"hyperbolic polynomial" meaning in English

See hyperbolic polynomial in All languages combined, or Wiktionary

Noun

Forms: hyperbolic polynomials [plural]
Head templates: {{en-noun}} hyperbolic polynomial (plural hyperbolic polynomials)
  1. (mathematics) A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t. Categories (topical): Mathematics
    Sense id: en-hyperbolic_polynomial-en-noun-CbCBn0UP Categories (other): English entries with incorrect language header Topics: mathematics, sciences

Inflected forms

Download JSON data for hyperbolic polynomial meaning in English (1.2kB)

{
  "forms": [
    {
      "form": "hyperbolic polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hyperbolic polynomial (plural hyperbolic polynomials)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t."
      ],
      "id": "en-hyperbolic_polynomial-en-noun-CbCBn0UP",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "multivariate",
          "multivariate"
        ],
        [
          "homogeneous",
          "homogeneous"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "root",
          "root"
        ],
        [
          "function",
          "function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hyperbolic polynomial"
}
{
  "forms": [
    {
      "form": "hyperbolic polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hyperbolic polynomial (plural hyperbolic polynomials)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Mathematics"
      ],
      "glosses": [
        "A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "multivariate",
          "multivariate"
        ],
        [
          "homogeneous",
          "homogeneous"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "root",
          "root"
        ],
        [
          "function",
          "function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hyperbolic polynomial"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-09 from the enwiktionary dump dated 2024-05-02 using wiktextract (4d5d0bb and edd475d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.