x;y;z;u;w;
/* Fixes x>y>z>y>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) );
##
liftall(H)