PrimeList( d, upper, l ) =
{
 local( p, i, puffer, PListe );
 p = 2;
 puffer = [];
 if ( !((d+1)%8) || !((d-1)%8), puffer = concat(puffer, [2]));
 p = nextprime(3);
 while( p < upper,
    kro = kronecker(d, p);
    if ( (kro == -1 && p^2 < upper && (!((p+1)%l) || !((p-1)%l))) || (kro == 0 && !((p-1)%l)) || (kro == 1 && !((p-1)%l)) || p == l,
        puffer = concat( puffer, [p] );
    );
    p = p + 1;
    p = nextprime( p );
 );
 PListe = [];
 for (i=1, length(puffer), PListe = concat(PListe, idealprimedec( K, puffer[i] )));
 return(PListe);
}

{EnumSubSets(PSet, K, E, l, r,
                      Subset, P, module, rcgp, sgl) =
    Subset = InitSubset(r, length(PSet));
    while (Subset,
        P  = vector(r, i, PSet[Subset[i]]);
        module = 1;
        for( i = 1, length( P ), 
	    if (P[i][1] == l,
	        module = idealmul( K, module, idealpow(K, P[i], 2 )) 
	    ,
		module = idealmul( K, module, P[i] )
	    );
	);
        rcgp = bnrinit( K, module, 1 );
        sgl = findsubgroup( rcgp, l );
        if (length(sgl) > 0, 
	    print("module = ", idealfactor(K, module), "\n Number of subgroups: ", length(sgl)));
        for (i=1, length(sgl), 
            print( " Subgroup ", i );
            Y = etnc(K, l, E, rcgp, sgl[i]);
	    if (Y[1] == 0, return(Y[2]));
            print("\n\n ******************************************************* \n\n")
	);
        Subset = NextSubset(Subset, length(PSet));
    );
    return(1);
}

false = 0;


{InitSubset(r, t,
		 i) =
    return(vector(r, i, i));
}

{NextSubset(s, t,
		 i, r, s1, j, carry)=
    i = r = length(s); carry = true;
    s1 = concat(s, [t+1]);
    while ( i > 0 && carry,
	if (s1[i] < s1[i+1]-1,
	   s1[i]++; carry = false
	,
	   i--
	);
    );
    if (carry, return(false));
    if (i < r,
        for (j = i+1, r, s1[j] = s1[j-1]+1)
    );
    return(vector(r, i, s1[i]));
}