See rational function in All languages combined, or Wiktionary
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"name": "Algebraic geometry",
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"examples": [
{
"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": "quotation"
},
{
"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.",
"type": "quotation"
},
{
"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.",
"type": "quotation"
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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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"word": "proper rational function"
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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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"algebraic-geometry",
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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"
},
{
"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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"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": "quotation"
},
{
"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.",
"type": "quotation"
},
{
"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.",
"type": "quotation"
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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)."
],
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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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"algebraic-geometry",
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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"
},
{
"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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