{
  "id": "0807.4065",
  "version": "v3",
  "published": "2008-07-25T11:26:57.000Z",
  "updated": "2008-11-03T14:40:52.000Z",
  "title": "Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields",
  "authors": [
    "Jordi Guardia",
    "Jesus Montes",
    "Enric Nart"
  ],
  "comment": "References to [HN] have been updated",
  "categories": [
    "math.NT"
  ],
  "abstract": "We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good: for a given prime number p, it computes the p-valuation of the discriminant and the factorization of p in a number field of degree 1000 in a few seconds, in a personal computer.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-11-03T14:40:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y40",
      "11R04",
      "11R29"
    ],
    "keywords": [
      "prime ideal decomposition",
      "number field",
      "higher newton polygons",
      "discriminant",
      "computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4065G"
    }
  }
}