"rational function" meaning in English

See rational function in All languages combined, or Wiktionary

Noun

Forms: rational functions [plural]
Head templates: {{en-noun}} rational function (plural rational functions)
  1. (mathematics, complex analysis, algebraic geometry) Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator). Categories (topical): Algebraic geometry, Complex analysis, Functions, Mathematics Hypernyms: function, meromorphic function Hyponyms: proper rational function Translations (function expressible as the quotient of polynomials): rationaalifunktio (Finnish), rationale Funktion [feminine] (German), racionális függvény (Hungarian), рациона́льная фу́нкция (racionálʹnaja fúnkcija) [feminine] (Russian), rasyonel fonksiyon (Turkish)

Inflected forms

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          "name": "Algebraic geometry",
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          "ref": "1960, J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd edition, American Mathematical Society, page 184:",
          "text": "Our first problem is that of interpolation in prescribed points to a given function by a rational function whose poles are given.",
          "type": "quote"
        },
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          "ref": "1970, Ellis Horowitz, Algorithms for Symbolic Integration of Rational Functions, University of Wisconsin-Madison, page 24:",
          "text": "By Theorem 2.3.2., we have that the right-hand side of this equation can be equal to a rational function only if that rational function is equal to zero.",
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          "ref": "2000, Alan F. Beardon, Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer, page 45:",
          "text": "Let #x5C;mathcal#x7B;C#x7D; be the class of continuous maps of #x5C;mathbb#x7B;C#x7D;#x5F;#x5C;infty into itself and let #x5C;mathcal#x7B;R#x7D; be the subclass of rational functions.[…]Now #x5C;mathcal#x7B;R#x7D; is a closed subset of #x5C;mathcal#x7B;C#x7D;#x5F;#x5C;infty because if the rational functions R#x5F;n converge uniformly to R on the complex sphere, then R is analytic on the sphere and so it too is rational.",
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      "glosses": [
        "Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator)."
      ],
      "hypernyms": [
        {
          "word": "function"
        },
        {
          "word": "meromorphic function"
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      ],
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          "word": "proper rational function"
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          "algebraic geometry",
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          "quotient",
          "quotient"
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          "coprime",
          "coprime"
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          "polynomial",
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        "(mathematics, complex analysis, algebraic geometry) Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator)."
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      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "function expressible as the quotient of polynomials",
          "word": "rationaalifunktio"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "function expressible as the quotient of polynomials",
          "tags": [
            "feminine"
          ],
          "word": "rationale Funktion"
        },
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          "code": "hu",
          "lang": "Hungarian",
          "sense": "function expressible as the quotient of polynomials",
          "word": "racionális függvény"
        },
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          "code": "ru",
          "lang": "Russian",
          "roman": "racionálʹnaja fúnkcija",
          "sense": "function expressible as the quotient of polynomials",
          "tags": [
            "feminine"
          ],
          "word": "рациона́льная фу́нкция"
        },
        {
          "code": "tr",
          "lang": "Turkish",
          "sense": "function expressible as the quotient of polynomials",
          "word": "rasyonel fonksiyon"
        }
      ]
    }
  ],
  "word": "rational function"
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    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "function expressible as the quotient of polynomials",
      "word": "rationaalifunktio"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "function expressible as the quotient of polynomials",
      "tags": [
        "feminine"
      ],
      "word": "rationale Funktion"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "function expressible as the quotient of polynomials",
      "word": "racionális függvény"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "racionálʹnaja fúnkcija",
      "sense": "function expressible as the quotient of polynomials",
      "tags": [
        "feminine"
      ],
      "word": "рациона́льная фу́нкция"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "function expressible as the quotient of polynomials",
      "word": "rasyonel fonksiyon"
    }
  ],
  "word": "rational function"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.

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