/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
/* returns true if this is QR */
public bool Sqrt()
{
if (IsZilch())
{
return(true);
}
FP w1 = new FP(b);
FP w2 = new FP(a);
w1.Sqr();
w2.Sqr();
w1.Add(w2);
if (w1.Jacobi() != 1)
{
Zero();
return(false);
}
w1 = w1.Sqrt();
w2.Copy(a);
w2.Add(w1);
w2.Norm();
w2.Div2();
if (w2.Jacobi() != 1)
{
w2.Copy(a);
w2.Sub(w1);
w2.Norm();
w2.Div2();
if (w2.Jacobi() != 1)
{
Zero();
return(false);
}
}
w2 = w2.Sqrt();
a.Copy(w2);
w2.Add(w2);
w2.Inverse();
b.Mul(w2);
return(true);
}
/* this/=2 */
public void Div2()
{
a.Div2();
b.Div2();
}
