Let f__0 denote the factors of the "absolute factorization" of the following bivariate polynomial (i.e., p):
p := product(x^3*k^2 + (x*(y + 2) + 2)*k - x^3 + y^3 + y + 1, k = RootOf(_Z^3 + _Z + 1)):
f__0 := (evala@AFactors)(p)[2, .., 1]; # Assume that we do not know the extension field in advance.
It is unfortunate that the output is not easy to read, so I have to
simplify it here. However, it appears that none of the results (i.e., f__1, f__2, and f__3) is eminently readable.
The f__4 above (whose "size" is smaller) comes from manual simplification, but this is not a easy work. Is there a way to get the much simplified result programmatically?