{"paper":{"title":"Local computation of differents and discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart","submitted_at":"2012-05-07T10:54:05Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1340","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}