2 | | - make `ANRoot` be a descriptor for roots of '''irreducible''' polynomials with '''rational''' coefficients |

3 | | - get rid of `ANUnaryExpr` and `ANBinaryExpr` and use the code from #18356 for addition/subtraction/multiplication/division |

| 2 | - create a new descriptor `ANRootRational` as a descriptor for roots of '''irreducible''' polynomials with '''rational''' coefficients |

| 3 | - write exactification code to go from `ANRoot` to `ANRootRational` (i.e. go from a `QQbar` polynomial anihilator to the minimal polynomial over `QQ`) |

| 4 | - get rid of `ANUnaryExpr` and `ANBinaryExpr` and use the code from #18356 for addition/subtraction/multiplication/division of anihilator polynomial or minimal polynomial |

| 5 | |

| 6 | We might want to force elements of small degrees to lies into number fields (possibly using a global threshold value). |