{
  "id": "1301.6641",
  "version": "v1",
  "published": "2013-01-28T18:46:55.000Z",
  "updated": "2013-01-28T18:46:55.000Z",
  "title": "Normal forms of convex lattice polytopes",
  "authors": [
    "Roland Grinis",
    "Alexander Kasprzyk"
  ],
  "comment": "28 pages, 2 figures. Includes an appendix describing the Kreuzer-Skarke algorithm",
  "categories": [
    "math.CO"
  ],
  "abstract": "We describe an algorithm for determining whether two convex polytopes P and Q, embedded in a lattice, are isomorphic with respect to a lattice automorphism. We extend this to a method for determining if P and Q are equivalent, i.e. whether there exists an affine lattice automorphism that sends P to Q. Methods for calculating the automorphism group and affine automorphism group of P are also described. An alternative strategy is to determine a normal form such that P and Q are isomorphic if and only if their normal forms are equal. This is the approach adopted by Kreuzer and Skarke in their PALP software. We describe the Kreuzer-Skarke method in detail, and give an improved algorithm when P has many symmetries. Numerous examples, plus two appendices containing detailed pseudo-code, should help with any future reimplementations of these techniques. We conclude by explaining how to define and calculate the normal form of a Laurent polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-28T18:46:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52B55",
      "52C07"
    ],
    "keywords": [
      "normal form",
      "convex lattice polytopes",
      "affine lattice automorphism",
      "affine automorphism group",
      "convex polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6641G"
    }
  }
}