? x;y;z;u;w;    /* Fixes x>y>z>u>w */
? p = 2^25-855; /* p = 2^62-923; */
? m1 = w^2+w+1;
? m2 = u^4-u*w-2;
? m3 = z^2-z*u-4;
? m4 = y^2-3*y*z-u;
/* K = Z/pZ[y,z,u,w]/<m1,m2,m3,m4>  */
? zero = Mod(Mod(Mod(Mod(Mod(0,p),m1),m2),m3),m4);
? g = x+2*u*y+5*z+4*w*u+3 + zero;
? a = x+y*w+6*z+7*w*u+8 + zero;
? b = x+y*z+9*y*u+2*w+2 + zero;
? n = 7; /* n = 3, 4, 7, 15, 31, 61, 127 */
? aa = g*a^n; bb = g*b^n;
? monicgcd = (a,b) -> {G = gcd(a,b); G/pollead(G)};
? for( i=1, 100, H=monicgcd(aa,bb) );
? ##
  ***   last result: cpu time 4,360 ms, real time 4,373 ms.
? liftall(H)
%276 = x + (2*u*y + (5*z + (4*w*u + 3)))