{
  "id": "1005.1156",
  "version": "v3",
  "published": "2010-05-07T08:50:22.000Z",
  "updated": "2010-07-15T15:21:11.000Z",
  "title": "A new computational approach to ideal theory in number fields",
  "authors": [
    "Jordi Guardia",
    "Jesus Montes",
    "Enric Nart"
  ],
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the defining equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-07-15T15:21:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y40",
      "11Y05",
      "11R04",
      "11R27"
    ],
    "keywords": [
      "number field",
      "ideal theory",
      "computational approach",
      "prime ideals",
      "fractional ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1156G"
    }
  }
}