{
  "id": "2404.06858",
  "version": "v1",
  "published": "2024-04-10T09:29:12.000Z",
  "updated": "2024-04-10T09:29:12.000Z",
  "title": "Number Theory in OSCAR",
  "authors": [
    "Claus Fieker",
    "Tommy Hofmann"
  ],
  "comment": "Submitted as chapter for the upcoming book on the computer algebra system OSCAR",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we showcase the functionality in two examples related to the investigation of the Cohen-Lenstra heuristic for quadratic fields and the Galois module structure of rings of integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-10T09:29:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y40",
      "11-04",
      "11R29",
      "11R33",
      "11R37",
      "11N45"
    ],
    "keywords": [
      "computational algebraic number theory",
      "galois module structure",
      "brief introduction",
      "quadratic fields",
      "cohen-lenstra heuristic"
    ],
    "tags": [
      "book chapter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}