Local computation of differents and discriminants

Abstract

We obtain several results on the computation of different and discriminant ideals of finite extensions of local fields. As an application, we deduce routines to compute the $\p$-adic valuation of the discriminant $\dsc(f)$, and the resultant $\res(f,g)$, for polynomials $f(x),g(x)\in A[x]$, where $A$ is a Dedekind domain and $\p$ is a non-zero prime ideal of $A$ with finite residue field. These routines do not require the computation of neither $\dsc(f)$ nor $\res(f,g)$; hence, they are useful in cases where this latter computation is inefficient because the polynomials have a large degree or very large coefficients.

References in corpus (1)

• A new computational approach to ideal theory in number fields

Cited by in corpus (1)

• Genus computation of global function fields