# Question:How to get rid of some lengthy `RootOf` expressions?

## Question:How to get rid of some lengthy `RootOf` expressions?

Maple 2023

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.

 > restart;
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >
 (5)

Unfortunately, none of , , , and  is very readable.
It can be proved that the following one is also the factors.

 > f__4 := [x^3 + RootOf(3*_Z^3 - 4*_Z^2 + _Z - 1, index = 3)*(x*(y + 2) + 2) + RootOf(3*_Z^3 + 8*_Z^2 + 5*_Z + 1, index = 3)*(y^3 + y + 1), x^3 + RootOf(3*_Z^3 - 4*_Z^2 + _Z - 1, index = 2)*(x*(y + 2) + 2) + RootOf(3*_Z^3 + 8*_Z^2 + 5*_Z + 1, index = 1)*(y^3 + y + 1), x^3 + RootOf(3*_Z^3 - 4*_Z^2 + _Z - 1, index = 1)*(x*(y + 2) + 2) + RootOf(3*_Z^3 + 8*_Z^2 + 5*_Z + 1, index = 2)*(y^3 + y + 1)];
 >
 (6)
 >
 (7)
 >
 (8)

As you can see,  is of lower mathematical complexity.