{
  "abstract": "We consider real monic polynomials with simple complex critical points. Critical values of such polynomial $p$ can be considered as vertices of the uniquely defined polygon, symmetric with respect to the $x$-axis. The inverse image of this polygon is a tree-like system of ovals that touch each other externally in critical points. This system of ovals will be called the geometrical code of $p$. Let $a_1+i\\cdot b_1,\\ldots,a_n+i\\cdot b_n$, $a_1<a_2<\\ldots<a_n$ and $b_i>0$, $i=1,\\ldots,n$, be the set of critical points of our polynomial $p$ in the upper halfplane, and $c_1+i\\cdot d_1,\\ldots,c_n+i\\cdot d_n$ be their images. The order of numbers $c_k$ and the list of signs of numbers $d_k$ will be called the algebraic code of $p$. In our experimental work we study geometrical and algebraic codes of the 7-th degree polynomials and the relations between them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06695",
  "author_total": 2,
  "authors": [
    {
      "name": "Elizaveta Khokhlova"
    },
    {
      "name": "Yury Kochetkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ect21ttztv12b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06695",
  "fulltext_url": null,
  "id": "ect21ttztv12b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06695",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06695",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ect21ttztv12b.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06695",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06695"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the geometry of real polynomials of the 7-th degree with simple complex critical points",
  "title_text": "On the geometry of real polynomials of the 7-th degree with simple complex critical points",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/ect21ttztv12b",
  "venue": "arXiv",
  "versions": []
}