Normalization of defining polynomials for number fields (reviewed)

A number field can be defined by many different irreducible polynomials $f(x)\in\Q[x]$. The normalized polynomial is the output of gp/pari's polredabs, which is effectively a canonically chosen defining polynomial.

Normalized polynomials are always monic with integer coefficients, such that the sum of the squares of the absolute values of all complex roots of $f(x)$ is minimized. When there is more than one such polynomial, the tie is broken based on the size of the polynomial's coefficients and discriminant.