{
  "abstract": "Given a polynomial dynamical system $\\mathbf{x}'=\\mathbf{f}(\\mathbf{x},\\mathbf{u})$ together with an observation function $y=g(\\mathbf{x},\\mathbf{u})$, where $\\mathbf{x}=(x_1,\\ldots,x_n)$, $\\mathbf{u}=(u_1,\\ldots,u_m)$ and $y$ are differential variables, and $\\mathbf{f}=(f_1,\\ldots,f_n)$, $g$ are polynomials with coefficients in a differential field, we study the problem of determining a minimal polynomial differential equation satisfied by the inputs $\\mathbf{u}$ and the output $y$ which follows as a differential consequence of the system. We provide a characterization of a finite superset of the set of monomials appearing with non-zero coefficients in this input-output equation. Specifically, we establish an upper bound for the degree of the minimal polynomial and a family of inequalities that define a polytope containing its Newton polytope. These results extend recent work by Mukhina and Pogudin for systems with constant parameters, and enable the use of evaluation-interpolation techniques for the efficient computation of such eliminant polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03828",
  "author_total": 2,
  "authors": [
    {
      "name": "Gabriela Jeronimo"
    },
    {
      "name": "Leonardo Lanciano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/chce1yt7826zb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03828",
  "fulltext_url": null,
  "id": "chce1yt7826zb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03828",
  "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",
      "cs.SC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7208711142",
  "pdf_url": "https://arxiv.org/pdf/2609.03828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/chce1yt7826zb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "New bounds for the support of input-output equations in differential-algebraic systems",
  "title_text": "New bounds for the support of input-output equations in differential-algebraic systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/chce1yt7826zb",
  "venue": "arXiv",
  "versions": []
}