{
  "abstract": "We introduce Lagrange functions associated with height and distance-squared functions on implicit plane curves. We show that degeneracies of these functions characterize geometric properties of the curves, such as inflections and vertices, and give geometric interpretations of the corresponding Lagrange multipliers in terms of contact with lines and circles.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19517",
  "author_total": 1,
  "authors": [
    {
      "name": "Masaru Hasegawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48d66vcy6m5zw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19517",
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  "id": "48d66vcy6m5zw",
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  "landing_url": "https://arxiv.org/abs/2608.19517",
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  "native_subjects": [
    [
      "arxiv",
      "math.DG"
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7203890744",
  "pdf_url": "https://arxiv.org/pdf/2608.19517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48d66vcy6m5zw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2608.19517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19517"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Degeneracies of Lagrange functions and geometric interpretations of Lagrange multipliers",
  "title_text": "Degeneracies of Lagrange functions and geometric interpretations of Lagrange multipliers",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/48d66vcy6m5zw",
  "venue": "arXiv",
  "versions": []
}