{
  "id": "1810.11396",
  "version": "v1",
  "published": "2018-10-26T15:45:50.000Z",
  "updated": "2018-10-26T15:45:50.000Z",
  "title": "On the complexity of class group computations for large degree number fields",
  "authors": [
    "Alexandre Gélin"
  ],
  "categories": [
    "math.NT",
    "cs.SC"
  ],
  "abstract": "In this paper, we examine the general algorithm for class group computations, when we do not have a small defining polynomial for the number field. Based on a result of Biasse and Fieker, we simplify their algorithm, improve the complexity analysis and identify the optimal parameters to reduce the runtime. We make use of the classes $\\mathcal D$ defined in [GJ16] for classifying the fields according to the size of the extension degree and prove that they enable to describe all the number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-26T15:45:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large degree number fields",
      "class group computations",
      "general algorithm",
      "extension degree",
      "small defining polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}