{
  "id": "2102.08741",
  "version": "v1",
  "published": "2021-02-17T13:12:27.000Z",
  "updated": "2021-02-17T13:12:27.000Z",
  "title": "Computing the Length of Sum of Squares and Pythagoras Element in a Global Field",
  "authors": [
    "Mawunyo Kofi Darkey-Mensah",
    "Beata Rothkegel"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field $K$ of characteristic different from $2$. In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if $K$ is a number field) completion of $K$. These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-17T13:12:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y16",
      "11E12"
    ],
    "keywords": [
      "global field",
      "pythagoras element",
      "length equals",
      "second part",
      "first part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}