliard on Thu, 18 Jun 2009 22:13:42 +0200

 RE: Elliptic curve x^3 - y^2 = p

 Hi Karim,   > From: Karim.Belabas@math.u-bordeaux1.fr> Date: Thu, 18 Jun 2009 14:12:36 +0200> To: pari-users@list.cr.yp.to> Subject: Re: Elliptic curve x^3 - y^2 = p> > * cino hilliard [2009-06-18 12:35]:> > (05:26:04) gp > ?diffcubes> > diffcubes(n,p)=local(x,y);setintersect(vector(n,x,x^3-p),vector(n,y,y^2))> > > > > > > > getting this> > > > (05:20:04) gp > diffcubes(10000,431)> > *** setintersect: not a set in setintersect.> > also for ver 2.4.2 > > OK, that's for 2.4.3 only then :-(.> > (14:10) gp > ??setintersect> setintersect(x,y):> > intersection of the two sets x and y (see setisset). The function also works> if both x and y are vectors of stricly increasing entries ( according to < );> in that case we return a vector of strictly increasing entries, not a set.> Otherwise, the result is undefined.Oh boy. I always get   Could not find translation file, docdir='C:/Program Files/PARI' at C:/Program Files/PARI/gphelp line 152.   with  super help ??     > For "older" versions than that, use > > setintersect(Set(vector(n,x,x^3-p)), Set(vector(n,y,y^2)))> > ( slower but not *much* slower... ) Bravo! This does what I want.     diffcubes(n,p) =                         {                        local(j,x,y,c);                        a=eval(setintersect(Set(vector(n,x,x^3-p)), Set(vector(n,y,y^2))));                        c=length(a);                        a=vecsort(a);                        for(j=1,c,                        y=round(sqrt(a[j]));                        x=round((a[j]+p)^(1/3));                        print(j": "x"^3 - "y"^2 = "p); \\ Too fancy? Change it.                        );                        c;                         }   (14:51:50) gp > diffcubes(300000,431)1: 8^3 - 9^2 = 4312: 11^3 - 30^2 = 4313: 20^3 - 87^2 = 4314: 30^3 - 163^2 = 4315: 36^3 - 215^2 = 4316: 138^3 - 1621^2 = 4317: 150^3 - 1837^2 = 4318: 575^3 - 13788^2 = 4319: 3903^3 - 243836^2 = 431(15:02:35) gp > ##  ***   last result computed in 2,250 ms.(15:02:39) gp >   This finds all instances because I new a prori 243836 was the big kahuna. I guess it will still be trial and error?   Oh well, we are at least 2 quanta over what I had.    Thank you  >>>Cino