exo1.gp

default(realprecision, 9000);
t=[28,29,24,25,0,0,7];
k=20
p=751
{
for (i=1,7,
r=t[i]*k + 1;
q= Mod(r^3 -r + 188, 751);

for(j=0,t[i]+1,
  if(1==kronecker(lift(q),p), break );
  r = r + 1;
  q= Mod(r^3 -r + 188, 751);
);
print(q);
s = sqrt(q) + 375;

print("x="r",y="s);
);
}

xinit=[361,241,201,461,581];
yinit=[383,605,380,467,395];



{
  for(i=1,5,
    for(j=0,k+1,
      e=((xinit[i] - 1 -j)/20);
      if(type(e)=="t_INT", break );
    );
    print(e);
  );
}

exo2.gp

dedoublement(xp,yp,p) = {

  s = Mod( ((3*(xp^2) + a)/(2*yp)), p);

  xr = Mod(s^2 - 2xp, p);
  yr = Mod(-yp + s*(xp - xr), p);

  return([xr,yr]);
}





adding(xp,yp,xq,yp) = {
  if(xp==xq&&yp==yq, break );

  s= Mod( (yp-yq) / (xp - xq), p);

  xr = Mod(s^2 - xp - xq, p);
  yr = Mod(-yp + s*(xp - xr),p);

    return([xr,yr]);
}





compter_avec_legendre(a,b,p) = {
 t=0;
 for(i=0, p-1,
   tmp= i^3 + a*i + b;
   t += kronecker(tmp,p);
 );
 print(p + 1 + t);
}

compter_avec_legendre(4,4,751);

quit;