{
  "id": "math/0612358",
  "version": "v2",
  "published": "2006-12-13T16:29:21.000Z",
  "updated": "2007-01-11T04:42:30.000Z",
  "title": "Sufficient conditions for a real polynomial to be a sum of squares",
  "authors": [
    "Jean B. Lasserre"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We provide explicit conditions for a real polynomial $f$ of degree 2d to be a sum of squares (s.o.s.), stated only in terms of the coefficients of $f$, i.e. with no lifting. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most 2d. We also provide a simple condition to ensure that $f$ is s.o.s., possibly modulo a constant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-11T04:42:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12E05",
      "12Y05"
    ],
    "keywords": [
      "real polynomial",
      "sufficient conditions",
      "convex polyhedral subcone",
      "degree 2d",
      "explicit description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12358L"
    }
  }
}