//define basering as follow
//ring GZ=(0,i),x,dp;
//minpoly=i2+1;
//setring GZ;

proc re(poly f)
{
        ring h=(0,i),x,dp;
        minpoly = i;

        setring h;
        poly b=imap(GZ,f);


        setring GZ;
        return (imap(h,b));
}

proc im(poly f)
{
        return ((f-re(f))*(-i));
}

proc conj(poly f)
{
        return (re(f)-im(f)*i);
}

proc abs(poly f)
{
        return(re(f)^2+im(f)^2);
}