"quadratic integer" meaning in All languages combined

See quadratic integer on Wiktionary

Noun [English]

Forms: quadratic integers [plural]
Etymology: Blend of quadratic + algebraic integer. The idea of integer here is that if the coefficient of the x² term is set to 1 (i.e., if the polynomial is made monic), the other coefficients are integers. Etymology templates: {{blend|en|quadratic|algebraic integer}} Blend of quadratic + algebraic integer Head templates: {{en-noun}} quadratic integer (plural quadratic integers)
  1. (mathematics) A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2. Categories (topical): Mathematics, Numbers Hypernyms (algebraic integer): algebraic number Hyponyms: phi, golden ratio Hyponyms (Gaussian integer / Eisenstein integer): integer, rational integer
    Sense id: en-quadratic_integer-en-noun-DhwWsV0x Categories (other): English blends, English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, sciences

Inflected forms

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      "args": {
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        "2": "quadratic",
        "3": "algebraic integer"
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      "expansion": "Blend of quadratic + algebraic integer",
      "name": "blend"
    }
  ],
  "etymology_text": "Blend of quadratic + algebraic integer. The idea of integer here is that if the coefficient of the x² term is set to 1 (i.e., if the polynomial is made monic), the other coefficients are integers.",
  "forms": [
    {
      "form": "quadratic integers",
      "tags": [
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  "head_templates": [
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        {
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          "langcode": "en",
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          "orig": "en:Mathematics",
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            "Terms by semantic function",
            "Fundamental"
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          "source": "w"
        }
      ],
      "glosses": [
        "A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2."
      ],
      "hypernyms": [
        {
          "sense": "algebraic integer",
          "word": "algebraic number"
        }
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      "hyponyms": [
        {
          "sense": "Gaussian integer / Eisenstein integer",
          "word": "integer"
        },
        {
          "sense": "Gaussian integer / Eisenstein integer",
          "word": "rational integer"
        },
        {
          "word": "phi"
        },
        {
          "word": "golden ratio"
        }
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      "id": "en-quadratic_integer-en-noun-DhwWsV0x",
      "links": [
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      "raw_glosses": [
        "(mathematics) A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2."
      ],
      "topics": [
        "mathematics",
        "sciences"
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    }
  ],
  "etymology_text": "Blend of quadratic + algebraic integer. The idea of integer here is that if the coefficient of the x² term is set to 1 (i.e., if the polynomial is made monic), the other coefficients are integers.",
  "forms": [
    {
      "form": "quadratic integers",
      "tags": [
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  "head_templates": [
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      "sense": "Gaussian integer / Eisenstein integer",
      "word": "rational integer"
    },
    {
      "word": "phi"
    },
    {
      "word": "golden ratio"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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      "glosses": [
        "A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2."
      ],
      "links": [
        [
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      "raw_glosses": [
        "(mathematics) A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2."
      ],
      "topics": [
        "mathematics",
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    }
  ],
  "word": "quadratic integer"
}

Download raw JSONL data for quadratic integer meaning in All languages combined (1.6kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.