{
  "id": "1603.03959",
  "version": "v1",
  "published": "2016-03-12T19:59:49.000Z",
  "updated": "2016-03-12T19:59:49.000Z",
  "title": "On the computation of the straight lines contained in a rational surface",
  "authors": [
    "Juan Gerardo Alcázar",
    "Jorge Caravantes"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.AG",
    "cs.SC"
  ],
  "abstract": "In this paper we present an algorithm to compute the real and complex straight lines contained in a rational surface, defined by a rational parametrization. The algorithm relies on the well-known theorem of Differential Geometry that char- acterizes real straight lines contained in a surface as curves that are simulta- neously asymptotic lines, and geodesics. We also report on an implementation carried out in Maple 18. Examples and timings show the efficiency of the algo- rithm for moderate degrees, compared with a brute-force approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-12T19:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Q10"
    ],
    "keywords": [
      "rational surface",
      "acterizes real straight lines",
      "computation",
      "complex straight lines",
      "rational parametrization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}