"Gauss-Lucas theorem" meaning in All languages combined

{
  "etymology_text": "Named after Carl Friedrich Gauss and Félix Lucas.",
  "forms": [
    {
      "form": "the Gauss-Lucas theorem",
      "tags": [
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
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          "kind": "other",
          "name": "English entries with incorrect language header",
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      "glosses": [
        "A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P."
      ],
      "id": "en-Gauss-Lucas_theorem-en-name-ck2Riekr",
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        [
          "geometric",
          "geometric"
        ],
        [
          "relation",
          "relation"
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        [
          "root",
          "root"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "convex hull",
          "convex hull"
        ]
      ],
      "raw_glosses": [
        "(complex analysis) A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P."
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Gauss-Lucas theorem"
}

{
  "etymology_text": "Named after Carl Friedrich Gauss and Félix Lucas.",
  "forms": [
    {
      "form": "the Gauss-Lucas theorem",
      "tags": [
        "canonical"
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  ],
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  "lang_code": "en",
  "pos": "name",
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      "glosses": [
        "A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P."
      ],
      "links": [
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "geometric",
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        ],
        [
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          "relation"
        ],
        [
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          "root"
        ],
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          "polynomial",
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        ],
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      "raw_glosses": [
        "(complex analysis) A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P."
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Gauss-Lucas theorem"
}