Again my mistake. I forgot that in Mathematica the symbol "=" is represented by "=="
Anyway, thank you for all the help.
Joaquim Nogueira
It could be structured like this.
Reap[Do[If[f[i,j,k]==0&&g[i,l,k]==1,Sow[{i,j,k}], {i,0.728}, {j,0,728}, {k,0,728}]]
That at least is a way to start out. There may be better ways to go about this, I'm not sure.
It's less than a billion cases. Should not take too long.
Also I should mention that nested PolynomialMod statements are not needed.
PolynomialMod
One other thing: if you are treating integers mod 729 as equivalent to the field of 3^6 elements, that won't work.
Thank you for your reply. I knw that the integers mod 729 are not the field with 729 elements. One can write that field as the splitting field of an irreducible polynomial of degree 6 in GF(3). I agree with you that the computation shouldn´t take long... but I don't know how to do it!