{
  "id": "2006.09362",
  "version": "v1",
  "published": "2020-06-16T17:55:46.000Z",
  "updated": "2020-06-16T17:55:46.000Z",
  "title": "Solving polynomials with ordinary differential equations",
  "authors": [
    "Armengol Gasull",
    "Hector Giacomini"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). More concretely, it satisfies several simple separated variables ODE, a first order generalized Abel ODE of degree n-1 and an (n-1)-th order linear ODE. Although some of our results are not new, our approach is simple and self-contained. For n=2, 3 and 4 we recover, from these ODE, the classical formulas for solving these polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T17:55:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ordinary differential equations",
      "solving polynomials",
      "first order generalized abel ode",
      "simple separated variables ode",
      "order linear ode"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}