Normalization of defining polynomials for number fields

A number field can be {{ KNOWL('nf.defining_polynomial', 'defined') }} by many different irreducible polynomials $f(x)\in\Q[x]$. The normalized polynomial is the {{ KNOWL('nf.polredabs', "output of gp/pari's <code>polredabs</code>") }}, 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.