{
  "id": "1504.00979",
  "version": "v1",
  "published": "2015-04-04T04:22:59.000Z",
  "updated": "2015-04-04T04:22:59.000Z",
  "title": "A lifted square formulation for certifiable Schubert calculus",
  "authors": [
    "Nickolas Hein",
    "Frank Sottile"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.NA"
  ],
  "abstract": "Formulating a Schubert problem as the solutions to a system of equations in either Pl\\\"ucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal-dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smale's \\alpha-theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-04T04:22:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "14Q20"
    ],
    "keywords": [
      "certifiable schubert calculus",
      "lifted square formulation",
      "schubert problem",
      "fewer equations",
      "lifting incidence conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400979H"
    }
  }
}