{
  "id": "1507.04058",
  "version": "v1",
  "published": "2015-07-15T00:35:26.000Z",
  "updated": "2015-07-15T00:35:26.000Z",
  "title": "Computation of Integral Bases",
  "authors": [
    "Jens-Dietrich Bauch"
  ],
  "comment": "22 pages, 4 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be a Dedekind domain, $K$ the fraction field of $A$, and $f\\in A[x]$ a monic irreducible separable polynomial. For a given non-zero prime ideal $\\mathfrak{p}$ of $A$ we present in this paper a new method to compute a $\\mathfrak{p}$-integral basis of the extension of $K$ determined by $f$. Our method is based on the use of simple multipliers that can be constructed with the data that occurs along the flow of the Montes Algorithm. Our construction of a $\\mathfrak{p}$-integral basis is significantly faster than the similar approach from $[7]$ and provides in many cases a priori a triangular basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-15T00:35:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11Y40",
      "14G15",
      "14H05"
    ],
    "keywords": [
      "integral basis",
      "computation",
      "non-zero prime ideal",
      "monic irreducible separable polynomial",
      "triangular basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150704058B"
    }
  }
}