{
  "id": "0704.3363",
  "version": "v2",
  "published": "2007-04-25T12:42:10.000Z",
  "updated": "2008-04-02T09:15:51.000Z",
  "title": "Topology and Factorization of Polynomials",
  "authors": [
    "Hani Shaker"
  ],
  "comment": "Accepted in Mathematica Scandinavica. 8 pages",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "For any polynomial $P \\in \\mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-02T09:15:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12D05",
      "14F40",
      "14J70"
    ],
    "keywords": [
      "polynomial",
      "algebraic partial differential equations",
      "complete factorization",
      "linear system",
      "vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3363S"
    }
  }
}